This thesis analyzes the elastic behavior of honeycombs and auxetic materials with variations in cell geometry using finite element analysis. Models of honeycomb and auxetic structures with different cell angles and wall thicknesses were developed and analyzed in ABAQUS to determine their elastic moduli, Poisson's ratios, and stress-strain behaviors under compression loading. 3D printed prototypes of selected geometries were also experimentally tested and showed good agreement with FEA results. Key trends identified include increasing elastic modulus and Poisson's ratio with decreasing cell angle for honeycombs, and negative Poisson's ratio values for auxetic geometries.
The document discusses analyzing violations of assumptions in multiple linear regression. It presents data on the oxidation of NH3 to HNO3 over 21 days. Initial regression analysis shows heteroscedasticity, with unequal variances. Taking the square root transformation of Y results in a more homogeneous model with R-sq increasing to 85.8%. Removing outliers further improves the model, with R-sq rising to 97.7% and better statistical significance of predictors. Transformation and outlier removal produced a linear regression model that satisfies the assumptions of homoscedasticity and normality of residuals.
The document defines and provides examples for calculating the coefficient of variation, which is a measure used to compare the dispersion of data sets. It gives the formula for coefficient of variation as the standard deviation divided by the mean, expressed as a percentage. Two examples are shown comparing the stability of prices between two cities and production between two manufacturing plants, with the data set having the lower coefficient of variation considered more consistent or stable.
This document provides information about standard normal distributions and z-scores:
1) It gives the probabilities associated with different z-score ranges in a standard normal distribution table.
2) It provides examples of calculating z-scores given probabilities or data values, and calculating data values given z-scores or probabilities.
3) Other examples include finding the z-score for a sample given the sample size, mean, standard deviation and data point.
1. 445: Posttreatment stability in Class II nonextraction and two-maxillary p...Rafi Romano
This study compared the long-term stability of Class II malocclusion treatments with and without extraction of two maxillary premolars. 60 patients were divided into two groups - one treated with non-extraction and the other with extraction of two premolars. Cephalograms were taken before, after treatment, and 8 years post-treatment on average. The results showed similar stability between the two protocols for overjet, overbite, and canine and molar relationships over the long-term. However, the extraction group showed greater counterclockwise rotation compared to the non-extraction group. The conclusion was that both protocols provide similar long-term stability for treating Class II malocclusions.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
The document presents new 5x5 stiffness matrices for stability and dynamic analyses of line continua. The matrices were derived using energy variational principles and a five-term polynomial shape function. Analyses of four line continua and a portal frame using the new 5x5 matrices found results very close to exact solutions, with average percentage differences of 2.55% for stability and 0.14% for vibration. In contrast, analyses using traditional 4x4 matrices differed greatly from exact results, demonstrating the 5x5 matrices are better suited for stability and dynamic analyses of frame structures.
Formability study of layered material based on numerical analysisvikrammistry
1) The document analyzes the formability and springback of layered metallic materials through numerical analysis.
2) It studies how material properties like yield strength, strength coefficient, and strain hardening exponent affect the springback in bending. Higher yield strength and strength coefficient with lower strain hardening results in greater springback.
3) Thickness also impacts springback, with thinner materials experiencing more springback. Layering high ductility materials can help reduce springback in high strength materials.
Future work could involve deriving more complex equations to model bending moment and springback in multi-layer strips.
This document provides information about the normal distribution including formulas and tables for calculating probabilities based on z-scores. It includes the formulas for finding a z-score given mean, standard deviation, and value. It also includes a table of z-scores and their corresponding probabilities/areas under the normal curve. The document is intended to help students understand how to perform calculations involving the normal distribution.
The document discusses analyzing violations of assumptions in multiple linear regression. It presents data on the oxidation of NH3 to HNO3 over 21 days. Initial regression analysis shows heteroscedasticity, with unequal variances. Taking the square root transformation of Y results in a more homogeneous model with R-sq increasing to 85.8%. Removing outliers further improves the model, with R-sq rising to 97.7% and better statistical significance of predictors. Transformation and outlier removal produced a linear regression model that satisfies the assumptions of homoscedasticity and normality of residuals.
The document defines and provides examples for calculating the coefficient of variation, which is a measure used to compare the dispersion of data sets. It gives the formula for coefficient of variation as the standard deviation divided by the mean, expressed as a percentage. Two examples are shown comparing the stability of prices between two cities and production between two manufacturing plants, with the data set having the lower coefficient of variation considered more consistent or stable.
