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Equivalence Groups of Inhomogeneous Hyperelasticity

  • Saadet S. Özer
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Abstract

Equivalence groups associated with the field equations of arbitrary motions of inhomogeneous hyperelastic solids are investigated. The explicit forms of the infinitesimal generators, namely the components of the isovector field associated with the equivalence groups are derived. Additional constraints on the isovector components are established to ensure that the transformed equations are supported by a strain energy function. Possible mappings between the equations of materials with different properties are examined. Not only the transformations between homogeneous and inhomogeneous hyperelasticity equations, but also the transformations between the equations and strain energy functions of isotropic and anisotropic materials are investigated. The results are illustrated with several examples.

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Cite

BibTeXRIS
BibTeX
@misc{ozer2026equivalence,
  title = {{Equivalence Groups of Inhomogeneous Hyperelasticity}},
  author = {Saadet S. Özer},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28701},
  eprint = {2609.28701},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28701},
}
RIS
TY  - UNPB
TI  - Equivalence Groups of Inhomogeneous Hyperelasticity
AU  - Saadet S. Özer
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28701
UR  - https://arxiv.org/abs/2609.28701
AB  - Equivalence groups associated with the field equations of arbitrary motions of inhomogeneous hyperelastic solids are investigated. The explicit forms of the infinitesimal generators, namely the components of the isovector field associated with the equivalence groups are derived. Additional constraints on the isovector components are established to ensure that the transformed equations are supported by a strain energy function. Possible mappings between the equations of materials with different properties are examined. Not only the transformations between homogeneous and inhomogeneous hyperelasticity equations, but also the transformations between the equations and strain energy functions of isotropic and anisotropic materials are investigated. The results are illustrated with several examples.
ER  -