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Homogeneous Cauchy stress induced by non‐homogeneous deformations
Author(s) -
Schweickert Eva,
Mihai L. Angela,
Neff Patrizio
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800185
Subject(s) - homogeneous , isotropy , cauchy distribution , elasticity (physics) , mathematics , linear elasticity , stress (linguistics) , nonlinear system , mathematical analysis , regular polygon , physics , geometry , optics , combinatorics , thermodynamics , linguistics , philosophy , quantum mechanics , finite element method
We discuss whether homogeneous Cauchy stress implies homogeneous strain in isotropic nonlinear elasticity. While for linear elasticity the positive answer is clear, we exhibit an example with inhomogeneous continuous deformation but constant Cauchy stress. The example is derived from a non rank‐one convex elastic energy.