This document provides information about standard normal distributions and z-scores:
1) It gives the probabilities associated with different z-score ranges in a standard normal distribution table.
2) It provides examples of calculating z-scores given probabilities or data values, and calculating data values given z-scores or probabilities.
3) Other examples include finding the z-score for a sample given the sample size, mean, standard deviation and data point.
1. 445: Posttreatment stability in Class II nonextraction and two-maxillary p...Rafi Romano
This study compared the long-term stability of Class II malocclusion treatments with and without extraction of two maxillary premolars. 60 patients were divided into two groups - one treated with non-extraction and the other with extraction of two premolars. Cephalograms were taken before, after treatment, and 8 years post-treatment on average. The results showed similar stability between the two protocols for overjet, overbite, and canine and molar relationships over the long-term. However, the extraction group showed greater counterclockwise rotation compared to the non-extraction group. The conclusion was that both protocols provide similar long-term stability for treating Class II malocclusions.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
The document presents new 5x5 stiffness matrices for stability and dynamic analyses of line continua. The matrices were derived using energy variational principles and a five-term polynomial shape function. Analyses of four line continua and a portal frame using the new 5x5 matrices found results very close to exact solutions, with average percentage differences of 2.55% for stability and 0.14% for vibration. In contrast, analyses using traditional 4x4 matrices differed greatly from exact results, demonstrating the 5x5 matrices are better suited for stability and dynamic analyses of frame structures.
Formability study of layered material based on numerical analysisvikrammistry
1) The document analyzes the formability and springback of layered metallic materials through numerical analysis.
2) It studies how material properties like yield strength, strength coefficient, and strain hardening exponent affect the springback in bending. Higher yield strength and strength coefficient with lower strain hardening results in greater springback.
3) Thickness also impacts springback, with thinner materials experiencing more springback. Layering high ductility materials can help reduce springback in high strength materials.
Future work could involve deriving more complex equations to model bending moment and springback in multi-layer strips.
This document provides information about the normal distribution including formulas and tables for calculating probabilities based on z-scores. It includes the formulas for finding a z-score given mean, standard deviation, and value. It also includes a table of z-scores and their corresponding probabilities/areas under the normal curve. The document is intended to help students understand how to perform calculations involving the normal distribution.
Sreyas Sriram completed a summer internship from May to July 2016 under Professor G.K Ananthasuresh at the M2D2 Laboratory in IISC Bangalore. The internship involved studying compliant mechanisms, developing analytical models for beam bending using finite element analysis software ABAQUS, and validating the models. Key activities included mesh convergence studies, modeling beams with fillet radii, and comparing finite element analysis results to calculations from a modified beam bending code.
Finite Element Analysis of Magnesium Alloys using OOF2jitin_22
FEM is used to generate stress contours at varying strains using the open source software OOF2. The materials used are cast and rolled magnesium alloys LAT971 and LATZ9531.
Monitoring of strain and seismic vibrations in structureskalyanabooshnam
This document discusses monitoring strain and seismic vibrations in structures through various approaches. It compares using electrical strain gauges, piezoelectric materials, and vibration monitoring to assess structural health. Experimental work was conducted on reinforced concrete beams to measure strain using electrical gauges under loading. Piezoelectric patches were also bonded to the beams to monitor vibrations from 100-250 kHz and detect changes caused by damage. The results showed the electrical strain gauges and vibration monitoring techniques can effectively monitor structures and detect damage.
This master's thesis presentation examines the influence of plate thickness on contact time during elastic, elastic-plastic, and plastic impacts of brass spheres on thin glass plates. The experimental setup involves dropping brass spheres from varying heights onto glass plates of different thicknesses to impact at different velocities. Contact time is measured using an electrical circuit. Results show that contact time increases with sphere diameter and decreases with increasing plate thickness and impact velocity. Measured contact times are slightly higher than values predicted by existing theoretical models.
This document discusses tensile testing and summarizes key material properties that can be determined from tensile tests. It describes how tensile tests are conducted according to standardized procedures, with specifications for specimen geometry. The document presents an example tensile test data set and calculations to determine properties like elastic modulus, yield strength, ultimate strength, and ductility metrics like elongation and reduction of area. It also summarizes definitions for other material properties like shear modulus, bulk modulus, resilience, and toughness that can provide further characterization of a material's mechanical behavior.
