The document discusses key concepts related to forces and deformation in materials including:
1. It defines important terms like stress, strain, and deformation and explains how forces can result in changes to an object's shape or velocity.
2. Stress is introduced as a measure of force acting over an area, and different types of stress like tension, compression, and shear are described.
3. Strain refers to changes in an object's shape or volume due to applied forces and can be measured through factors like elongation or changes in angular dimensions.
4. The response of rocks to stresses like compression can result in distortion, which involves changes in the spacing of points within the rock and alterations to its overall shape
- Stress is defined as force per unit area and can be divided into normal and shear components at a point. Stress around a point in 3D forms a stress ellipsoid with three orthogonal principal stress directions.
- Strain is the change in size and shape of a body due to applied stresses. It includes extension, shear and changes to the ellipsoid shape defined by finite stretches.
- The relationship between stress and strain is evaluated through rock deformation experiments using triaxial apparatus to measure shortening, strain rates, and ductility. The results relate to the rheology and deformation mechanisms in rocks.
This document discusses stress and strain ellipsoids in structural geology. It defines stress as a force applied over an area that causes rock deformation. Stress can be tensional, compressional, or shear. Strain is the response of rock to stress and describes the change in shape of an object under stress. Stress and strain are represented geometrically using ellipsoids. The relationship between stress and strain ellipsoids is that the greatest and least axes are opposite. The orientation of stress and strain ellipsoids provides information about the deformative forces acting on rocks.
joints and its classification and its recognitionShivam Jain
Joints are fractures in rock without displacement. They form due to tension, shear, or compressive stresses. Joints can be classified based on their orientation relative to bedding, their geometry, genesis, and dip. Systematic joints are parallel while nonsystematic joints have irregular distributions. Joints influence groundwater flow, construction, and are important in mining and resource exploration. They provide pathways for fluid migration and impact slope stability.
1) Shear zones are tabular zones of higher strain than the surrounding rock, where ductile deformation occurs. Shear zones are thicker than fault zones.
2) Shear sense indicators in shear zones include asymmetric structures like S-C fabrics and mica fish, which indicate the direction of shear. Porphyroclast geometries also indicate shear sense.
3) Tension gashes and fractures that open parallel to the minimum stress axis can be used to determine the sense of shear in the zone. Their orientation and folding indicates whether shear was dextral or sinistral.
Mohr circle mohr circle anaysisand applicationShivam Jain
Mohr's circle is a graphical representation used to analyze the state of stress at a point. It relates the normal and shear stresses acting on planes of all orientations passing through that point. The document discusses how to construct Mohr's circle through an example and how it can be used to analyze principal stresses, maximum shear stress, and normal and tangential stresses on any given plane. Applications of Mohr's circle include studying brittle deformation features like faults and fractures, pore pressure effects, and stability of structures like bridges, dams and tunnels.
This document discusses different types of folds that can form in the Earth's crust. It describes how folds are caused by plastic deformation from compressive forces acting under conditions of stress, pressure, temperature gradients. There are three main mechanisms of folding: flexural folding where both competent and incompetent beds are bent, shear folding which involves slip along fractures, and flow folding where rocks fold like a fluid at high temperatures and depths. Common fold types include anticlines, synclines, and monoclines. Folds can form from tectonic processes like horizontal compression or mantle convection, or from non-tectonic processes like hillside creep or collapse structures.
The document discusses the classification of folds based on various parameters such as fold closure, symmetry, plunge, orientation of the axial plane, and nature of the hinge line. Folds are classified into different types including antiform, synform, symmetrical, asymmetrical, horizontal, plunging, upright, recumbent, and overturned folds based on these parameters. The classification schemes proposed by Fluety (1964) and Ramsay (1967) are also summarized.
The document discusses the geology of island arcs. An island arc is formed at a subduction zone, where one tectonic plate is pushed underneath another. Magma is generated from the melting of the subducted plate and rises to form volcanoes along the overriding plate. As the plate subducts at an angle, the volcanoes form in a curved chain shape. Island arcs are characterized by andesitic volcanic rocks and occur in settings with a deep ocean trench on one side and a back-arc basin on the other.
- Stress is defined as force per unit area and can be divided into normal and shear components at a point. Stress around a point in 3D forms a stress ellipsoid with three orthogonal principal stress directions.
- Strain is the change in size and shape of a body due to applied stresses. It includes extension, shear and changes to the ellipsoid shape defined by finite stretches.
- The relationship between stress and strain is evaluated through rock deformation experiments using triaxial apparatus to measure shortening, strain rates, and ductility. The results relate to the rheology and deformation mechanisms in rocks.
This document discusses stress and strain ellipsoids in structural geology. It defines stress as a force applied over an area that causes rock deformation. Stress can be tensional, compressional, or shear. Strain is the response of rock to stress and describes the change in shape of an object under stress. Stress and strain are represented geometrically using ellipsoids. The relationship between stress and strain ellipsoids is that the greatest and least axes are opposite. The orientation of stress and strain ellipsoids provides information about the deformative forces acting on rocks.
joints and its classification and its recognitionShivam Jain
Joints are fractures in rock without displacement. They form due to tension, shear, or compressive stresses. Joints can be classified based on their orientation relative to bedding, their geometry, genesis, and dip. Systematic joints are parallel while nonsystematic joints have irregular distributions. Joints influence groundwater flow, construction, and are important in mining and resource exploration. They provide pathways for fluid migration and impact slope stability.
1) Shear zones are tabular zones of higher strain than the surrounding rock, where ductile deformation occurs. Shear zones are thicker than fault zones.
2) Shear sense indicators in shear zones include asymmetric structures like S-C fabrics and mica fish, which indicate the direction of shear. Porphyroclast geometries also indicate shear sense.
3) Tension gashes and fractures that open parallel to the minimum stress axis can be used to determine the sense of shear in the zone. Their orientation and folding indicates whether shear was dextral or sinistral.
Mohr circle mohr circle anaysisand applicationShivam Jain
Mohr's circle is a graphical representation used to analyze the state of stress at a point. It relates the normal and shear stresses acting on planes of all orientations passing through that point. The document discusses how to construct Mohr's circle through an example and how it can be used to analyze principal stresses, maximum shear stress, and normal and tangential stresses on any given plane. Applications of Mohr's circle include studying brittle deformation features like faults and fractures, pore pressure effects, and stability of structures like bridges, dams and tunnels.
This document discusses different types of folds that can form in the Earth's crust. It describes how folds are caused by plastic deformation from compressive forces acting under conditions of stress, pressure, temperature gradients. There are three main mechanisms of folding: flexural folding where both competent and incompetent beds are bent, shear folding which involves slip along fractures, and flow folding where rocks fold like a fluid at high temperatures and depths. Common fold types include anticlines, synclines, and monoclines. Folds can form from tectonic processes like horizontal compression or mantle convection, or from non-tectonic processes like hillside creep or collapse structures.
