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PreprintCC BY 4.0arXiv

A new perspective in linear Cauchy Elasticity: variational minimum principles for statics, dynamics, and heterogeneous materials

  • Amit Acharya
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Abstract

A variational minimum principle for linear elastodynamics of a possibly heterogeneous material without a stored energy function is developed. It involves a change of variables to dual fields, and results in a degenerate elliptic Euler-Lagrange system, even when the primal elastodynamics is hyperbolic. Uniqueness assertions for the dual dynamic and static problems and implications of the degenerate ellipticity are sketched. Some implications pertaining to heterogeneous materials and ones with indefinite elastic moduli are discussed.

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Cite

BibTeXRIS
BibTeX
@misc{acharya2026perspective,
  title = {{A new perspective in linear Cauchy Elasticity: variational minimum principles for statics, dynamics, and heterogeneous materials}},
  author = {Amit Acharya},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2606.24782},
  eprint = {2606.24782},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.24782},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A new perspective in linear Cauchy Elasticity: variational minimum principles for statics, dynamics, and heterogeneous materials
AU  - Amit Acharya
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2606.24782
UR  - https://arxiv.org/abs/2606.24782
AB  - A variational minimum principle for linear elastodynamics of a possibly heterogeneous material without a stored energy function is developed. It involves a change of variables to dual fields, and results in a degenerate elliptic Euler-Lagrange system, even when the primal elastodynamics is hyperbolic. Uniqueness assertions for the dual dynamic and static problems and implications of the degenerate ellipticity are sketched. Some implications pertaining to heterogeneous materials and ones with indefinite elastic moduli are discussed.
ER  -