2019/03/27 by Tomáš Roubı́ček, Roubicek, Tomas, Christos G. Panagiotopoulos +3 · 1 citation
Computer Science · Engineering · #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1903.11654
openalex publication_date 2019/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The 2-step staggered (also called leap-frog) time discretisation of linear 2nd-order Hamiltonian systems (typically linear elastodynamics in a stress-velocity form) is extended for a 3-step staggered discretisation applicable for systems involving some internal variables subjected to a dissipative evolution. After spatial discretisation, a-priori estimates and convergence is proved under the usual CFL-condition. Applications to specific problems in continuum mechanics of solids at small stains are considered, in particular linearized plasticity, diffusion in poroelastic media, damage, or adhesive contact. Numerical implementation and some computational 2-dimensional simulation of waves emitted by a rupture (delamination) of an adhesive contact illustrate the abstract theory and efficiency of the explicit method.