The document discusses the classification of folds based on various parameters such as fold closure, symmetry, plunge, orientation of the axial plane, and nature of the hinge line. Folds are classified into different types including antiform, synform, symmetrical, asymmetrical, horizontal, plunging, upright, recumbent, and overturned folds based on these parameters. The classification schemes proposed by Fluety (1964) and Ramsay (1967) are also summarized.
The document discusses the geology of island arcs. An island arc is formed at a subduction zone, where one tectonic plate is pushed underneath another. Magma is generated from the melting of the subducted plate and rises to form volcanoes along the overriding plate. As the plate subducts at an angle, the volcanoes form in a curved chain shape. Island arcs are characterized by andesitic volcanic rocks and occur in settings with a deep ocean trench on one side and a back-arc basin on the other.
Igneous structure and genesis (structural geology)Shivam Jain
This presentation summarizes igneous rock structures formed from the cooling and solidification of magma. It describes both intrusive and extrusive igneous rock structures. Intrusive structures include concordant structures like laccoliths, lopoliths, sills, and discordant structures like batholiths, stocks, dikes, and volcanic necks. Extrusive structures include primary structures like pillow structures, lava flow structures, vesicular structures, and columnar structures. The presentation provides examples and diagrams to illustrate different igneous rock formations and the geological processes that create their characteristic shapes and features.
This document discusses various mechanisms of rock folding. It defines folding as the bending of rock strata due to compressional forces. There are several types of fold mechanisms including buckling, bending, flexure folding, flexural slip, flexural flow, passive flow, and kink folding. Each mechanism is influenced by factors like temperature, pressure, fluid properties, and the composition and texture of the rock. Buckling involves shortening of rock layers under lateral pressure. Bending involves applying force across layers to produce gentle folds. Flexural slip forms parallel concentric folds through buckling or bending with slip along layering.
The document discusses different types of unconformities:
- Angular unconformity occurs when rock layers above and below are not parallel due to erosion and deposition over a long period of time with changes in bedding orientation.
- Nonconformity separates older crystalline rocks from overlying younger sedimentary or volcanic rocks, representing a long period of erosion.
- Disconformity has parallel bedding above and below, separated by erosion over some time.
- Local unconformity is similar to a disconformity but represents only a short period of non-deposition over a small area.
This document defines and describes different types of unconformities in geology. It begins by defining an unconformity as a break or gap in the geological record representing a period of erosion or non-deposition. It then describes the major types of unconformities, including angular, disconformity, non-conformity, and local unconformities. Finally, it outlines several ways that unconformities provide significance, such as indicating time intervals missing from the geological record, structural discordances between rock layers, evidence of past topography, and signs of weathering at the contact surface.
This document provides information about strain analysis and the relationship between stress and strain. Some key points:
- Strain is defined as the change in size and shape of a body resulting from an applied stress. Kinematic analysis is used to reconstruct deformation.
- There are different types of strain including elastic, brittle, and plastic, which depend on the magnitude and rate of applied stress. Homogeneous and inhomogeneous strain can occur.
- Strain is measured using various techniques at different scales from regional to microscopic. Equations relate changes in length, shear, and elongation to strain.
- The relationship between stress and strain in rocks is evaluated experimentally. Stress-strain diagrams show properties like strength and duct
This document provides an overview of fold classification and its elements. It begins with an introduction to folds and their historical development. It then describes the key elements of folds such as hinge points, limbs, and axial planes. The majority of the document focuses on various systems for classifying folds based on criteria like fold closure, symmetry, plunge of the axial plane, and interlimb angle. It discusses classifications proposed by Ramsay and Fluety. In conclusion, it provides a geometrical classification of folds based on dip isogons, axial plane thickness, and orthogonal thickness as defined by Ramsay.
Structural geology is the study of the three-dimensional of the rock units with respect to their deformational histories, Structure is spatial and geometrical configuration of rock components.
Structures are classified into two types:
Primary structures.
Secondary structures
Primary structures
Structures that form during deposition or crystallization of the rock, are the result of two processes:
Settling of solid particles from fluid medium in which they have been suspended, in most of the sedimentary rocks.
Crystallization of mineral grains from a liquid in which they have been dissolved as in igneous rocks.
The document discusses the textures of sedimentary rocks. It defines texture as the shape, size, and arrangement of particles that make up sediments and sedimentary rocks. There are three main aspects of texture discussed: grain size, particle shape, and fabrics. Grain size is measured using various scales and distributions are analyzed mathematically. Particle shape is defined by form, roundness, and surface texture. Fabrics consider grain orientation, packing, and relations which influence porosity. Texture provides insight into the depositional environment and post-depositional changes sediments undergo.
Origin& evolution of magma ,magmatism related to plate tectonics.Devashish Sahu
This document summarizes a seminar on the origin and evolution of magma and its relationship to plate tectonics. It discusses how magma originates from partial melting of the solid earth due to increased temperature and pressure. Magma composition evolves through processes like fractional crystallization, assimilation, and magma mixing. Magmatism is related to plate tectonics through mechanisms like decompression melting at mid-ocean ridges and continental rifts, flux melting near subduction zones, and intraplate volcanism from mantle plumes not associated with plate boundaries. Examples discussed include the Deccan Traps basalts formed by a mantle plume in India.
Contact metamorphism occurs where cooler country rocks are thermally altered by nearby intrusive bodies. The textures that develop under these low-pressure conditions typically lack strain and preserve relict features. Common textures include granoblastic polygonal textures in isotropic minerals like quartz, decussate textures in anisotropic minerals, and porphyroblasts. With increasing metamorphic grade, recrystallization becomes more prominent, grains grow larger, and evidence of strain decreases.
This document discusses various primary sedimentary structures that form as a result of mechanical processes during sediment deposition. It describes bedforms such as ripples and dunes that form under different flow regimes. It also discusses cross-bedding and other structures including graded bedding, soft-sediment deformation, and bedding-plane markings. Various sedimentary environments and the structures associated with them are outlined, such as turbidites and hummocky cross-stratification.
The document discusses Mohr's circle, which is a graphical representation used to analyze stresses on inclined planes. It introduces Mohr's circle, describing its three fundamental principles and how it relates normal and shear stresses. The importance of Mohr's circle in structural geology is discussed, including determining stress states, depicting maximum shear stresses, and visualizing the stress condition. Different types of faults - normal, reverse, strike-slip - and diapirs are also defined.
