A first order hyperbolic framework for large strain computational solid dynamics. Part III: Thermo-elasticity

In Parts I (Bonet et al., 2015) and II (Gil 2016) of this series, a novel computational framework was presented for the numerical analysis large strain fast solid dynamics in compressible nearly/truly incompressible isothermal hyperelasticity. The methodology exploited use system first order Total Lagrangian conservation laws formulated terms linear momentum triplet deformation measures comprised gradient tensor, its co-factor Jacobian. Moreover, consideration polyconvex constitutive to guarantee hyperbolicity show existence convex entropy function (sum kinetic energy per unit undeformed volume) necessary symmetrisation. new paper, is extended more general case thermo-elasticity by incorporating law thermodynamics as an additional law, written either (suitable smooth solutions) or total density discontinuous system. paper further enhanced with following key novelties. First, sufficient conditions are put forward internal measured at reference temperature ensure ab-initio polyconvexity set entropy. Second, study eigenvalue structure performed proof purpose obtaining correct time step bounds explicit integrators. Application two well-established thermo-elastic models presented: Mie–Grüneisen modified entropic elasticity. Third, enables definition generalised function, namely ballistic energy, associated fluxes, allowing symmetrisation entropy-conjugate fields. Fourth, line previous papers stabilised Petrov–Galerkin solution when considering unknown Finally, series examples assess applicability robustness proposed formulation.