Non-linearizable isotropic elasticity with arbitrary Poisson’s ratios

Extreme Mechanics Letters, vol. 86, pp. 102499

Abstract

In a previous paper (Itskov, 2026) we presented a hyperelastic isotropic material model whose stress–strain response is nonlinear even at infinitesimal deformations and cannot thus be linearized. As a result values of Poisson’s ratio greater than one half were obtained. In this contribution, we further propose an isotropic strain energy function which is always positive-definite and depending on material constants predicts arbitrary values of Poisson’s ratio (except of − 1 ) in agreement with the laws of thermodynamics. The model response appears plausible in various strain states and stable within a wide range of deformations. • Non-linearizable hyperelastic isotropic model based on a positive-definite strain energy function is proposed. • Non-Hookean elasticity theory without superposition principle is presented. • Poisson’s ratios beyond the classical range [ − 1 , 0 . 5 ] for isotropic materials are predicted in agreement with the thermodynamics laws.

Authors 1

1. Mikhail Itskov corresponding Aachen Department of Continuum Mechanics

   RWTH Aachen University · Keele University

   Affiliation as printed

   Department of Continuum Mechanics, RWTH Aachen University, Eilfschornsteinstr. 18, Aachen, 52062, Germany

   School of Computer Science & Mathematics, Keele University, Staffordshire, ST5 5BG, United Kingdom