Thermoelasticity

Abstract

AbstractDeformation of a crystalline solid is labeled, in this book, as purely elastic in the absence of defect motion and temperature changes. In an elastic material of grade one, the mechanical stress supported by a material particle located at a particular point in space and the deformation gradient or strain in the material at that point are related by a constitutive law, e.g., a local tensor-valued version of Hooke’s law relating force and stretch. A hyperelastic material of grade one can be defined as a material possessing a strain energy density function depending on the first-order deformation gradient, or on a symmetric deformation tensor or strain tensor constructed from this deformation gradient (Truesdell and Noll 1965). In such a material, the partial derivative of strain energy density with respect to a deformation gradient component produces a corresponding stress component, more precisely a component of the first Piola-Kirchhoff stress tensor. Thermoelasticity by definition addresses recoverable mechanical deformation (i.e., elastic deformation from body and surface forces) and thermal effects (e.g., temperature rates, temperature gradients, heat sources, and heat flux) as well as their couplings (e.g., thermal expansion or contraction).KeywordsDeformation GradientStrain Energy DensityHyperelastic MaterialAngular Momentum BalanceUnit Reference VolumeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.