This document discusses tensile testing and summarizes key material properties that can be determined from tensile tests. It describes how tensile tests are conducted according to standardized procedures, with specifications for specimen geometry. The document presents an example tensile test data set and calculations to determine properties like elastic modulus, yield strength, and ultimate tensile strength. It also summarizes how tensile tests can be used to characterize a material's ductility and define properties like resilience, toughness, and Poisson's ratio.
This document discusses two damage models for predicting ductile fracture initiation: 1) the Rice and Tracey cavity growth model, which relates cavity growth rate to stress triaxiality and plastic strain increment, and predicts initiation when cavity radius reaches a critical value. 2) A damage work model, which combines plastic strain work with a term accounting for cavity growth related to hydrostatic stress, predicting initiation when damage work reaches a critical value. Finite element simulations of notched tensile specimens of two steel materials were performed to evaluate these models based on experimental crack initiation locations and steps. Both models were able to predict initiation location and step for a relatively constant critical damage value.
1) Computational techniques are essential for accurately simulating high-speed coating flows that conventional asymptotic models cannot capture. Accessing smaller spatio-temporal scales through computation and experiment is needed to identify the true physics.
2) Gas dynamics, particularly the mean free path of gas molecules, play a key role in phenomena like air entrainment in coating flows. At reduced pressures, the longer mean free path can delay air entrainment.
3) There is still debate around wetting because different models can describe experiments reasonably well using different parameter values. Fully resolving interfaces and accessing microscales may be needed to definitively identify the governing physics.
1) The document presents the results of a 3D structural analysis and optimization of a variable cross-section steel plate fixed at the top end and carrying a 1500 lb load at the bottom.
2) The analysis examined the relationship between fillet radii and deflection/von misses stress in the plate.
3) The results show relationships between fillet radii and von mises stress and deflection, with R-squared values indicating a moderate fit. Areas for improving the model are identified.
The document discusses concepts related to tension testing of materials including:
- Stress-strain diagrams and key points like proportional limit, yield point, ultimate tensile strength
- Ductile and brittle material behaviors
- Calculations of properties from test data like modulus of elasticity, resilience, toughness
- Effects of factors like carbon content, temperature, specimen geometry
Worked examples are provided to calculate properties from given tension test load-extension data.
This document presents a static analysis of a non-spinning three-disc rotor system conducted using finite element analysis in ANSYS. Numerical results for deflection, bending moment, and stresses are obtained and compared to theoretical calculations. A rotor model with three rigid discs supported by bearings is simulated in ANSYS under fixed and simply supported boundary conditions. The numerical results closely match the theoretical values, validating the ANSYS model.
This document summarizes an implementation of economic gas-like models to analyze the influence of underlying network topologies. It introduces random symmetric and directed exchange rules for money transfers between agents. For random symmetric exchanges on networks like complete graphs, spatial networks, and scale-free networks, the money distribution converges to a Boltzmann-Gibbs form and is robust to network structure. A model with uniform savings is also introduced, where the money distribution takes a gamma-like form.
The document provides details about the acceptance testing and commissioning of a new TrueBeam linear accelerator installed at the facility. Some key details include:
- The machine was installed in an existing bunker previously occupied by a Siemens Primus Plus with additional shielding added.
- Acceptance testing verifies a small subset of beam data based on manufacturer guidelines to check specifications, while commissioning involves comprehensive beam measurements and treatment planning system configuration.
- Beam data measurements included depth doses, profiles, output, symmetry, flatness, and other dosimetric parameters which were analyzed and entered into the treatment planning system.
