Plasticity — J2 Hydrostatic Invariance

PlasticityPASS · <0.01%

Plastic constitutive integration, history variables, and structural limit-load verification. Checks: deviatoric split and pressure-independent yielding.

Tolerance:: 5%

Open & Solve in BrowserSign in or register to launch this verified model in WebCAE

Open & Solve in Browser

Problem statement

Geometry: Apply equal normal stresses -1000 MPa in x/y/z with no deviatoric component.
Material: Constitutive or analytical definition: J2 depends only on deviatoric stress; hydrostatic stress has s=0.
Boundary conditions: Required solver capability: small_strain_j2. Use the loading/path control stated in the setup and preserve the complete response history.
Measured quantity: von Mises equivalent stress=0, plastic multiplier=0, equivalent plastic strain=0 for every increment.

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=10 dy=10 dz=10
mesh tet size=3
fix surface number 1 component=x
fix surface number 3 component=y
fix surface number 5 component=z
load surface number 2 pressure=1000000000
load surface number 4 pressure=1000000000
load surface number 6 pressure=1000000000
nlgeom material
solve
probe vonMises id="vm"
probe plastic_strain_max id="epmax"
probe stress_xx id="sxx"
probe stress_yy id="syy"
probe stress_zz id="szz"

Results comparison

Reference value	vm = 0εp = 0 на каждом шагеσ = −1000 МПа по x, y, z
Our result	vm/1000МПа = 9.31e-16max εp по 6 шагам = 0ε_vol = -0.00571428593
Deviation	<0.01%
Tolerance	5%
Status	PASS · <0.01%
Mesh details	куб 10 мм, тет4 (≈100 тетр.); давление 1000 МПа на трёх гранях, роликовые опоры на трёх

Updated: 2026-10-21 · WebCAE solver