Hyperelasticity — Arruda Boyce Uniaxial

HyperelasticPASS · 0.01%

Finite-strain hyperelastic response and objectivity verification. Checks: five-term chain-locking series.

Tolerance:: 5%

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Problem statement

Geometry: Incompressible Arruda-Boyce five-term series with mu=1 MPa, lambda_m=3, uniaxial lambda=2.
Material: Constitutive or analytical definition: Differentiate the five-term Arruda-Boyce W(I1) given in the source and use P=2(lambda-lambda^-2)dW/dI1.
Boundary conditions: Required solver capability: arruda_boyce_hyperelasticity. Use the loading/path control stated in the setup and preserve the complete response history.
Measured quantity: Nominal stress=1.98619498928 MPa using the published five coefficients.

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 m
material hyperelastic=arruda_boyce mu=1000000 lambda_m=3 kappa=10000000000
primitive box dx=1 dy=1 dz=1
mesh hex size=1
fix surface number 1 component=x
fix surface number 3 component=y
fix surface number 5 component=z
displacement surface number 2 value=1.0 component=x
solve static nlgeom=on solidMaterial=arruda-boyce steps=5

Results comparison

Reference value	P = 1.986195 MPa
Our result	P = 1.985964 MPa
Deviation	0.01%
Tolerance	5%
Status	PASS · 0.01%
Element family	Solid element
Mesh details	1 HEX8/HEX20 куб 1×1×1 м, 5-членный 8-цепочечный потенциал Arruda-Boyce mu=1 MPa, lambda_m=3, kappa=10000 MPa, одноосное растяжение lambda=2

Updated: 2026-10-28 · version not recorded