- Electron and photon beam energies and characteristics were evaluated to ensure they met tolerance limits. Other
Computation of a gearbox for a wind power plantPietro Galli
The project Computation of a Gearbox for a Wind Power Plant dealt with the study and the analysis of the Generator in order to provide data about the following characteristics
o Static Design of the gearbox:
Design of shaft 1
Design of bearings
Internal stresses
Safety factor
Design of shaft 2
o Fatigue analysis:
Shaft 1 section 3
Shaft 1 section 4
Shaft 2 section 1
Shaft 2 section 2
o Rolling bearings analysis, life and fatique:
Roller bearings C and D
Bearing E
Rating life_bearing D
Rating life_bearing E
o Spur gears analysis:
Computation of transmission ratio, pt and b
Tooth bending strength
Tooth surface fatigue strength
This poster summarizes the use of small-angle X-ray scattering (SAXS) to characterize the inhomogeneous structures in various glass and glass-related materials. SAXS can be used to determine the shape, size, and size distribution of nanostructures in heterogeneous glasses such as two-phase glasses, glass ceramics, and nanoporous glasses. Examples are presented where SAXS data has been fitted to models to obtain structural information and compare with other techniques like transmission electron microscopy and gas adsorption methods. The versatility of SAXS for nanostructure analysis in a wide range of glass and glass-ceramic systems is demonstrated.
This document discusses common design issues and failure modes encountered at the microscale. As devices decrease in size, surface area to volume ratio increases significantly. This impacts heat dissipation, storage, and transfer. Spring constants and stresses also scale with device dimensions. Common MEMS failure modes include particulate contamination, component fusion from overdriving, stiction, electrostatic clamping, static overload, delamination, and creep. Careful consideration of scaling effects is important for reliable microsensor design.
This document discusses stresses in beams, including:
1) Bending stresses in beams, shear flow, and shearing stress formulae for beams.
2) Inelastic bending of beams and deflection of beams using various calculation methods.
3) Elementary treatment of statically indeterminate beams like fixed and continuous beams.
It provides theories, formulae, and examples for calculating stresses in beams undergoing bending loads.
This document presents a higher-order finite element model to predict the linear buckling behavior of laminated beam structures. The model is based on a displacement field that assumes a non-linear variation of displacements through the beam width and depth, eliminating the need for shear correction factors. Numerical applications show the model accurately predicts buckling loads for isotropic and anisotropic beams of various cross-sections when compared to other models and closed-form solutions. The higher-order model is more versatile and accurate than lower-order models like Euler-Bernoulli for a range of slenderness ratios and beam geometries.
Sreyas Sriram completed a summer internship from May to July 2016 under Professor G.K Ananthasuresh at the M2D2 Laboratory in IISC Bangalore. The internship involved studying compliant mechanisms, developing analytical models for beam bending using finite element analysis software ABAQUS, and validating the models. Key activities included mesh convergence studies, modeling beams with fillet radii, and comparing finite element analysis results to calculations from a modified beam bending code.
Finite Element Analysis of Magnesium Alloys using OOF2jitin_22
FEM is used to generate stress contours at varying strains using the open source software OOF2. The materials used are cast and rolled magnesium alloys LAT971 and LATZ9531.
Monitoring of strain and seismic vibrations in structureskalyanabooshnam
This document discusses monitoring strain and seismic vibrations in structures through various approaches. It compares using electrical strain gauges, piezoelectric materials, and vibration monitoring to assess structural health. Experimental work was conducted on reinforced concrete beams to measure strain using electrical gauges under loading. Piezoelectric patches were also bonded to the beams to monitor vibrations from 100-250 kHz and detect changes caused by damage. The results showed the electrical strain gauges and vibration monitoring techniques can effectively monitor structures and detect damage.
This master's thesis presentation examines the influence of plate thickness on contact time during elastic, elastic-plastic, and plastic impacts of brass spheres on thin glass plates. The experimental setup involves dropping brass spheres from varying heights onto glass plates of different thicknesses to impact at different velocities. Contact time is measured using an electrical circuit. Results show that contact time increases with sphere diameter and decreases with increasing plate thickness and impact velocity. Measured contact times are slightly higher than values predicted by existing theoretical models.
This document discusses tensile testing and summarizes key material properties that can be determined from tensile tests. It describes how tensile tests are conducted according to standardized procedures, with specifications for specimen geometry. The document presents an example tensile test data set and calculations to determine properties like elastic modulus, yield strength, ultimate strength, and ductility metrics like elongation and reduction of area. It also summarizes definitions for other material properties like shear modulus, bulk modulus, resilience, and toughness that can provide further characterization of a material's mechanical behavior.
This document discusses tensile testing and summarizes key material properties that can be determined from tensile tests. It describes how tensile tests are conducted according to standardized procedures, with specifications for specimen geometry. The document presents an example tensile test data set and calculations to determine properties like elastic modulus, yield strength, and ultimate tensile strength. It also summarizes how tensile tests can be used to characterize a material's ductility and define properties like resilience, toughness, and Poisson's ratio.
