Explicit dynamics: multilinear hardening curve

Explicit dynamics (material model)PASS · <0.01%

A three-segment tabulated hardening curve (plastic strain : stress) is followed by the explicit solver. The stress at three strains is compared with the curve evaluated at the plastic strain that satisfies eps = sigma/E + eps_p (found by bisection in the refer… show full text

Tolerance:: 5%

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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 with the curve (0 ; 300), (0.004 ; 400), (0.012 ; 470) MPa, constant beyond the last point.
Boundary conditions: The face x = 100 mm: velocity ramp to 200 mm/s over 0.5 ms, then constant (strain rate 2 1/s).
Measured quantity: Mean von Mises stress at strains of 0.4, 0.8 and 1.4 %.

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 curve="0:300000000,0.004:400000000,0.012:470000000"
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=0.0022500000 id="s0"
probe explicit_von_mises time=0.0042500000 id="s1"
probe explicit_von_mises time=0.0072500000 id="s2"

Results comparison

Reference value	355.56416.77467.07 MPa at ε = 0.40.81.4 %
Our result	355.55416.77467.07 MPa
Deviation	<0.01%
Tolerance	5%
Status	PASS · <0.01%
Element family	Solid element
Mesh details	tet 43 elements, 29 nodes (Netgen, native);: webcae_solve (native)

Updated: 2026-10-21 · WebCAE solver