An entropy-stable Smooth Particle Hydrodynamics algorithm for large strain thermo-elasticity

This paper presents a novel Smooth Particle Hydrodynamics computational framework for the simulation of large strain fast solid dynamics in thermo-elasticity. The formulation is based on Total Lagrangian description system first order conservation laws written terms linear momentum, triplet deformation measures (also known as minors gradient tensor) and total energy system, extending thus previous work carried out by some authors context isothermal elasticity elasto-plasticity [1-3]. To ensure stability (i.e. hyperbolicity) from continuum point view, internal density expressed polyconvex combination entropy density. Moreover, to guarantee spatial discretisation consistently derived Riemann-based numerical dissipation carefully introduced where local production demonstrated via technique time rate so-called ballistic free system. For completeness, an alternative equally competitive (in case smooth solutions), density, also implemented compared. A series examples presented assess applicability robustness proposed formulations, scheme benchmarked against in-house Finite Volume Vertex Centred implementation.