Elastic solids

Abstract

In this section we derive, by consistent linearisation of nonlinear equations considered in Sect. 4, linearised stress-strain relations for general elastic and hyper-elastic solids within the scope of the finite (large) initial deformations theory and two variants of the small initial deformations theory. In so doing, we shall follow the procedure (2.1)–(2.5). Particular results will be obtained both for an arbitrary and the uniform (2.69) initial states separately for compressible and incompressible isotropic and anisotropic solids. Linearised stress-strain relations, which are the subject of this section, together with the appropriate relationships describing the states of stress and strain (Sect. 7), set up the closed (full) problem statement of the linearised elasticity theory for prestrained solids in the context of the finite initial deformations theory and two variants of the small initial deformations theory.