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Static Analysis with Plasticity Problems
This chapter contains a static analysis with elasto-plastic behaviour in which the structure is loaded past the yield point.
This chapter contains the following models:
mvspl001 : Small Strain Elasto-Plastic Analysis of Square Plate
mvspl002 : Small Strain Elasto-Plastic Analysis of 3D Cube
mvspl001 : Small Strain Elasto-Plastic Analysis of Square Plate
 Analysis Type: Small Strain Elasto-Plastic Analysis Model Type: 2D Plane Strain Comparison: NAFEMS Benchmark Reference: Fundamental 2D Plasticity Benchmark, Understanding Non-linear Finite Element Analysis through Illustrative Benchmark,NAFEMS, pp. 31. Description: The problem consists of a simple 2D geometry subjected to prescribed displacements in order to demonstrate plastic behavior.
Specifications
Element Type:
2D Solid
Units:
mmNs
Dimensions:
L: 1.0 Unit length
Material Properties:
Mass Density: 0
Young's Modulus: 2.5e5
Poisson's Ratio: 0.25
Plasticity Model:
1. Perfect Plasticity—Yield Stress : 5.0
2. Isotropic Hardening—Tangent Modulus :5e4
 There are two sample models for this exercise. One has an elasto-plastic material that uses perfect plasticity—mvspl001a and the other uses a material with Isotropic hardening—mvspl001b.
Constraint
Location
Degree of freedom
Translation along X- fixed
Placed on edge AB
Translation along Y- fixed
Placed on edge BC
TransX-: 2.5e-5
Placed on edge CD
TransY-: 2.5e-5
TransX and Trans Y are applied in 8 steps as follows (R=TransX=TransY)
Step
TransX
TransY
Step 1
R
0.0
Step 2
2R
0.0
Step 3
2R
R
Step 4
2R
2R
Step 5
R
2R
Step 6
0.0
2R
Step 7
0.0
R
Step 8
0.0
0.0
Comparison of Results Data
 Stress Variation per load step for NAFEMS Structure Perfect Plasticity Isotropic Hardening
 Effective Plastic Strain Variation per load step for1. Perfect Plasticity2. Isotropic Hardening
mvspl002 : Small Strain Elasto-Plastic Analysis of 3D Cube
 Analysis Type: Small Strain Elasto-Plastic Analysis Model Type: 3D Comparison: NAFEMS Benchmark Reference: Fundamental 3D Plasticity Benchmark, Understanding Non-linear Finite Element Analysis through Illustrative Benchmark,NAFEMS, pp. 39. Description: The problem consists of a simple 3D geometry subjected to prescribed displacements in order to demonstrate multi-axial plastic behavior.
Specifications
Element Type:
3D Solid
Units:
mmNs
Dimensions:
L: 1.0
Material Properties:
Mass Density: 0
Young's Modulus: 2.5e5
Poisson's Ratio: 0.25
Plasticity Model:
1. Perfect Plasticity—Yield Stress : 5.0
2. Isotropic Hardening—Tangent Modulus :5e4
 There are two sample models for this exercise. One has an elasto-plastic material that uses perfect plasticity—mvspl002a and the other uses a material with isotropic hardening—mvspl002b.
Constraint
Location
Degree of freedom
Placed on face AEHD
Trans X- fixed
Placed on face ABFE
Trans Y- fixed
Placed on face ABCD
Trans Z- fixed
Placed on face BCGF
TransX: 2.5e-5
Placed on face CDHG
TransY: 2.5e-5
Placed on face EFGH
TransZ: 2.5e-5
TransX,TransY, and TransZ are applied in 12 steps as follows (R=TransX=TransY=TransZ)
Step
TransX
TransY
TransZ
Step 1
R
0.0
0.0
Step 2
2R
0.0
0.0
Step 3
2R
R
0.0
Step 4
2R
2R
0.0
Step 5
2R
2R
R
Step 6
2R
2R
2R
Step 7
R
2R
2R
Step 8
0.0
2R
2R
Step 9
0.0
R
2R
Step 10
0.0
0.0
2R
Step 11
0.0
0.0
R
Step 12
0.0
0.0
0.0
Comparison of Results Data
 Stress Variation per load step for NAFEMS Structure Perfect Plasticity Isotropic Hardening
 Effective Plastic Strain Variation per load step for1. Perfect Plasticity2. Isotropic Hardening