A New Updated Reference Lagrangian Smooth Particle Hydrodynamics algorithm for isothermal elasticity and elasto-plasticity

This paper presents a new Updated Reference Lagrangian Smooth Particle Hydrodynamics (SPH) algorithm for the analysis of large deformation isothermal elasticity and elasto-plasticity. Taking as point departure Total setting considering referential configuration an intermediate process, equation conservation linear momentum three geometric laws (for gradient, its cofactor determinant) are re-written leading to very generic system first order laws. The key feature formulation is suitable multiplicative decomposition variables, simple final set equations with striking similarities conventional albeit in terms alternative Referential variables which evolved time. advantage this formalism, second entropy-stable SPH upwinding stabilisation method will be introduced. With respect previous publications by group, three-stage Runge–Kutta time integration implemented increase CFL stability restriction. Finally, demonstrate robustness applicability methodology, wide spectrum challenging problems presented compared, including some benchmark three-dimensional elasto-plasticity problems. To facilitate ease implementation, explores use series novel expressions evaluation kernels gradients provide user freedom choose amongst various options, all equally convincingly robust results. • A algorithm. Conservation incremental configuration. Explicit along Rankine Hugoniot jump conditions. Three-stage preservation angular momentum. Exploration