A Total Lagrangian SPH method for modelling damage and failure in solids

An algorithm is proposed to model crack initiation and propagation within the Total Lagrangian Smoothed Particle Hydrodynamics (TLSPH) framework. TLSPH avoids the tensile instability encountered in conventional Eulerian kernel-based Smoothed Particle Hydrodynamics (SPH) by making use of the Lagrangian kernel. In the present approach, the support domain of a particle is modified, where it only interacts with its immediately neighbouring particles. The gradient correction is employed to avoid the inconsistency of SPH approximation induced by insufficient neighbouring particles. A virtual link is used to define the level of interaction between each particle pair. The state of the virtual link is determined by damage law or cracking criterion. The virtual link approach allows easy and natural modelling of cracking surfaces without explicit cracking treatments such as particle splitting, field enrichment or visibility criterion. The performance of the proposed approach is demonstrated via a few numerical examples of both brittle and ductile failure under impact loading.