Structural geology is the study of rock structures and deformations within the Earth's crust. There are several types of rock structures that provide evidence of past deformation, including folds, faults, joints, and foliations. Folds occur when rock layers are bent, and there are different types such as anticlines, synclines, tight folds, overfolds, recumbent folds, and nappe folds. Understanding rock structures provides insight into the stress fields and tectonic processes that shaped the geological past.
Tectonites are deformed rocks whose fabric is due to systematic movement under external forces. Their fabric reflects the deformation history. Fabric includes the geometric arrangement of mineral grains, layers, and other features at a scale that includes many samples. Tectonites can have planar (S-tectonite), linear (L-tectonite), or both (L-S tectonite) fabrics indicating different strain types. Foliations like cleavage, schistosity, and gneissosity are planar fabrics that cause rocks to break along parallel surfaces. Lineations indicate preferred linear fabrics, such as fold axes, boudins, and quartz rods. The orientation and interaction of foliations and lineations provide information about tect
Shear Zone Structural Geology by Misson Choudhury Misson Choudhury
This document provides an introduction to shear zones in structural geology. It defines a shear zone as a tabular zone of strain localization in the crust that can form under brittle, ductile, or intermediate conditions. Shear zones display heterogeneous strain distribution and can be continuous or discontinuous. They form in plate boundaries during plate convergence, divergence, or strike-slip motion. Rocks in shear zones may include mylonite, cataclasite, tectonites, pseudotachylyte, and breccia. Shear zones can be classified as brittle, ductile, or brittle-ductile based on the dominant deformation mechanisms.
This document summarizes a seminar on Ramsay classification of folds and folding mechanisms. It introduces Ramsay fold classification, which divides folds into three classes based on criteria like dip isogon patterns and curvature. Class 1 folds have convergent dip isogons and greater inner curvature. Mechanisms of folding discussed include buckling, which can form Class 1b folds of constant thickness, and bending due to intrusion or between boudins. Applications of the classification include hydrocarbon and salt dome exploration.
This document summarizes the key mechanical properties of rocks, including density, specific gravity, strength, strain, stress, porosity, and permeability. It defines each property, provides examples for common rock types, and notes that mechanics refers to how materials respond to applied loads. The conclusion restates that the document covered the mechanical characteristics of rocks according to these seven properties.
Strain markers are objects in deformed rocks that can be used to measure strain. Good strain markers include reduction spots, pebbles, fossils, fold sets, and lineations. Spherical markers originally circular in cross-section become elliptical due to homogeneous deformation, with the ratio of major to minor axes indicating strain. Fossils with lines of symmetry like trilobites and brachiopods can indicate the principal strain directions. Fold sets allow comparing initial and final layered sequences to analyze strain. Schistosity and lineations in metamorphic rocks can also act as strain markers.
This lecture includes the fold terminology and classification of folds based of different criteria.
Classification of folds based on:
Direction of closing
Attitude of axial surface
Size of interlimb angle
Profile
Ramsay Classification of folds
Climbing ripple laminations are formed by the superimposition of migrating ripples where deposition occurs rapidly during ripple migration, causing the ripples to climb upon one another rather than migrate laterally. They are classified based on the angle of climbing relative to the stoss side angle, and form under conditions of abundant suspended sediment supply and rapid burial, preserving the original rippled layers. Climbing ripples indicate deposition exceeded migration and are found in environments with high sedimentation rates like river floodplains, point bars, and deltas.
The document discusses various topics related to stress and strain including: principal stresses and strains, Mohr's stress circle theory of failure, 3D stress and strain, equilibrium equations, and impact loading. It provides examples of stresses acting in different planes including normal, shear, oblique, and principal planes. It also gives examples of calculating normal and tangential stresses on an oblique plane subjected to stresses in one, two, or multiple directions with and without shear stresses.
1. Deformation occurs when an applied force causes a change in the shape of an object. There are two types of deformation: elastic and plastic.
2. Elastic deformation is reversible - the object returns to its original shape once the force is removed. Plastic deformation causes a permanent change in shape.
3. Hooke's law states that the extension of a spring is directly proportional to the applied load, provided the load does not exceed the elastic limit. Extension-load graphs can be used to study the elastic behavior of materials.
Igneous structure and genesis (structural geology)Shivam Jain
This presentation summarizes igneous rock structures formed from the cooling and solidification of magma. It describes both intrusive and extrusive igneous rock structures. Intrusive structures include concordant structures like laccoliths, lopoliths, sills, and discordant structures like batholiths, stocks, dikes, and volcanic necks. Extrusive structures include primary structures like pillow structures, lava flow structures, vesicular structures, and columnar structures. The presentation provides examples and diagrams to illustrate different igneous rock formations and the geological processes that create their characteristic shapes and features.
This document discusses various mechanisms of rock folding. It defines folding as the bending of rock strata due to compressional forces. There are several types of fold mechanisms including buckling, bending, flexure folding, flexural slip, flexural flow, passive flow, and kink folding. Each mechanism is influenced by factors like temperature, pressure, fluid properties, and the composition and texture of the rock. Buckling involves shortening of rock layers under lateral pressure. Bending involves applying force across layers to produce gentle folds. Flexural slip forms parallel concentric folds through buckling or bending with slip along layering.
The document discusses different types of unconformities:
- Angular unconformity occurs when rock layers above and below are not parallel due to erosion and deposition over a long period of time with changes in bedding orientation.
- Nonconformity separates older crystalline rocks from overlying younger sedimentary or volcanic rocks, representing a long period of erosion.
- Disconformity has parallel bedding above and below, separated by erosion over some time.
- Local unconformity is similar to a disconformity but represents only a short period of non-deposition over a small area.
This document defines and describes different types of unconformities in geology. It begins by defining an unconformity as a break or gap in the geological record representing a period of erosion or non-deposition. It then describes the major types of unconformities, including angular, disconformity, non-conformity, and local unconformities. Finally, it outlines several ways that unconformities provide significance, such as indicating time intervals missing from the geological record, structural discordances between rock layers, evidence of past topography, and signs of weathering at the contact surface.
This document provides information about strain analysis and the relationship between stress and strain. Some key points:
- Strain is defined as the change in size and shape of a body resulting from an applied stress. Kinematic analysis is used to reconstruct deformation.
- There are different types of strain including elastic, brittle, and plastic, which depend on the magnitude and rate of applied stress. Homogeneous and inhomogeneous strain can occur.
- Strain is measured using various techniques at different scales from regional to microscopic. Equations relate changes in length, shear, and elongation to strain.