This document discusses two damage models for predicting ductile fracture initiation: 1) the Rice and Tracey cavity growth model, which relates cavity growth rate to stress triaxiality and plastic strain increment, and predicts initiation when cavity radius reaches a critical value. 2) A damage work model, which combines plastic strain work with a term accounting for cavity growth related to hydrostatic stress, predicting initiation when damage work reaches a critical value. Finite element simulations of notched tensile specimens of two steel materials were performed to evaluate these models based on experimental crack initiation locations and steps. Both models were able to predict initiation location and step for a relatively constant critical damage value.
1) Computational techniques are essential for accurately simulating high-speed coating flows that conventional asymptotic models cannot capture. Accessing smaller spatio-temporal scales through computation and experiment is needed to identify the true physics.
2) Gas dynamics, particularly the mean free path of gas molecules, play a key role in phenomena like air entrainment in coating flows. At reduced pressures, the longer mean free path can delay air entrainment.
3) There is still debate around wetting because different models can describe experiments reasonably well using different parameter values. Fully resolving interfaces and accessing microscales may be needed to definitively identify the governing physics.
1) The document presents the results of a 3D structural analysis and optimization of a variable cross-section steel plate fixed at the top end and carrying a 1500 lb load at the bottom.
2) The analysis examined the relationship between fillet radii and deflection/von misses stress in the plate.
3) The results show relationships between fillet radii and von mises stress and deflection, with R-squared values indicating a moderate fit. Areas for improving the model are identified.
The document discusses concepts related to tension testing of materials including:
- Stress-strain diagrams and key points like proportional limit, yield point, ultimate tensile strength
- Ductile and brittle material behaviors
- Calculations of properties from test data like modulus of elasticity, resilience, toughness
- Effects of factors like carbon content, temperature, specimen geometry
Worked examples are provided to calculate properties from given tension test load-extension data.
This document presents a static analysis of a non-spinning three-disc rotor system conducted using finite element analysis in ANSYS. Numerical results for deflection, bending moment, and stresses are obtained and compared to theoretical calculations. A rotor model with three rigid discs supported by bearings is simulated in ANSYS under fixed and simply supported boundary conditions. The numerical results closely match the theoretical values, validating the ANSYS model.
This document summarizes an implementation of economic gas-like models to analyze the influence of underlying network topologies. It introduces random symmetric and directed exchange rules for money transfers between agents. For random symmetric exchanges on networks like complete graphs, spatial networks, and scale-free networks, the money distribution converges to a Boltzmann-Gibbs form and is robust to network structure. A model with uniform savings is also introduced, where the money distribution takes a gamma-like form.
The document provides details about the acceptance testing and commissioning of a new TrueBeam linear accelerator installed at the facility. Some key details include:
- The machine was installed in an existing bunker previously occupied by a Siemens Primus Plus with additional shielding added.
- Acceptance testing verifies a small subset of beam data based on manufacturer guidelines to check specifications, while commissioning involves comprehensive beam measurements and treatment planning system configuration.
- Beam data measurements included depth doses, profiles, output, symmetry, flatness, and other dosimetric parameters which were analyzed and entered into the treatment planning system.
- Electron and photon beam energies and characteristics were evaluated to ensure they met tolerance limits. Other
Computation of a gearbox for a wind power plantPietro Galli
The project Computation of a Gearbox for a Wind Power Plant dealt with the study and the analysis of the Generator in order to provide data about the following characteristics
o Static Design of the gearbox:
Design of shaft 1
Design of bearings
Internal stresses
Safety factor
Design of shaft 2
o Fatigue analysis:
Shaft 1 section 3
Shaft 1 section 4
Shaft 2 section 1
Shaft 2 section 2
o Rolling bearings analysis, life and fatique:
Roller bearings C and D
Bearing E
Rating life_bearing D
Rating life_bearing E
o Spur gears analysis:
Computation of transmission ratio, pt and b
Tooth bending strength
Tooth surface fatigue strength
This poster summarizes the use of small-angle X-ray scattering (SAXS) to characterize the inhomogeneous structures in various glass and glass-related materials. SAXS can be used to determine the shape, size, and size distribution of nanostructures in heterogeneous glasses such as two-phase glasses, glass ceramics, and nanoporous glasses. Examples are presented where SAXS data has been fitted to models to obtain structural information and compare with other techniques like transmission electron microscopy and gas adsorption methods. The versatility of SAXS for nanostructure analysis in a wide range of glass and glass-ceramic systems is demonstrated.
