To allow the existence of phase transformations, shock waves and other phenomena, the response of a body must be nonlinear. As this book is designed to treat bodies with a response of general symmetry, the deformation gradient must be used as the basic measure of deformation. The passage to specific symmetries — isotropic solids, fluids, or crystals — is made only to reach conclusions that do not hold generally, or to give the general assertions a more concrete form in the variables of the specific situation. The relationship between the response functions and the material behavior is established by isolating leading features of the response functions rather than by examining concrete models. Apart from the natural restrictions from the entropy inequality, frame indifference, and symmetry, the main unifying concepts are the convexity/nonconvexity properties of the thermodynamic potentials.
KeywordsShock Wave Deformation Gradient Riemann Problem Singular Surface Eshelby Tensor
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