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Journal of Advances in Applied Mathematics
JAAM > Volume 5, Number 2, April 2020

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

Download PDF  (11946.8 KB)PP. 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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