This document discusses common design issues and failure modes encountered at the microscale. As devices decrease in size, surface area to volume ratio increases significantly. This impacts heat dissipation, storage, and transfer. Spring constants and stresses also scale with device dimensions. Common MEMS failure modes include particulate contamination, component fusion from overdriving, stiction, electrostatic clamping, static overload, delamination, and creep. Careful consideration of scaling effects is important for reliable microsensor design.
This document discusses stresses in beams, including:
1) Bending stresses in beams, shear flow, and shearing stress formulae for beams.
2) Inelastic bending of beams and deflection of beams using various calculation methods.
3) Elementary treatment of statically indeterminate beams like fixed and continuous beams.
It provides theories, formulae, and examples for calculating stresses in beams undergoing bending loads.
This document presents a higher-order finite element model to predict the linear buckling behavior of laminated beam structures. The model is based on a displacement field that assumes a non-linear variation of displacements through the beam width and depth, eliminating the need for shear correction factors. Numerical applications show the model accurately predicts buckling loads for isotropic and anisotropic beams of various cross-sections when compared to other models and closed-form solutions. The higher-order model is more versatile and accurate than lower-order models like Euler-Bernoulli for a range of slenderness ratios and beam geometries.
Buckling of laminated beam higher order discrete model-main
Thesis presentation
1. Analysis of Elastic Behaviour of Honeycombs and
Auxetic Materials with Variation in its Cell Geometry
MS THESIS PRESENTED BY
VISHWATEJ MANE
ADVISOR- PROF. MAEN ALKHADER
DEPARTMENT OF MECHANICAL ENGINEERING
STONY BROOK UNIVERSITY
2. Introduction
Honeycombs used as core in sandwich panels of lightweight structure
Progressive collapse with retaining functionality
Auxetic materials exhibits NPR
Auxetic material has improved Shear, indentation resistance and fracture toughness
Potential applications in defense and aerospace
Relative density
Outline of the study
3. Deformation mechanism and Theory
Flexure, stretching and hinging mechanism
Cell Geometry and General Mathematical model
“ I.G. Masters and K E Evans, ”Models for the elastic deformation of honeycombs”, composite
strucutres,0263-8223/96
5. FEA Model development
Development of Geometry for different cellular models
In Property module used Al 6061 as material
ρ=2700 kg/m3, E= 68950 MPa, ν= 0.3, plastic strain
Static, general analysis type
meshing - structured Quad shell elements (S4R)
Node Sets- TOP, BOTTOM, LEFT, RIGHT
6. BCs for Poisson’s ratio ν21
Hex30 model
U3=0
Bottom, U2=UR1=UR2=UR3=0
Top, UR1=UR2=UR3=0
U2= -2.5
7. BCs for Poisson’s ratio ν12
Hex30 model
U3= 0
LEFT, U1=UR1=UR2=UR3=0
RIGHT, UR1=UR2=UR3=0
U1= -2.5
8. FEA results and Trends for Honeycombs
Hex 30, t= 0.25mm Hex 10, t=0.3mm
9. Stress 22, Young’s Modulus E22 and Poisson’s ratio ν21 vs. Strain 22 for Hex05 model and Hex10 model
10. Stress 22, Young’s Modulus E22 and Poisson’s ratio ν21 vs. Strain 22 for Hex20 model and Hex30 model
11. FEA Results and Trends for Auxetics
Hex -05, t= 0.2mm Hex -10, t= 0.15mm
12. Stress 22, Young’s Modulus E22, Poisson’s ratio ν21 vs. Strain 22 for Hex-05 model and Hex-10 model
13. Stress 22, Young’s Modulus E22 and Poisson’s ratio ν21 vs. Strain 22 curve for Hex -20 model
