Javier Bonet's KTH Solid Mechanics KEYNOTE Seminar "First order conservation law formulations in solid dynamics: applications to dynamic crack propagation, contact mechanics and stable SPH discretizations"

Javier Bonet June 26 2025.pdf (pdf 156 kB)

Abstract. The presentation will describe the latest advances in the novel conservation based formulation of solid and structural dynamics developed by the author. The formulation differs from standard displacement based approaches in using linear momentum and strain like variables as problem unknowns. The resulting mixed equations are written in the form of a system of first order conservation laws in a manner similar to Computational Fluid Dynamics (CFD). This formulation has been exploited by the authors to improve the discretization techniques of solid dynamics resolving issues such as incompressible locking and poor stress convergence. A variety of common CFD discretization techniques have been exploited for this purpose, from upwind finite volume to Petrov-Galerkin finite elements. Recent work has applied these concepts to problems such as crack propagation and contact mechanics as well to the stabilisation of Smooth Particle Hydrodyamics (SPH) models using the concept of ballistic energy as a convex entropy like variable. Extensions to Arbitrary Eulerian Lagrangian mechanics within the framework of first order conservative formulations will also be presented. The lecture will provide examples based on elasticity and thermoelasticity using the Mie-Gruneisen equation of state. A number of benchmark test will be provided that demonstrate that all variables conserved, and their conjugates (that is stresses and temperature) converge at the same rate as the velocities and displacements. This is in contrast to standard displacement based formulations where strains and stresses converge at one order below the rate of displacements. The application of the technology to dynamic crack propagation in linear elasticity will show that analytical models predicting intersonic and supersonic crack propagation with Mach like shock waves can be developed, which closely resemble experimental results observed and reported in the literature.