Plasticity — J2 Rotation Objectivity

PlasticityPASS · 0.57%

Plastic constitutive integration, history variables, and structural limit-load verification. Checks: stress and history rotation covariance.

Tolerance:: 5%

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Problem statement

Geometry: Run the same deviatoric strain path in the base frame and in frames rotated by 17, 53, and 121 degrees.
Material: Constitutive or analytical definition: sigma'=R sigma R^T; scalar J2 invariants are unchanged.
Boundary conditions: Required solver capability: objective_stress_update_if_finite_rotation. Use the loading/path control stated in the setup and preserve the complete response history.
Measured quantity: Equivalent stress and equivalent plastic strain are invariant; stress tensor in the rotated run equals R sigma R^T.

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=200 dy=10 dz=10
rotate body1 angle=53 axis=1,2,2 at=0,0,0
let f = list faces of body2
let cx = (f[0].centroid[0] + f[1].centroid[0]) / 2
let cy = (f[0].centroid[1] + f[1].centroid[1]) / 2
let cz = (f[0].centroid[2] + f[1].centroid[2]) / 2
mesh tet size=4
fix surface number 1
load surface number 2 pressure=-258809523.81
nlgeom on pressure=dead
solve
probe stress_xx at x=cx y=cy z=cz tol=4 id="sxx"
probe stress_yy at x=cx y=cy z=cz tol=4 id="syy"
probe stress_zz at x=cx y=cy z=cz tol=4 id="szz"
probe stress_xy at x=cx y=cy z=cz tol=4 id="sxy"
probe stress_yz at x=cx y=cy z=cz tol=4 id="syz"
probe stress_zx at x=cx y=cy z=cz tol=4 id="szx"
probe vonMises at x=cx y=cy z=cz tol=4 id="vm"
probe plastic_strain at x=cx y=cy z=cz tol=4 id="ep"
minmax displacement_magnitude

Results comparison

Reference value	vm и εp инвариантныσ' = R σ Rᵀ при поворотах 17°, 53°, 121° (ось (1,2,2)/3)
Our result	max\|σ'−RσRᵀ\|/max\|σ\| = 0.00388 %vm и εp — см. сверки
Deviation	0.57%
Tolerance	5%
Status	PASS · 0.57%
Mesh details	брус 200×10×10 мм зажат с одного торца (все степени свободы — инвариантно к повороту), давление на другом; тет4 1265/2744/1849 тетр. для 17°/53°/121°; TL, мёртвое давление; тензор осреднён по кубу ±4 мм вокруг середины оси

Updated: 2026-10-21 · WebCAE solver