A Generalized Ogden-Type Elastically Isotropic Hyperelastic Model Including Elastic-Viscoplastic Response

The objective of this paper is to generalize an Ogden-type model for elastically isotropic response to include elastic-viscoplastic response. The proposed model uses a strain energy function that depends on the total dilatation and the maximum and minimum elastic distortional stretches. A novel feat...

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Bibliographic Details
Published in:Journal of elasticity 2023-04, Vol.153 (3), p.359-372
Main Authors: Rubin, M. B., Heiduschke, K.
Format: Article
Language:English
Subjects:
Biomechanics
Classical and Continuum Physics
Classical Mechanics
Elastic deformation
Engineering
Materials Science
Mathematical analysis
Mathematical Applications in the Physical Sciences
Strain energy
Tensors
Theoretical and Applied Mechanics
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Summary:The objective of this paper is to generalize an Ogden-type model for elastically isotropic response to include elastic-viscoplastic response. The proposed model uses a strain energy function that depends on the total dilatation and the maximum and minimum elastic distortional stretches. A novel feature of the model is that these elastic distortional stretches are expressed in terms of two independent invariants of an elastic distortional deformation tensor that is determined by an evolution equation. The Cauchy stress is determined by derivatives of the strain energy function, the dilatation and the elastic distortional deformation tensor without the need for determining its principal directions. Examples demonstrate the response of the model for hyperelastic response but the proposed formulation can also model a smooth elastic-plastic transition with rate-independent or rate-dependent response with hardening.
ISSN:0374-3535
1573-2681
DOI:10.1007/s10659-023-09995-8