Explicit dynamics: adiabatic heating with Johnson-Cook thermal softening
Explicit dynamics (thermo-plastic coupling)PASS · 0.04%Adiabatic temperature rise dT = eta * integral(sigma d(eps_p)) / (rho * cp) of copper deformed at 100 1/s, where the flow stress falls with temperature through the Johnson-Cook thermal term. The reference is an independent fourth-order Runge-Kutta integration of the same ODE; the specific heat is deliberately low (20 J/(kg K)) so that the softening is visible, and the card checks that the reference actually distinguishes the coupling (without softening the rise would be higher).Adiabatic temperature rise dT = eta * integral(sigma d(eps_p)) / (rho * cp) of copper deformed at 100 1/s, where the flow stress falls with temperature through the Johnson-Cook thermal term. The reference is an independent fourth-order Runge-Kutta integration… 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
- 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, m = 1.09, Tmelt = 1356 K, reference rate 1 1/s, specific heat 20 J/(kg K), Taylor-Quinney 0.9, initial temperature 293.15 K.
- Boundary conditions
- The face x = 10 mm moves with a velocity ramp (0.2 ms) to 1000 mm/s (strain rate 100 1/s), constant afterwards. Adiabatic: no heat leaves a material point.
- Measured quantity
- Mean temperature rise and mean plastic strain at the end; the rise against the RK4 solution of the ODE at that plastic strain.
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=1 cp=20 taylor=0.9
box dx=10 dy=1 dz=1
mesh tet size=1
explicit endTime=0.00155 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;0.0002:1000;0.00155:1000"
solve explicit
probe explicit_temperature id="T"
probe explicit_temperature time=0 id="T0"
probe explicit_plastic_strain id="ep"
probe explicit_von_mises id="vm"Results comparison
| Reference value | ΔT = 159.3 K (RK4 of η∫σdεp/(ρ·cp) with thermal softening) at εp = 0.143 |
| Our result | ΔT = 159.2 K |
| Deviation | 0.04% |
| Tolerance | 5% |
| Status | PASS · 0.04% |
| Element family | Solid element |
| Mesh details | tet 60 elements, 44 nodes (Netgen, native), adiabatic heating;: webcae_solve (native) |
Updated: 2026-10-21 · WebCAE solver