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 two main deficiencies of conventional SPH, i.e., tensile instability and inconsistency, by making use of the Lagrangian kernel and gradient correction, respectively. In the present approach, the support domain of a particle is modified, where it only interacts with its immediately neighbouring particles. A virtual link defines 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.