Abstract
The standard nonlinear thermoelastic model most often used for modeling wave mechanics in single crystals and polycrystals, either anisotropic or isotropic, is described. The theoretical formulation is based on a Lagrangian finite strain tensor. General kinematics and thermodynamics are developed, followed by application to planar shock loading along a pure mode direction. An explicit analytical solution is reported for planar shock compression of a solid characterized by an internal energy potential of order four in strain but truncated at first order in entropy. Particular forms of material coefficients are presented for cubic crystals and isotropic materials.
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Clayton, J.D. (2019). Lagrangian Formulation. In: Nonlinear Elastic and Inelastic Models for Shock Compression of Crystalline Solids. Shock Wave and High Pressure Phenomena. Springer, Cham. https://doi.org/10.1007/978-3-030-15330-4_3
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DOI: https://doi.org/10.1007/978-3-030-15330-4_3
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