VMR049-PL1

VMR049-PL1
2D Plane Strain Plasticity Benchmark

Test Description

A square of length L and height L is constrained in the Y-direction along the bottom edge and in the X-direction along the left edge. The model is displaced in the X and Y directions.

Geometric Properties

Material Properties

L = 1.0 mm

E = 250.0 x 10³ N/mm²

ν = 0.25

Plasticity Model

Perfect Plasticity: σ_ys = 5.0 N/mm²

Isotropic Hardening: E_T = 50.0 x 10³ N/mm²

Boundary Conditions

Left Edge: u_x = 0

Bottom Edge: u_y = 0

Right Edge: u_x = δ_x

Top Edge: u_y = δ_y

Loading

No applied forces

Displacements prescribed in 8 increments (R = 2.5x10^-5), as follows:

Step: Disp. Change

Step: Stress State

Step 1: Δu_x= +R

Step 1: First Yield

Step 2: Δu_x = +R

Step 2: Plastic Flow

Step 3: Δu_y = +R

Step 3: Elastic Unloading

Step 4: Δu_y = +R

Step 4: Plastic Reloading

Step 5: Δu_x = -R

Step 5: Plastic Flow

Step 6: Δu_x = -R

Step 6: Plastic Flow

Step 7: Δu_y = -R

Step 7: Elastic Unloading

Step 8: Δu_y = -R

Step 8: Plastic Flow

Results

Reference: Stress results are displayed as the step is incremented by 1 starting with 0 and ending at 8.


             |   Mechanical APDL   |   RATIO  |         INPUT         |
  
 PLANE182
  RESULTS LISTED USING LOAD STEP 6
  SX                 5.1140           0.9961       vmr049-pl1a-182
  SY                10.6919           0.9951       vmr049-pl1a-182
  SZ                 9.1935           1.0081       vmr049-pl1a-182
 PLANE183
  RESULTS LISTED USING LOAD STEP 6
  SX                 5.1140           0.9961       vmr049-pl1a-183
  SY                10.6919           0.9951       vmr049-pl1a-183
  SZ                 9.1935           1.0081       vmr049-pl1a-183
  
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             |   Mechanical APDL   |   RATIO  |         INPUT         |
  
 PLANE182
  RESULTS REPORTED USING LOAD STEP 7
  SX                 1.5057           0.9701       vmr049-pl1b-182
  SY                 4.9217           0.9937       vmr049-pl1b-182
  SZ                 6.0725           1.0129       vmr049-pl1b-182
 PLANE183
  RESULTS REPORTED USING LOAD STEP 7
  SX                 1.5057           0.9701       vmr049-pl1b-183
  SY                 4.9217           0.9937       vmr049-pl1b-183
  SZ                 6.0725           1.0129       vmr049-pl1b-183
  
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vmr049-pl1a-182.dat (a)

vmr049-pl1a-183.dat (a)

vmr049-pl1b-182.dat (b)

vmr049-pl1b-183.dat (b)