Explicit dynamics: Johnson-Cook strain-rate sensitivity (copper)
Explicit dynamics (material model)PASS · 0.04%Stress at 2 % plastic strain of OFHC copper at two strain rates, 10 and 1000 1/s, with reference rate 10 1/s. The ratio must equal the Johnson-Cook rate factor 1 + C ln(1000/10). The explicit solver uses the instantaneous plastic strain rate of the step (an implicit-Euler viscoplastic law); a step-count study shows the result does not depend on the time step.Stress at 2 % plastic strain of OFHC copper at two strain rates, 10 and 1000 1/s, with reference rate 10 1/s. The ratio must equal the Johnson-Cook rate factor 1 + C ln(1000/10). The explicit solver uses the instantaneous plastic strain rate of the step (an im… show full text
- Tolerance:
- 5%
Problem statement
- Geometry
- Bar 10 × 1 × 1 mm, tetrahedral mesh (Netgen), the face x = 0 is a symmetry plane.
- Material
- OFHC copper: E = 124 GPa, ν = 0.34, ρ = 8960 kg/m³; Johnson-Cook A = 90 MPa, B = 292 MPa, n = 0.31, C = 0.025, reference rate 10 1/s, isothermal (no heating).
- Boundary conditions
- The face x = 10 mm moves with a prescribed velocity: a ramp lasting about 12 % of the loading time (well above the 2 µs wave transit time), then constant, for rates 10 and 1000 1/s.
- Measured quantity
- Stress at εp = 2 % (interpolated over five probe times around it) for each rate; the ratio σ(1000)/σ(10) and σ(10) against A + B·εp^n.
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=124e9 nu=0.34 density=8960 plasticity=jc A=90e6 B=292e6 n=0.31 C=0.025 m=1.09 tmelt=1356 epsdot0=10
box dx=10 dy=1 dz=1
mesh tet size=1
bc explicit_symmetry surface number 1
explicit endTime=0.0025449000 dtScale=0.8 saveStride=10 bulkQ1=0 bulkQ2=0
bc explicit_motion surface number 2 direction 1 0 0 velocity="0:0;0.000270000:100;0.0025449000:100"
solve explicit
probe explicit_von_mises time=0.00225500000 id="s10_0"
probe explicit_plastic_strain time=0.00225500000 id="p10_0"
probe explicit_von_mises time=0.00231500000 id="s10_1"
probe explicit_plastic_strain time=0.00231500000 id="p10_1"
probe explicit_von_mises time=0.00237500000 id="s10_2"
probe explicit_plastic_strain time=0.00237500000 id="p10_2"
probe explicit_von_mises time=0.00243500000 id="s10_3"
probe explicit_plastic_strain time=0.00243500000 id="p10_3"
probe explicit_von_mises time=0.00249500000 id="s10_4"
probe explicit_plastic_strain time=0.00249500000 id="p10_4"
explicit endTime=0.000025449000 dtScale=0.8 saveStride=10 bulkQ1=0 bulkQ2=0
bc explicit_motion surface number 2 direction 1 0 0 velocity="0:0;0.00000270000:10000;0.000025449000:10000"
solve explicit
probe explicit_von_mises time=0.0000225500000 id="s1000_0"
probe explicit_plastic_strain time=0.0000225500000 id="p1000_0"
probe explicit_von_mises time=0.0000231500000 id="s1000_1"
probe explicit_plastic_strain time=0.0000231500000 id="p1000_1"
probe explicit_von_mises time=0.0000237500000 id="s1000_2"
probe explicit_plastic_strain time=0.0000237500000 id="p1000_2"
probe explicit_von_mises time=0.0000243500000 id="s1000_3"
probe explicit_plastic_strain time=0.0000243500000 id="p1000_3"
probe explicit_von_mises time=0.0000249500000 id="s1000_4"
probe explicit_plastic_strain time=0.0000249500000 id="p1000_4"Results comparison
| Reference value | σ(10 1/s) = 176.8 MPaσ(1000)/σ(10) = 1.11513 |
| Our result | σ(10 1/s) = 176.8 MPaσ(1000)/σ(10) = 1.11466 |
| Deviation | 0.04% |
| Tolerance | 5% |
| Status | PASS · 0.04% |
| Element family | Solid element |
| Mesh details | tet 60 elements, 44 nodes (Netgen, native), two explicit;: webcae_solve (native) |
Updated: 2026-10-21 · WebCAE solver