Hyperelasticity — Objectivity

HyperelasticPASS · 0%

Finite-strain hyperelastic response and objectivity verification. Checks: frame indifference and energy invariance.

Tolerance:: 5%

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Problem statement

Geometry: Apply a finite stretch, then prepend/append proper rotations; compare rotated stresses and stored energy.
Material: Constitutive or analytical definition: W(QF)=W(F) for objective isotropic hyperelasticity.
Boundary conditions: Required solver capability: finite_strain_hyperelasticity. Use the loading/path control stated in the setup and preserve the complete response history.
Measured quantity: Strain energy and invariants are unchanged; Cauchy stress transforms as R sigma R^T; pure rotation adds zero energy.

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 hyperelastic=neo_hookean E=10000000 nu=0.3
primitive box dx=10 dy=10 dz=10
mesh hex size=5
transform rotate angle=45 axis="0.9,-1.3,0.5"
solve static nlgeom=on solidMaterial=neo-hookean

Results comparison

Reference value	max\|f\|/(E*V^(2/3)) < 1e-9
Our result	max\|f\|/(E*V^(2/3)) = 3.60e-16
Deviation	0%
Tolerance	5%
Status	PASS · 0%
Element family	Solid element
Mesh details	конечный жесткий поворот SO(3) + сдвиг, твердотельные элементы hex8/hex20/tet4/tet10

Updated: 2026-10-19 · WebCAE solver