The Universal Program of Nonlinear Hyperelasticity

Abstract For a given class of materials, universal deformations are those that can be maintained in the absence body forces by applying only boundary tractions. Universal play crucial role nonlinear elasticity. To date, their classification has been accomplished for homogeneous isotropic solids following Ericksen’s seminal work, and anisotropic inhomogeneous our recent works. In this paper we study defined as materials whose energy function depends on position. We consider both compressible incompressible transversely isotropic, orthotropic, monoclinic solids. show universality constraints —the dictated equilibrium equations arbitrariness function—for include solids, material preferred directions uniform. each three classes find corresponding inhomogeneities —those consistent with constraints. six known families deformations. This work provides systematic approach to analytically functionally-graded fiber-reinforced elastic