Element-splitting for Simulation of Fracture in 3d Solid Continua

Algorithms for simulation of strain localisation and fracture in 3D solid continua subjected to impact loading are presented. The methodology relies upon the classical continuous Galerkin Finite Element Method for spatial semi-discretisation and the leap-frog central difference scheme for temporal discretisation of the governing partial differential equations. The material behaviour is represented using a rate and temperature dependent hypoelastic-viscoplastic constitutive model with coupled damage and regularised softening. The results presented in this paper are obtained using the constant strain tetrahedral elements. The crack initiation and propagation are modelled using an element splitting method which relies upon quasi-non-local criteria assessed at nodal positions thus allowing for mesh-independent solutions to be achieved. The proposed method uses an efficient local adaptive re-meshing technique in which the elements are divided along the emerging discontinuity using piece-wise planar segments.