Plasticity — J2 Unload Residual

PlasticityPASS · <0.01%

Plastic constitutive integration, history variables, and structural limit-load verification. Checks: elastic unloading and history variables.

Tolerance:: 5%

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Problem statement

Geometry: Load the previous uniaxial model to eps=0.01, then unload in strain control through eps=0.008 and to zero stress.
Material: Constitutive or analytical definition: Unloading slope is E until reverse yield; eps_p=eps_max-sigma_max/E.
Boundary conditions: Required solver capability: small_strain_j2_isotropic_hardening. Use the loading/path control stated in the setup and preserve the complete response history.
Measured quantity: sigma(eps=0.008)=-161.19047619 MPa; zero-stress residual strain=0.00876757369615.

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=210e9 nu=0.3 plasticity=j2 yield=250e6 hardening=linear et=1e9
primitive box dx=100 dy=10 dz=10
mesh tet size=5
fix surface number 1 component=x
fix surface number 3 component=y
fix surface number 5 component=z
load surface number 2 pressure=-258809523.81
nlgeom material loadpath="1,-0.6228150873935183,0"
solve
probe displacement_x at x=100 tol=0.01 id="ux"
probe stress_xx id="sxx"
probe plastic_strain_max id="epmax"
probe plastic_fraction id="pfrac"

Results comparison

Reference value	σ(ε=0.008) = −161.19047619 МПаостаточная ε при σ=0: 0.00876757369615
Our result	σ(ε=0.008) = -161.19048 МПаостаточная ε = 0.00876757383
Deviation	<0.01%
Tolerance	5%
Status	PASS · <0.01%
Mesh details	брус 100×10×10 мм, тет4 (≈1500 тетр.); путь λ: 1 → −0.6228 → 0; управление по НАПРЯЖЕНИЮ (нелинейное ядро ведёт нагрузку, не перемещение): на одноосном брусе σ(ε) однозначна, поэтому сверка ε при заданном σ эквивалентна σ при заданной ε

Updated: 2026-10-21 · WebCAE solver