14. FEA Results and Trends in honeycombs 11 direction
Hex30, t=0.3mm Hex20, t=0.25mm
15. Stress 11, Young’s Modulus E11 and Poisson’s ratio ν12 vs. Strain 11 for Hex 05 model and Hex10
model
16. Stress 11, Young’s Modulus E11 and Poisson’s ratio ν12 vs. Strain 11 for Hex20 model and Hex30
model
17. FEA Results and Trends in Auxetics
Hex-05, t=0.2mm Hex-10, t=0.15mm
18. Stress 11, Young’s Modulus E11 Poisson’s ratio ν12 vs. Strain 11 for Hex -05 model and Hex-10 model
19. Stress 11, Young’s Modulus E11 and Poisson’s ratio ν12 vs. Strain for Hex-20 model
20. Specifications of 3D printed models
MakerBot Replicator 2.0 3D printer
Sr No. Model by cell angle geometry
(wall thickness= 0.8mm)
Constant width= 15mm
Length
in mm
Height
in mm
1 -20 28.33 27.85
2 -10 24.94 25.45
3 -5 24.12 24.35
4 5 24.15 26.02
5 10 29.63 28.69
6 20 28.02 25.94
7 30 26.38 27.54
21. 3D printed Honeycombs test results
Stress vs Strain curves over entire period of compression test on MTS machine
0
5
10
15
20
25
0 0.1 0.2 0.3
StressY
Strain Y
Hex 05
0
2
4
6
8
10
12
14
16
18
0 0.05 0.1 0.15 0.2 0.25
StressY
Strain Y
Hex 10
0
1
2
3
4
5
6
7
0 0.1 0.2 0.3
StressY
Strain Y
Hex 20
0
1
2
3
4
5
6
7
8
0 0.1 0.2 0.3
StressY
Strain Y
Hex 30
37. Conclusions for honeycomb samples
FEA methods can be used to predict trends in elastic constants
E22 and E11 increases with increase in relative density
E22 increases with decrease in cell angle closer to zero
E11 increases with increase in angle closer to 30 degrees
Trends of ν21 and ν12 are linear and independent of relative density in elastic region
ν21 increase with decrease in cell angle closer to 0
ν12 increases with increase in cell angle closer to 30
Waviness in stress vs. strain trend in plastic region represents cell arrays collapse
38. Conclusions for Auxetic samples
E22 and E11 increases with relative density
Exhibits Negative Poisson’s ratio (NPR) property
Trends ν21 and ν12 independent of relative density in elastic region
ν21 increases with decrease in cell angle
ν12 decreases with increase in cell angle
Waviness in stress, Poisson’s ratio vs. strain trends represents cell arrays collapse
39. Young’s modulus 22 vs. cell angle
0
5000
10000
15000
20000
25000
30000
5 10 20 30 -5 -10 -20
Young'sModulusE22
Cell angle in degrees
t=0.15 mm t= 0.2 mm t= 0.25 mm t=0.3 mm
40. Poisson’s ratio 21 vs. cell angle
-6
-4
-2
0
2
4
6
5 10 20 30 -5 -10 -20
Poisson'sratioν21
Cell angle in degrees
t=0.15 mm t=0.2 mm t=0.25 mm t=0.3 mm
41. Young’s modulus 11 vs cell angle
0
500
1000
1500
2000
2500
3000
3500
5 10 20 30 -5 -10 -20
Young'sModulusE11
cell angles in degrees
t=0.15 mm t=0.2 mm t=0.25 mm t=0.3 mm
42. Poisson’s ratio12 vs cell angle
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
5 10 20 30 -5 -10 -20
Poisson'sratioν12
Cell angles in degrees
t=0.15 mm t=0.2 mm t=0.25 mm t=0.3 mm
43. Bibliography
I.G. Masters and K E Evans, “ Models for the elastic deformation of honeycombs”
composite structures,0263-8223/96
Q.Liu,” Literature Review: Material with Negative Poisson’s ratio and potential
applications to aerospace and defence” DSTO-GD-0472, August 2006
Yanping Liu and Hong Hu, “ A Review on Auxetic structures and polymeric materials”,
ISSN 1992-2248, May 2010
M. Bianchi, S. Frontoni, F. Scarpa, and C.W.Smith, “Density change during the
manufacturing process of PU-PE open cell Auxetic foams”, pssb.201083966, May 2010
Kim Alderson, Andrew Alderson, Naveen Ravirala, Virginia Simkins, and Philip Davies,
“Manufacture and characterization of thin flat and curved Auxetic foam sheets”,
pssb.201084215, March 2012