The context of this work is the development first order total variation diminishing (TVD) implicit-explicit (IMEX) Runge-Kutta (RK) schemes as a basis Multidimensional Optimal Order detection (MOOD) approach to approximate solution hyperbolic multi-scale equations. A key feature our newly proposed TVD that resulting CFL condition does not depend on fast waves considered model, long they are int...

The phase field method integrates the Griffith theory and damage mechanics approach to predict crack initiation, propagation, and branching within one framework. No crack tracking topology is needed, and complex crack shapes can be captures without user intervention. In this paper, a detailed description of how the phase field method is implemented with explicit dynamics into LS-DYNA is provide...