- The relationship between stress and strain in rocks is evaluated experimentally. Stress-strain diagrams show properties like strength and duct
This document provides an overview of fold classification and its elements. It begins with an introduction to folds and their historical development. It then describes the key elements of folds such as hinge points, limbs, and axial planes. The majority of the document focuses on various systems for classifying folds based on criteria like fold closure, symmetry, plunge of the axial plane, and interlimb angle. It discusses classifications proposed by Ramsay and Fluety. In conclusion, it provides a geometrical classification of folds based on dip isogons, axial plane thickness, and orthogonal thickness as defined by Ramsay.
Structural geology is the study of the three-dimensional of the rock units with respect to their deformational histories, Structure is spatial and geometrical configuration of rock components.
Structures are classified into two types:
Primary structures.
Secondary structures
Primary structures
Structures that form during deposition or crystallization of the rock, are the result of two processes:
Settling of solid particles from fluid medium in which they have been suspended, in most of the sedimentary rocks.
Crystallization of mineral grains from a liquid in which they have been dissolved as in igneous rocks.
The document discusses the textures of sedimentary rocks. It defines texture as the shape, size, and arrangement of particles that make up sediments and sedimentary rocks. There are three main aspects of texture discussed: grain size, particle shape, and fabrics. Grain size is measured using various scales and distributions are analyzed mathematically. Particle shape is defined by form, roundness, and surface texture. Fabrics consider grain orientation, packing, and relations which influence porosity. Texture provides insight into the depositional environment and post-depositional changes sediments undergo.
Origin& evolution of magma ,magmatism related to plate tectonics.Devashish Sahu
This document summarizes a seminar on the origin and evolution of magma and its relationship to plate tectonics. It discusses how magma originates from partial melting of the solid earth due to increased temperature and pressure. Magma composition evolves through processes like fractional crystallization, assimilation, and magma mixing. Magmatism is related to plate tectonics through mechanisms like decompression melting at mid-ocean ridges and continental rifts, flux melting near subduction zones, and intraplate volcanism from mantle plumes not associated with plate boundaries. Examples discussed include the Deccan Traps basalts formed by a mantle plume in India.
Contact metamorphism occurs where cooler country rocks are thermally altered by nearby intrusive bodies. The textures that develop under these low-pressure conditions typically lack strain and preserve relict features. Common textures include granoblastic polygonal textures in isotropic minerals like quartz, decussate textures in anisotropic minerals, and porphyroblasts. With increasing metamorphic grade, recrystallization becomes more prominent, grains grow larger, and evidence of strain decreases.
This document discusses various primary sedimentary structures that form as a result of mechanical processes during sediment deposition. It describes bedforms such as ripples and dunes that form under different flow regimes. It also discusses cross-bedding and other structures including graded bedding, soft-sediment deformation, and bedding-plane markings. Various sedimentary environments and the structures associated with them are outlined, such as turbidites and hummocky cross-stratification.
The document discusses Mohr's circle, which is a graphical representation used to analyze stresses on inclined planes. It introduces Mohr's circle, describing its three fundamental principles and how it relates normal and shear stresses. The importance of Mohr's circle in structural geology is discussed, including determining stress states, depicting maximum shear stresses, and visualizing the stress condition. Different types of faults - normal, reverse, strike-slip - and diapirs are also defined.
Structural geology is the study of rock structures and deformations within the Earth's crust. There are several types of rock structures that provide evidence of past deformation, including folds, faults, joints, and foliations. Folds occur when rock layers are bent, and there are different types such as anticlines, synclines, tight folds, overfolds, recumbent folds, and nappe folds. Understanding rock structures provides insight into the stress fields and tectonic processes that shaped the geological past.
Tectonites are deformed rocks whose fabric is due to systematic movement under external forces. Their fabric reflects the deformation history. Fabric includes the geometric arrangement of mineral grains, layers, and other features at a scale that includes many samples. Tectonites can have planar (S-tectonite), linear (L-tectonite), or both (L-S tectonite) fabrics indicating different strain types. Foliations like cleavage, schistosity, and gneissosity are planar fabrics that cause rocks to break along parallel surfaces. Lineations indicate preferred linear fabrics, such as fold axes, boudins, and quartz rods. The orientation and interaction of foliations and lineations provide information about tect
Shear Zone Structural Geology by Misson Choudhury Misson Choudhury
This document provides an introduction to shear zones in structural geology. It defines a shear zone as a tabular zone of strain localization in the crust that can form under brittle, ductile, or intermediate conditions. Shear zones display heterogeneous strain distribution and can be continuous or discontinuous. They form in plate boundaries during plate convergence, divergence, or strike-slip motion. Rocks in shear zones may include mylonite, cataclasite, tectonites, pseudotachylyte, and breccia. Shear zones can be classified as brittle, ductile, or brittle-ductile based on the dominant deformation mechanisms.
This document summarizes a seminar on Ramsay classification of folds and folding mechanisms. It introduces Ramsay fold classification, which divides folds into three classes based on criteria like dip isogon patterns and curvature. Class 1 folds have convergent dip isogons and greater inner curvature. Mechanisms of folding discussed include buckling, which can form Class 1b folds of constant thickness, and bending due to intrusion or between boudins. Applications of the classification include hydrocarbon and salt dome exploration.
This document summarizes the key mechanical properties of rocks, including density, specific gravity, strength, strain, stress, porosity, and permeability. It defines each property, provides examples for common rock types, and notes that mechanics refers to how materials respond to applied loads. The conclusion restates that the document covered the mechanical characteristics of rocks according to these seven properties.
Strain markers are objects in deformed rocks that can be used to measure strain. Good strain markers include reduction spots, pebbles, fossils, fold sets, and lineations. Spherical markers originally circular in cross-section become elliptical due to homogeneous deformation, with the ratio of major to minor axes indicating strain. Fossils with lines of symmetry like trilobites and brachiopods can indicate the principal strain directions. Fold sets allow comparing initial and final layered sequences to analyze strain. Schistosity and lineations in metamorphic rocks can also act as strain markers.
This lecture includes the fold terminology and classification of folds based of different criteria.
Classification of folds based on:
Direction of closing
Attitude of axial surface
Size of interlimb angle
Profile
Ramsay Classification of folds
Climbing ripple laminations are formed by the superimposition of migrating ripples where deposition occurs rapidly during ripple migration, causing the ripples to climb upon one another rather than migrate laterally. They are classified based on the angle of climbing relative to the stoss side angle, and form under conditions of abundant suspended sediment supply and rapid burial, preserving the original rippled layers. Climbing ripples indicate deposition exceeded migration and are found in environments with high sedimentation rates like river floodplains, point bars, and deltas.
