Explicit dynamics: bar tension, J2 with linear hardening
Explicit dynamics (material model)PASS · <0.01%A bar is stretched at a nominal strain rate of 2 1/s by a prescribed face velocity (smooth 0.5 ms start, much longer than the wave transit time). The stress-strain curve and the plastic strain computed by the explicit solver on the shared material-point kernel are checked against the closed-form bilinear law. The previous built-in explicit law depended on the number of time steps; this one does not.A bar is stretched at a nominal strain rate of 2 1/s by a prescribed face velocity (smooth 0.5 ms start, much longer than the wave transit time). The stress-strain curve and the plastic strain computed by the explicit solver on the shared material-point kernel… 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, the lateral faces are free.
- Material
- Steel: E = 200 GPa, ν = 0.3, ρ = 7850 kg/m³; J2 plasticity, yield 300 MPa, linear isotropic hardening with tangent modulus 20 GPa.
- Boundary conditions
- The face x = 100 mm moves along x with a prescribed velocity law: linear ramp to 200 mm/s over 0.5 ms, then constant (strain rate 2 1/s). No bulk viscosity.
- Measured quantity
- Mean von Mises stress (= |σ| in the uniaxial state) at strains of 0.25, 0.5, 1 and 2 %, the plastic strain at 1 and 2 %; the actual strain is taken from the prescribed face displacement.
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
material E=2e11 nu=0.3 density=7850 plasticity=j2 yield=300e6 hardening=linear et=20e9
box dx=100 dy=10 dz=10
mesh tet size=25
explicit endTime=0.0105 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;0.0105:200"
solve explicit
probe explicit_von_mises time=0.0015000000 id="s0"
probe explicit_plastic_strain time=0.0015000000 id="p0"
probe explicit_displacement_x x=100 time=0.0015000000 id="u0"
probe explicit_von_mises time=0.0027500000 id="s1"
probe explicit_plastic_strain time=0.0027500000 id="p1"
probe explicit_displacement_x x=100 time=0.0027500000 id="u1"
probe explicit_von_mises time=0.0052500000 id="s2"
probe explicit_plastic_strain time=0.0052500000 id="p2"
probe explicit_displacement_x x=100 time=0.0052500000 id="u2"
probe explicit_von_mises time=0.010250000 id="s3"
probe explicit_plastic_strain time=0.010250000 id="p3"
probe explicit_displacement_x x=100 time=0.010250000 id="u3"
probe explicit_energy kind=internal id="ie"
probe explicit_steps id="steps"Results comparison
| Reference value | σ(2 %) = 670 MPa, εp(2 %) = 0.01665 |
| Our result | σ(2 %) = 670 MPa, εp(2 %) = 0.01665 |
| Deviation | <0.01% |
| Tolerance | 5% |
| Status | PASS · <0.01% |
| Element family | Solid element |
| Mesh details | tet 43 elements, 29 nodes (Netgen, native), 56674 explicit steps;: webcae_solve (native) |
Updated: 2026-10-21 · WebCAE solver