Analysis Type:

Small Strain ElastoPlastic Analysis

Model Type:

2D Plane Strain

Comparison:

NAFEMS Benchmark

Reference:

Fundamental 2D Plasticity Benchmark, Understanding Nonlinear 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.

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
 
Constraint  Location  Degree of freedom  
Placed on edge AD  Translation along X fixed  
Placed on edge AB  Translation along Y fixed  
Placed on edge BC  TransX: 2.5e5  
Placed on edge CD  TransY: 2.5e5  
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 
Stress Variation per load step for  NAFEMS  Structure 
Perfect Plasticity  
Isotropic Hardening 
Effective Plastic Strain Variation per load step for 1. Perfect Plasticity 2. Isotropic Hardening 
Analysis Type:  Small Strain ElastoPlastic Analysis 
Model Type:  3D 
Comparison:  NAFEMS Benchmark 
Reference:  Fundamental 3D Plasticity Benchmark, Understanding Nonlinear 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 multiaxial plastic behavior. 
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
 
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: 2.5e5  
Placed on face CDHG  TransY: 2.5e5  
Placed on face EFGH  TransZ: 2.5e5  
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 
Stress Variation per load step for  NAFEMS  Structure 
Perfect Plasticity  
Isotropic Hardening 
Effective Plastic Strain Variation per load step for 1. Perfect Plasticity 2. Isotropic Hardening 