The document discusses various topics related to stress and strain including: principal stresses and strains, Mohr's stress circle theory of failure, 3D stress and strain, equilibrium equations, and impact loading. It provides examples of stresses acting in different planes including normal, shear, oblique, and principal planes. It also gives examples of calculating normal and tangential stresses on an oblique plane subjected to stresses in one, two, or multiple directions with and without shear stresses.
1. Deformation occurs when an applied force causes a change in the shape of an object. There are two types of deformation: elastic and plastic.
2. Elastic deformation is reversible - the object returns to its original shape once the force is removed. Plastic deformation causes a permanent change in shape.
3. Hooke's law states that the extension of a spring is directly proportional to the applied load, provided the load does not exceed the elastic limit. Extension-load graphs can be used to study the elastic behavior of materials.
The document discusses Deepak's academic and professional background, including an MBA from IE Business School in Spain and experience founding perfectbazaar.com. It also provides an overview of the topics to be covered in the Strength of Materials course, such as stresses, strains, Hooke's law, and analysis of bars with varying cross-sections. The grading policy and syllabus are outlined which divide the course into 5 units covering various strength of materials concepts.
This document contains a summary of key concepts related to stress and strain. It discusses different types of stresses like tensile stress, compressive stress, and shear stress. It also discusses different types of strains like tensile strain, compressive strain, and shear strain. Other important concepts covered include Hooke's law, true stress-strain curve, elastic constants like Young's modulus, shear modulus, Poisson's ratio, volumetric strain, and elongation of materials. The document provides definitions and formulas for calculating various stresses, strains, and material properties. It also includes examples to demonstrate calculations.
This document discusses plastic deformation in metals caused by the motion of dislocations. There are two main types of dislocations - edge and screw. Dislocations normally move under shear stress, allowing permanent deformation. Slip and twinning are two modes of plastic deformation that involve the motion of dislocations on specific crystallographic planes and directions. Strengthening methods like work hardening, solid solution strengthening, grain refinement, and precipitation hardening make it harder for dislocations to move by introducing barriers to their motion. This increases the strength of metals.
The document discusses various theories of failure that are used to determine the safe dimensions of components under combined loading conditions. It describes five theories: (1) Maximum principal stress theory, (2) Maximum principal strain theory, (3) Maximum strain energy theory, (4) Maximum distortion energy theory, and (5) Maximum shear stress theory. The maximum distortion energy theory provides the safest design for ductile materials as it results in the largest allowable stresses before failure compared to the other theories. The document also compares the various theories and discusses when each is best applied depending on the material type and stress conditions.
The document discusses the transformation of stress and strain under rotations of the coordinate axes. It introduces plane stress and strain states, and how the stress and strain components are transformed for different axis orientations. It describes Mohr's circle for representing the transformations graphically, and covers applications to analyzing stresses in thin-walled pressure vessels.
The section will cover the behaviour of materials by introducing the stress-strain curve. The concepts of elastic and plastic deformation will be covered. This will then lead to a discussion of the micro-structure of materials and a physical explanation of what is happening to a polycrystalline material as it is loaded to failure.
Loads can be tensile (pulling) or compressive (pushing) forces. Common types of loads include dead loads from structural weight, live loads from moving objects, impact loads from vibrations, and cyclic loads from repeated forces. When loads are applied, they cause stress in materials. Stress is the internal resisting force per unit area. Stresses can be tensile (pulling), compressive (pushing), or shear (tangential). Corresponding strains are the changes in dimensions from stresses. Hooke's law states that within the elastic limit, stress is proportional to strain by a constant modulus of elasticity.
This presentation includes two pages, with the first being the title slide and the second beginning to outline subtopics but leaving them unspecified. In just two slides the presentation introduces itself and hints at subdivision of contents but provides no details on the actual information to be presented.
Characterisation of salmonella abortusequi strains harbouring defined mutatio...Bhoj Raj Singh
This document describes research characterizing Salmonella Abortusequi strains with defined mutations in aroA, htrA and phoP/Q genes. Key findings include:
1) Mutations in aroA, htrA and phoP/Q genes were introduced into S. Abortusequi strains using genetic engineering techniques.
2) In mice, the mutant strains showed attenuated virulence and were cleared faster than the wild type strain. They also elicited stronger immune responses.
3) In macrophage cells, the mutant strains induced less cell death than the wild type and had reduced intracellular survival, suggesting impaired virulence.
The defined mutant strains showed promise as live attenuated vaccine candidates against S.
The document discusses research done at the University of New Orleans on developing multifunctional composite materials with properties of energy absorption, blast protection, and durability. The research applied nanotechnology by utilizing nanomaterials to dissipate shock and blast energy through mechanisms like friction and slip-stick motion. Experiments were conducted using nano-particle filled composites under impact loading and CNT reinforced composites for vibration damping. The research proved that energy absorption can be achieved through nanoparticle interfaces providing large energy sinks.
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The internet is a global network of interconnected computer networks that connects millions of devices. It allows for the exchange of data, messages, and access to shared resources between any connected devices. Some key aspects of the internet include the World Wide Web, email, file transfers, chat, and peer-to-peer services that enable sharing and communication between users around the world. Internet service providers give individuals and organizations access to the internet through connections like dial-up, DSL, cable or fiber.
This document discusses stress and strain analysis. It defines stress at a point and introduces the stress tensor. The stress tensor is symmetric. Principal stresses are the maximum and minimum normal stresses. Mohr's circle can be used to determine stresses on any plane through a point by graphically representing the transformation of stresses between planes. The principal planes contain no shear stress and maximum shear stress planes are 45 degrees from principal planes.
Flywheel Safety - Richard thompson - Jan 2011cahouser
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This document summarizes a seminar presentation on principal stresses and strains. It defines principal stresses as planes that experience only normal stresses and no shear stress. It then provides equations to calculate normal and shear stresses on oblique planes for members subjected to various loading conditions, including direct stress in one direction, direct stresses in two perpendicular directions, simple shear stress, and combinations of these. It derives equations to determine the position of principal planes and maximum shear stress. Examples are given for special cases where some stresses or shear terms are zero.
Explaining the AQHA Leveling Process - by Regina KerninLaura Hatch
The document provides information about AQHA levels and how they apply to riders, horses, and horse-rider combinations for different classes. It explains that levels determine which classes an exhibitor or horse is eligible for based on their experience level. Level 1 is for novice riders/horses, level 2 is intermediate, and level 3 is open. It provides steps and instructions for looking up an exhibitor or horse's level eligibility on the AQHA website to see which classes they can enter. It also discusses some additional rules for rookie, novice, and green classes.
