Explicit dynamics: Bauschinger effect, mixed and kinematic hardening
Explicit dynamics (material model)PASS · <0.01%A bar is stretched into the plastic range and reversed. The magnitude of the stress on the reversal branch is checked against the yield-surface translation: the reverse yield stress is sigma_max - 2R, where R = sigma_y + (1 - beta) H eps_p is the radius after loading and beta is the kinematic fraction (0 isotropic, 1 purely kinematic). Three fractions are solved in one script.A bar is stretched into the plastic range and reversed. The magnitude of the stress on the reversal branch is checked against the yield-surface translation: the reverse yield stress is sigma_max - 2R, where R = sigma_y + (1 - beta) H eps_p is the radius after… show full text
- Tolerance:
- 5%
Problem statement
- Geometry
- Prismatic bar 100 × 10 × 10 mm, tetrahedral mesh (Netgen), the face x = 0 is a symmetry plane.
- Material
- Steel: E = 200 GPa, ν = 0.3, ρ = 7850 kg/m³; J2, yield 300 MPa, linear hardening with tangent modulus 20 GPa; kinematic fraction beta = 0, 0.5 and 1.
- Boundary conditions
- The face x = 100 mm: velocity ramp to +200 mm/s (0.5 ms), plateau to 5 ms, reversal through zero over 0.5 ms to -200 mm/s, plateau to 16 ms.
- Measured quantity
- Mean von Mises stress on the reversal branch at strains 0, -0.2 and -0.4 % (times found from the exact piecewise-linear velocity law); the reference is sigma_max - 2R on the elastic unloading line and Et on the reversed plastic branch.
WebCAE Terminal
Paste these commands into the Terminal panel inside WebCAE. They use the same text DSL as the application; run one command per line:
units mm
box dx=100 dy=10 dz=10
mesh tet size=25
explicit endTime=0.0155 dtScale=0.8 saveStride=20 bulkQ1=0 bulkQ2=0
bc explicit_symmetry surface number 1
bc explicit_motion surface number 2 direction 1 0 0 velocity="0:0;0.0005:200;0.005:200;0.0055:-200;0.016:-200"
material E=2e11 nu=0.3 density=7850 plasticity=j2 yield=300e6 hardening=linear et=20e9 kinematic=0
solve explicit
probe explicit_von_mises time=0.0102500000 id="s0_0"
probe explicit_von_mises time=0.0112500000 id="s0_1"
probe explicit_von_mises time=0.0122500000 id="s0_2"
material E=2e11 nu=0.3 density=7850 plasticity=j2 yield=300e6 hardening=linear et=20e9 kinematic=0.5
solve explicit
probe explicit_von_mises time=0.0102500000 id="s0.5_0"
probe explicit_von_mises time=0.0112500000 id="s0.5_1"
probe explicit_von_mises time=0.0122500000 id="s0.5_2"
material E=2e11 nu=0.3 density=7850 plasticity=j2 yield=300e6 hardening=linear et=20e9 kinematic=1
solve explicit
probe explicit_von_mises time=0.0102500000 id="s1_0"
probe explicit_von_mises time=0.0112500000 id="s1_1"
probe explicit_von_mises time=0.0122500000 id="s1_2"Results comparison
| Reference value | |σ| on reversal at ε = 0-0.2-0.4 %: β=1 270.00310.00350.00 MPa (σmax − 2R) |
| Our result | β=1 270.01310.00349.99 MPa |
| Deviation | <0.01% |
| Tolerance | 5% |
| Status | PASS · <0.01% |
| Element family | Solid element |
| Mesh details | tet 43 elements, 29 nodes (Netgen, native), three explicit (β = 0, 0.5, 1);: webcae_solve (native) |
Updated: 2026-10-21 · WebCAE solver