Journal of Advances in Applied Mathematics

JAAM
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Volume 5, Number 2, April 2020

Modeling and Implementing Compressible Isotropic Finite Deformation without the Isochoric–Volumetric Split
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57-70

, Pub. Date:January 17, 2020
DOI:

10.22606/jaam.2020.52002
**Author(s)**
Fuzhang Zhao

**Affiliation(s)**
APD Optima Study, Lake Forest, CA 92630, USA

**Abstract**
Constitutive models and finite element implementations of compressible finite deformation
are straightforwardly formulated by the general isotropic continuum stored energy (CSE)
functional without the isochoric–volumetric split. Coupled stress and elasticity tensors in reference
and current configurations are derived. Modeling and predicting capabilities of the general CSE
functional are exhibited through multiaxial experimental tests of compressible NR and SBR rubbers.
Characterization of kinematic relation, rather than pressure–volume relation, is emphasized in
experimental tests of compressibility. The isochoric–volumetric split does not hold based on either
theoretical analyses or experimental validations.

**Keywords**
Compressible finite deformation, finite element implementation, isochoric–volumetric
split, Poisson function, work-conjugacy.

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