Austin's office market is leveling out after a period of high growth and rental rate increases. Net absorption was steady in 2016 around 1 million square feet absorbed, while average rental rates and vacancy remained largely unchanged. New construction is slowing down with over half of current space under construction already preleased. Sublease space is increasing due to new co-working options and a changing workforce seeking flexible space near amenities. The market is expected to remain stable in the next 12-18 months barring major changes from large tech firms or a slowdown in the tech sector.
This document discusses grain boundary strengthening as a technique for strengthening materials. It describes how grain boundaries separate grains of different crystallographic orientations and act as barriers to dislocation motion. High angle grain boundaries have higher surface energy than low angle grain boundaries. Strengthening can occur through restricting dislocation motion at grain boundaries, making the material harder but sometimes reducing ductility. Grain boundary sliding is another deformation mechanism above half the melting temperature, where sliding along boundaries can occur.
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1. The lecture goals were to describe oscillations and simple harmonic motion, analyze them using energy concepts, and apply SHM to different physical situations like pendulums and driving forces.
2. The document then covered topics like equilibrium, restoring forces, characteristics of periodic motion, and the mathematics of simple harmonic oscillators.
3. It concluded by discussing mechanical waves, including transverse and longitudinal waves, wave speed, interference, and standing waves on a string.
When a body moves through a fluid, it experiences two forces: drag and lift. Drag acts parallel to the flow and slows the body down, while lift acts perpendicular to the flow. These forces depend on factors like the fluid's velocity and density, the body's size and shape, and its angle of attack relative to the flow. Streamlined shapes with small frontal areas experience less pressure drag than blunt bodies, which experience boundary layer separation and higher pressures on one side. The forces can be calculated using drag and lift coefficients, which vary based on the Reynolds number and other flow properties.
This document defines key concepts related to strain analysis in geology. It discusses how strain is used to describe changes in size and shape during deformation. The goals of strain analysis are to explain how straight lines and circles in a body change during deformation. Important quantities like extension, stretch, and shear strain are defined. The document also covers homogeneous versus heterogeneous deformation, principal stretch directions via strain ellipses and ellipsoids, finite versus instantaneous strain, Mohr strain diagrams, types of plane strain like pure and simple shear, and strain rate calculations.
The document discusses tension formula, rotational motion, torque, rotational kinetic energy, elasticity, plasticity, Hooke's law, and simple pendulums. It provides formulas for calculating tension, rotational kinematics, torque, rotational kinetic energy, elastic modulus, Hooke's law, and the period of a simple pendulum. It also includes example problems and solutions for some of the formulas.
This document discusses linear wave theory and the governing equations for water wave mechanics. It introduces key wave parameters like amplitude, height, wavelength, frequency, period, and phase speed. It then covers the linearized equations of motion, including continuity, irrotationality, and the time-dependent Bernoulli equation. Boundary conditions at the bed and free-surface are also presented, including the kinematic and dynamic free-surface boundary conditions. The linearized equations and boundary conditions form the basis for solving for the velocity potential using separation of variables.
The document discusses concepts related to dynamics and relativity including:
1) Newton's laws of motion and forces such as gravity, tension, and friction. Simple harmonic motion and circular motion are also covered.
2) Key concepts in dynamics like position, velocity, acceleration, and their relationships are defined. Equations of motion for 1D and 2D are presented.
3) Projectile motion under gravity is modeled. Relative velocity in 2D frames of reference is discussed.
1. The document discusses various topics related to wave motion including the characteristics of waves, types of waves, and the formation of stationary waves.
2. It provides definitions for key wave concepts like amplitude, wavelength, frequency, longitudinal and transverse waves. Equations are given for plane progressive waves traveling in different directions.
3. Reflection of waves at fixed and free ends is explained. The principle of superposition is described and used to show how two identical waves traveling in opposite directions can form a stationary standing wave with nodes and antinodes.
This PPT contain the basic topic about the strength of the material. Such as stress, strain, energy, principle of super position and various other topic of solid mechanics.
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This document discusses the physical state of the lithosphere, including stresses, strains, heat flow, gravity, isostasy, and rock rheology. Specifically, it covers stress and strain in the lithosphere, including lithostatic stress, deviatoric stress, and principal stresses and strains. It also discusses heat flow through conduction and convection, and concepts of isostasy and compensation of topography through density differences. Finally, it examines rock rheology, including fundamentals of rheology, viscosity of the mantle and crust, and elastic versus plastic behavior.
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3. Formulas are given for average speed, velocity, acceleration, linear motion, momentum, impulse, work, power, and more.
4. Concepts around pressure, density, buoyancy, heat transfer, the gas laws, refraction, lenses, and telescopes are also summarized.
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2. Materials deform both elastically and plastically when stressed. Elastic deformation is reversible but plastic deformation causes a permanent change in shape. Hooke's law describes the linear elastic behavior of many materials, where stress is directly proportional to strain up to the elastic limit.
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Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
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In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
3. Mass: Dimension: [M] Unit: g or kg
Length: Dimension: [L] Unit: cm or m
Time: Dimension: [T] Unit: s
Velocity, v = distance/time = dx/dt
Change in distance per time)
v =[L/T] or [LT-1] units: m/s or cm/s
Acceleration (due to gravity): g = velocity/time
Acceleration is change in velocity per time (dv/dt).
g = [LT-1 ]/[T] = LT-2, units: m s -2
Force: F = mass . acceleration
F = mg F = [M][LT-2]
units: newton: N = kg m s-2
4. A property or action that changes or tends to
change the state of rest or velocity or direction
of an object in a straight line
In the absence of force, a body moves at
constant velocity, or it stays at rest
Force is a vector quantity; i.e., has magnitude,
direction
5. Gravitational force
Acts over large distances and is always attractive
Ocean tides are due to attraction between Moon & Earth
Thermally-induced forces
e.g., due to convection cells in the mantle.
Produce horizontal forces (move the plates)
The other three forces act only over short ranges
(atomic scales). May be attractive or repulsive
Electromagnetic force
Interaction between charged particles (electrons)
Nuclear or strong force
Holds the nucleus of an atom together.
Weak force
Is responsible for radioactivity
6. Any part of material experiences two types of
forces:
surface & body
Body Force: Results from action of a field at
every point within the body
Is always present
Could be due to gravity or inertia
e.g., gravity, magnetic, centrifugal
Its magnitude is proportional to the mass of the body
7. Act on a specific surface area in a body
Are proportional to the magnitude of the area
Reflect pull or push of the atoms on one side of a
surface against the atoms on the other side
e.g., force of a cue stick that hits a pool ball
8. Forces applied on a body do either or both of
the following:
Change the velocity of the body
Result in a shape change of the body
A given force applied by a sharp object (e.g.,
needle) has a different effect than a similar force
applied by a dull object (e.g., peg). Why?
We need another measure called stress which
reflect these effects
9.
