The document discusses different stress and failure criteria used to analyze materials. It describes the Tresca, Von Mises, and Rankine criteria, which use maximum shear stress, equivalent deviatoric strain energy, and limits on principal stresses respectively to determine failure. The Von Mises criterion applies best to isotropic ductile metals, while Tresca and Rankine criteria can also be used for such materials. Rankine is more suitable for low-cohesion materials like ceramics. The appropriate criterion depends on the material properties.
A review of constitutive models for plastic deformationSamir More
Materials like mild steel have defined yield point hence it is easy to distinguish between the elastic region and plastic region of deformation. But for materials that do not have specified yield point, it is hard to distinguish between elastic and plastic deformation region. In that case may be plastic deformation starts from beginning of the application of the load. For elastic region, stress and strain are in linear relationship with each other hence Hook’s law valid true. But for plastic region, the relation between stress and strain is nonlinear and complicated. So need for continuum plasticity model arises. The main aim of continuum plasticity model is to formulate mathematical model based on experimental results that can predict the plastic deformation of material under varying loading conditions and at different elevated temperature.
A review of constitutive models for plastic deformationSamir More
Materials like mild steel have defined yield point hence it is easy to distinguish between the elastic region and plastic region of deformation. But for materials that do not have specified yield point, it is hard to distinguish between elastic and plastic deformation region. In that case may be plastic deformation starts from beginning of the application of the load. For elastic region, stress and strain are in linear relationship with each other hence Hook’s law valid true. But for plastic region, the relation between stress and strain is nonlinear and complicated. So need for continuum plasticity model arises. The main aim of continuum plasticity model is to formulate mathematical model based on experimental results that can predict the plastic deformation of material under varying loading conditions and at different elevated temperature.
General steps of the finite element methodmahesh gaikwad
General Steps used to solve FEA/ FEM Problems. Steps Involves involves dividing the body into a finite elements with associated nodes and choosing the most appropriate element type for the model.
What is a multiple dgree of freedom (MDOF) system?
How to calculate the natural frequencies?
What is a mode shape?
What is the dynamic stiffness matrix approach?
#WikiCourses
https://wikicourses.wikispaces.com/Lect04+Multiple+Degree+of+Freedom+Systems
https://eau-esa.wikispaces.com/Topic+Multiple+Degree+of+Freedom+%28MDOF%29+Systems
General steps of the finite element methodmahesh gaikwad
General Steps used to solve FEA/ FEM Problems. Steps Involves involves dividing the body into a finite elements with associated nodes and choosing the most appropriate element type for the model.
What is a multiple dgree of freedom (MDOF) system?
How to calculate the natural frequencies?
What is a mode shape?
What is the dynamic stiffness matrix approach?
#WikiCourses
https://wikicourses.wikispaces.com/Lect04+Multiple+Degree+of+Freedom+Systems
https://eau-esa.wikispaces.com/Topic+Multiple+Degree+of+Freedom+%28MDOF%29+Systems
FellowBuddy.com is an innovative platform that brings students together to share notes, exam papers, study guides, project reports and presentation for upcoming exams.
We connect Students who have an understanding of course material with Students who need help.
Benefits:-
# Students can catch up on notes they missed because of an absence.
# Underachievers can find peer developed notes that break down lecture and study material in a way that they can understand
# Students can earn better grades, save time and study effectively
Our Vision & Mission – Simplifying Students Life
Our Belief – “The great breakthrough in your life comes when you realize it, that you can learn anything you need to learn; to accomplish any goal that you have set for yourself. This means there are no limits on what you can be, have or do.”
Like Us - https://www.facebook.com/FellowBuddycom
Finite Element Simulation of the Response of No-Tension MaterialsAlieh Alipour
Unbound granular materials that are used at base layer of flexible pavement
cannot resist tensile forces. These materials are called no-tension materials.
In this paper, a modified strain-energy function was used to describe the
constitutive behavior of granular materials to simulate flexible pavement
within the finite element framework CAPA3D .The constitutive model was
defined such that the positive stresses in principal directions were zero.
Comparisons between the no-tension materials and linear elastic materials for
different boundary conditions and geometries were presented in this paper.
The results of FE analysis show that effect of using no-tension model for base
layer on pavement performance is significant. The deformation at top and
horizontal strain at the bottom of asphalt concrete layer are higher when the
no-tension model is used.
Topology is the arrangement of the various elements of a computer network.
In communication networks, a topology is a usually schematic description of the arrangement of a network, including its nodes and connecting lines.
A computer network is made of computers which are linked to one another with communication lines (network cables, etc.) and hardware elements (network adapters, as well as other equipment for ensuring that data travels correctly.
InterTech is a Saint Petersburg based civil engineering companyMaxim Gavrik
InterTech is a Saint Petersburg based civil engineering company, which provides a full range of services for design, construction, installation, commissioning and start-up of the MEP systems in the buildings and structures under industrial, commercial and civil construction.
I am Titus B. I am a Mechanical Engineering Assignment Expert at mechanicalengineeringassignmenthelp.com. I hold a Ph.D. in Mechatronics Engineering Alcorn State University USA. I have been helping students with their assignments for the past 11 years. I solve assignments related to Mechanical Engineering.
