Properties of operator constitutive relations in mechanics of deformable solid

Abstract

The constitutive relations between stresses and strains in the mechanics of a deformable solid, including their operator connection, are considered. Some important and frequently occurring properties of tangent modulus and tangent pliability as rank four tensors are described. Depending on this, a possible classification of continuous media is proposed. Scleronomous and rheonomic media, homogeneous and inhomogeneous media (in particular, composites), media with memory, spatially nonlocal media, materials with hard or soft characteristics are distinguished. For non-linearly elastic isotropic media, the apparatus of tensor nonlinear isotropic functions of one argument is developed. Particular attention is paid to the three-term representation of power tensor series in three-dimensional space, reversibility of tensor functions, Taylor tensor series, tensor linearity (quasilinearity) and nonlinearity.