We present an energy-preserving mechanic formulation for dynamic quasi-brittle fracture in Eulerian–Lagrangian formulation, where a second-order phase-field equation controls the damage evolution. The numerical adapts space and time to bound errors, solving mesh-bias issues these models typically suffer. time-step adaptivity estimates temporal truncation error of partial differential that gover...

the objective of this research is to develop an accurate numerical method to be used in showing the deformation of a liquid fuel droplet in a convective field. to simultaneously solve the internal liquid droplet flow field as well as the external gas phase flow field, a nonstaggered rectangular grid system without any coordinate transformation is used. transition from the gas field to the liqui...

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...