Visit mechanicalengineeringassignmenthelp.com or email info@mechanicalengineeringassignmenthelp.com. You can also call on +1 678 648 4277 for any assistance with Mechanical Engineering.
Diseno en ingenieria mecanica de Shigley - 8th ---HDes
descarga el contenido completo de aqui http://paralafakyoumecanismos.blogspot.com.ar/2014/08/libro-para-mecanismos-y-elementos-de.html
Diseno en ingenieria mecanica de Shigley - 8th ---HDes
descarga el contenido completo de aqui http://paralafakyoumecanismos.blogspot.com.ar/2014/08/libro-para-mecanismos-y-elementos-de.html
Similar to Stress Measures And Failure Criteria (20)
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
for beginners, providing thorough training in areas such as SEO, digital communication marketing, and PPC training in Noida. After finishing the program, students receive the certifications recognised by top different universitie, setting a strong foundation for a successful career in digital marketing.
2. Stress tensor: principal components
By calculating its eigen-values & eigen-vectors, the stress tensors can be
written in its principal coordinate system in a purely diagonal form
containing only normal stress components which are called the principal
stress components. The eigenvectors of σ determine the orientation of the
principal coordinate system ê1,2,3 and thus of the principal stress directions :
σ1 0 0
σê = 0 σ2
0
1, 2 , 3
0 0
σ3
The principal stresses are also one set of invariants of the stress tensor.
Conventionally, the principal stresses σ1, σ2 and σ3 are ordered such that:
σ1 > σ2 > σ3
3. Stress tensor decomposition: hydrostatic - deviatoric parts
The stress tensor can be divided in hydrostatic and deviatoric part:
σ = σh + σ = pl + ~
~ σ
Where p = 3 σ ii is the hydrostatic pressure and ~ is called the deviatoric stress tensor.
1
σ
Strain energy decomposition
Using the hydrostatic - deviatoric stress & strain decomposition, the strain
energy can be written as:
~
E = 2 σ : ε = 2 σh : ε h + 2 σ : ~ = E h + E
1 1 1~
ε
4. Tresca equivalent stress criteria
The Tresca stress criteria is based on the comparison of maximum shear τmax
and is thus defined basically from the maximum principal stress difference :
σ eq = max( σ1 − σ2 , σ2 − σ3 , σ3 − σ1 )
tresca
The corresponding yield / failure criteria is simply written as a comparison
with the maximum allowed shear stress τy or from a uniaxial stress state
σ y : σ eq ≤ 2τ y = σ y
tresca
Postulates that yielding occur when the maximum shearing stress at a
particle of a body in a general, triaxial state of stress attains a value equal to
the maximum shearing stress at yielding in uniaxial tension.
Also known as the maximum shear stress criterion.
5. Tresca criteria τ
τmax = 2 (σ1 − σ3 ) ≤ τ y
1
σ3 σ1 σ
representation of Tresca criteria in Mohr diagram
6. Rankine stress criteria
The Rankine stress criteria simply imposes that the principal stress
components are bounded between σc (compression) and σt (tension) :
σ c < σi < σ t ∀i = 1,2,3
As a result, the maximum shear stress is also bounded: τmax ≤ 1
2 (σ t − σc )
7. Rankine criteria τ
τmax ≤ 2 (σ t − σ c )
1
σc σt σ
representation of Rankine criteria in Mohr diagram
8. Von Mises equivalent stress criteria
The Von Mises equivalent stress criteria is based on a comparison of maximum
~
deviatoric strain energy E and is thus defined from the deviatoric stress tensor ~ :
σ
σmises =
eq 3 ~:~
σ σ
2
It can also be written directly from the principal stresses σ1,2,3 or from the
stress tensor components:
(σ1 − σ2 )2 + (σ2 − σ3 )2 + (σ3 − σ1 )2
σ eq
mises = 2
(σ11 − σ22 )2 + (σ22 − σ33 )2 + (σ33 − σ11 )2 + 6 (σ12 − σ2 + σ2 )
2
= 2
23 31
The corresponding yield / failure criteria is simply written as a comparison
with the maximum allowed uniaxial stress y (yield stress):
σmises ≤ σ y
eq
11. Between Von Mises and Tresca Yield Criteria
• The Von Mises yield criterion is non-linear. whereas the Tresca yield
criterion is piecewise linear.
• However, if the ordering of the magnitudes of the principal components
of stress is not known, the Tresca yield surface involves singularities
(edges and corners) and is difficult to handle.
12. Stress criteria
• Use Von Mises criteria for isotropic, dense & ductile materials like metals which
failure does not depend on hydrostatic pressure.
• Von Mises criterion also gives a reasonable estimation of fatigue failure,
especially in cases of repeated tensile and tensile-shear loading
• Tresca criteria is more conservative than Von Mises, it is also valid for isotropic &
ductile materials and is also independent of hydrostatic pressure.
• Both Tresca & Mises criteria impose that the material has the same limit in
traction & compression. If not, consider another criteria or take the lowest limit
for safety.
• Rankine criteria is more suitable to low cohesion materials like ceramics where
the tension limit is significantly lower than the compression. In this case, you
should also check that the maximum shear (Tresca) is also below the admissible
values.
• Complex materials like concrete, ceramics, composites require much more
complex criteria taking into account the hydrostatic pressure, the
tension/compression asymmetry or the anisotropy of the material.