  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.