10.
11. A force acting on a small area such as the tip of a sharp nail,
has a greater intensity than a flat-headed nail!
s = [MLT-2] / [L2]=[ML -1T-2]
s = kg m-1 s-2 pascal (Pa) = newton/m2
1 bar (non-SI) = 105 Pa ~ 1 atmosphere
1 kb = 1000 bar = 108 Pa = 100 Mpa
1Gpa = 109 Pa = 1000 Mpa = 10 kb
P at core-mantle boundary is ~ 136 Gpa (at 2900 km)
P at the center of Earth (6371 km) is 364 Gpa
12. Tension: Stress acts _|_ to and away from a
plane
pulls the rock apart
forms special fractures called joint
may lead to increase in volume
Compression: stress acts _|_ to and toward a
plane
squeezes rocks
may decrease volume
Shear: acts parallel to a surface
leads to change in shape
13. Force (F) across any of these planes can be resolved into two
components: Shear stress: Fs , & normal stress: Fn, where:
Fs = F sin θ Fn = F cos θ
tan θ = Fs/Fn
Smaller θ means smaller Fs
14. Stress on an arbitrarily-oriented plane through a point, is
not necessarily perpendicular to the that plane
The stress (s) acting on a plane can be resolved into two
components:
Normal stress (sn)
Component of stress perpendicular to the plane, i.e.,
parallel to the normal to the plane
Shear stress (ss) or t
Components of stress parallel to the plane
15.
16. The average overburden pressure (i.e., lithostatic P) at
the base of a 1 km thick rock column (i.e., z = 1 km),
with density (r) of 2.5 gr/cm3 is 25 to 30 MPa
P = rgz [ML -1T-2]
P = (2670 kg m-3)(9.81 m s-2)(103 m)
= 26192700 kg m-1s-2 (pascal)
= 26 MPa
The geopressure gradient:
dP/dz 30 MPa/km 0.3 kb/km (kb = 100 MPa)
i.e. P is 3 kb at a depth of 10 km
17. Physical quantities, such as the density or
temperature of a body, which in no way depend on
direction
are expressed as a single number
e.g., temperature, density, mass
only have a magnitude (i.e., are a number)
are tensors of zero-order
18. Some physical quantities are fully specified
by a magnitude and a direction, e.g.:
Force, velocity, acceleration, and
displacement
Vectors:
relate one scalar to another scalar
have magnitude and direction
are tensors of the first-order
have 1 subscript (e.g., vi) and 21 and 31 components in
2D and 3D, respectively
19. Some physical quantities require nine
numbers for their full specification (in 3D)
Stress, strain, and conductivity are examples
of tensor
Tensors:
relate two vectors
are tensors of second-order
have 2 subscripts (e.g., sij); and 22 and 32 components
in 2D and 3D, respectively
20.
21. The stress tensor matrix:
| s11 s12 s13 |
sij = | s21 s22 s23 |
| s31 s32 s33 |
Can be simplified by choosing the coordinates so that they
are parallel to the principal axes of stress:
| s1 0 0 |
sij = | 0 s2 0 |
|0 0 s3 |
In this case, the coordinate planes only carry normal
stress; i.e., the shear stresses are zero
The s 1 , s2 , and s 3 are the major, intermediate, and
minor principal stress, respectively
s1>s3 ; principal stresses may be tensile or compressive
22.
23.
24. A component of deformation dealing with shape
and volume change
Distance between some particles changes
Angle between particle lines may change
The quantity or magnitude of the strain is given by
several measure based on change in:
Length (longitudinal strain) - e
Angle (angular or shear strain) -
Volume (volumetric strain) - ev
25.
26. Extension or Elongation, e: change in length per
length
e = (l´-lo) / lo = Dl/ lo [dimensionless]
Where l´ and lo are the final and original lengths of a
linear object
Note: Shortening is negative extension (i.e., e < 0)
e.g., e = - 0.2 represents a shortening of 20%
Example:
If a belemnite of an original length (lo) of 10 cm is now 12
cm (i.e., l´=12 cm), the longitudinal strain is positive, and
e = (12-10)/10 * 100% which gives an extension, e = 20%
27.
28. Stretch: s = l´/lo = 1+e = l [no dimension]
X = l1 = s1
Y = l2 = s2
Z = l3 = s3
These principal stretches represent the semi-length of
the principal axes of the strain ellipsoid. For Example:
Given lo = 100 and l´ = 200
Extension: e = (l´-lo)/ lo = (200-100)/100 = 1 or 100%
Stretch: s = 1+e = l´/lo = 200/100 = 2
i.e., The line is stretched twice its original length!
29. Gives the change of volume compared with its
original volume
Given the original volume is vo, and the final
volume is v´, then the volumetric stain, ev is:
ev =(v´-vo)/vo = dv/vo [no dimension]
30.
31.
32. Any deformed rock has passed through a whole
series of deformed states before it finally reached
its final state of strain
We only see the final product of this progressive
deformation (finite state of strain)
Progressive strain is the summation of small
incremental distortion or infinitesimal strains
33. Incremental strains are the increments of
distortion that affect a body during deformation
Finite strain represents the total strain
experienced by a rock body
If the increments of strain are a constant volume
process, the overall mechanism of distortion is
termed plane strain (i.e., one of the principal
strains is zero; hence plane, which means 2D)
Pure shear and simple shear are two end
members of plane strain
34. Distortion during a homogeneous strain leads to
changes in the relative configuration of particles
Material lines move to new positions
In this case, circles (spheres, in 3D) become
ellipses (ellipsoids), and in general, ellipses
(ellipsoids) become ellipses (ellipsoids).
Strain ellipsoid
Represents the finite strain at a point (i.e., strain
tensor)
Is a concept applicable to any deformation, no matter
how large in magnitude, in any class of material
35. Series of strain increments, from the original state,
that result in final, finite state of strain
A final state of quot;finitequot; strain may be reached by a
variety of strain paths
Finite strain is the final state; incremental strains
represent steps along the path
36.
37.
38.
39. We can think of the strain ellipse as the product
of strain acting on a unit circle
A convenient representation of the shape of the
strain ellipse is the strain ratio
Rs = (1+e1)/(1+e3) = S1/S3 = X/Z
It is equal to the length of the long axis over the
length of the short axis
40. If a line parallel to the radius of a unit circle, makes a
pre-deformation angle of with respect to the long
axis of the strain ellipse (X), it rotates to a new angle
of ´ after strain
The coordinates of the end point of the line on the
strain ellipse (x´, z´) are the coordinates before
deformation (x, z) times the principal stretches (S1,
S 3)
43. 3D equivalent - the ellipsoid produced by
deformation of a unit sphere
The strain ellipsoids vary from axially symmetric
elongated shapes –
cigars and footballs - to
axially shortened pancakes and cushions
44. If the strain axes have the same orientation in the
deformed as in undeformed state we describe the
strain as a non-rotational (or irrotational) strain
If the strain axes end up in a rotated position, then
the strain is rotational
45. An example of a non-rotational strain is pure shear
- it's a pure strain with no dilation of the area of the
plane
An example of a rotational strain is a simple shear
46.
47.
48.
49. 1. Axially symmetric extension
Extension in one principal direction (l1) and equal shortening
in all directions at right angles (l2 and l3)
l1 > l2 = l3 < 1
The strain ellipsoid is prolate spheroid or cigar shaped
2. Axially symmetric shortening
This involves shortening in one principal direction (l3) and
equal extension in all directions at right angles (l1 and l2 ).
l1 = l2 > 1 > l3
Strain ellipsoid is oblate spheroid or pancake-shaped
50. The sides of the parallelogram will progressively lengthen as
deformation proceeds but the top and bottom surfaces neither stretch
nor shorten. Instead they maintain their original length, which is the
length of the edge of the original cube
51. In contrast to simple shear, pure shear is a three-
dimensional constant-volume, irrotational, homogeneous
flattening, which involves either plane strain or general
strain.
Lines of particles that are parallel to the principal axes of
the strain ellipsoid have the same orientation before and
after deformation
It does not mean that the principal axes coincided
in all increments!
During homogeneous flattening a sphere is
transformed into a pancake-like shape and a box is
changed into a tablet or book-like form.
52. During pure shear the sides of the cube that are
parallel to the z-axis are shortened, while the lengths
of the sides that are parallel to the x-axis increase. In
contrast, the lengths of the sides of the cube that are
parallel to the y-axis remain unchanged.
When such geometrical changes occur during the
transformation of a rock body to a distorted state then
the mechanism of distortion is termed plane strain.
53.
54. Collective displacements of points in a body
relative to an external reference frame
Deformation describes the transformations from
some initial to some final geometry
Deformation of a rock body occurs in response to
a force
55. Deformation involves any one or a combination of
the following four components:
Ways that rocks respond to stress:
1. Rigid Body Translation
2. Rigid Body Rotation
3. Distortion or Strain
4. Dilation
58. Distortion is a non-rigid body operation that involves
the change in the spacing of points within a body of
rock in such a way that the overall shape of the body
is altered with or without a change in volume
Changes of points in body relative to each other
Particle lines may rotate relative to an external
coordinate system
Translation and spin are both zero
Example: squeezing a paste
In rocks we deal with processes that lead to both
movement and distortion
59.
60. Dilation is a non-rigid body operation
involving a change in volume
Pure dilation:
The overall shape remains the same
Internal points of reference spread apart (+ev) or
pack closer (-ev) together
Line lengths between points become uniformly longer
or shorter
61.
62. Though commonly confused with each other, strain
is only synonymous with deformation if there
has been distortion without any volume change,
translation, or rotation
Strain represents only one of four possible
components involved in the overall deformation
of a rock body where it has been transformed
from its original position, size, and shape to
some new location and configuration
Strain describes the changes of points in a body
relative to each other, or, in other words, the
distortions a body undergoes
The reference frame for strain is thus internal
63.
64. Originally straight lines remain straight
Originally parallel lines remain parallel
Circles (spheres) become ellipses (ellipsoids)
67. Heterogeneous strain affects non-rigid bodies in an
irregular, non-uniform manner and is sometimes referred
to as non-homogeneous or inhomogeneous strain
Leads to distorted
complex forms
68.
69.
70. Viscous deformation is a function of time
This means that strain accumulates over time
Hence deformation is irreversible, i.e. strain is
Non-recoverable
Permanent
• Flow of water is an example of viscous behavior.
• For a constant stress, strain will increase
linearly with time (with slope: s/h)
• Thus, stress is a function of strain and time!
s = he/t
71. The terms elastic and plastic describe the nature of
the material
Brittle and ductile describe how rocks behave.
Rocks are both elastic and plastic
materials, depending on the rate of
strain and the environmental
conditions (stress, pressure,
temperature), and we say that rocks are
viscoelastic materials.
72. Plasticity theory deals with the behavior of a
solid.
Plastic strain is continuous - the material
does not rupture, and the strain is
irreversible (permanent).
Occurs above a certain critical stress
(yield stress = elastic limit)
where strain is no longer linear with stress
Plastic strain is shear strain at constant
volume, and can only be caused by shear
stress
73. Brittle rocks fail by fracture at less
than 3-5% strain
Ductile rocks are able to sustain, under
a given set of conditions, 5-10% strain
before deformation by fracturing
74. Confining pressure, Pc
Effective confining pressure, Pe
Pore pressure, Pf is taken into account
Temperature, T
.
Strain rate, e
75. – Increasing T increases
ductility by activating
crystal-plastic processes
– Increasing T lowers the
yield stress (maximum
stress before plastic
flow), reducing the
elastic range
– Increasing T lowers the
ultimate rock strength
•Ductility: The % of strain that a rock can take
without fracturing in a macroscopic scale
76. The time interval it
takes to accumulate a
certain amount of
strain
Change of strain with
time (change in length
per length per time).
Slow strain rate means
that strain changes
slowly with time
– How fast change in
length occurs per unit
time
77. Shear strain rate:
. .
=2e [T-1]
Typical geological strain rates are on the order of
10-12 s-1 to 10-15 s-1
Strain rate of meteorite impact is on the order of
102 s-1 to 10-4 s-1
78. Decreasing strain rate:
decreases rock strength
increases ductility
.
Effect of slow e is analogous to increasing T
Think about pressing vs. hammering a silly putty
Rocks are weaker at lower strain rates
Slow deformation allows diffusional crystal-plastic
processes to more closely keep up with applied
stress
79. • Increasing
confining
pressure:
• Greater amount of
strain accumulates
before failure
• i.e., increases
ductility
–increases the viscous component and
enhances flow
–resists opening of fractures
•i.e., decreases elastic strain
80. • Increasing pore fluid pressure
– reduces rock strength
– reduces ductility
• The combined reduced ductility and strength
promotes flow under high pore fluid pressure
• Under ‘wet’ conditions, rocks deform more
readily by flow
– Increasing pore fluid pressure is analogous to
decreasing confining pressure
81. Rupture Strength (breaking strength)
Stress necessary to cause rupture at room
temperature and pressure in short time
experiments
Fundamental Strength
Stress at which a material is able to withstand,
regardless of time, under given conditions of T,
P and presence of fluids without fracturing or
deforming continuously