3D explicit-BEM fracture analysis for materials with anisotropic multifield coupling

An explicit and unified boundary element formulation for the linear fracture analysis of three-dimensional bodies with general anisotropic multifield coupling is presented. The herein considered multifield media include, as particular cases, the purely elastic, piezo-electric and magneto-electro-elastic material models. The proposed formulation is based on the fundamental solutions for displacements and tractions recently introduced by Buroni and Sáez (2010), which presents the remarkable features of being exact, explicit in terms of the Stroh's eigenvalues and valid for mathematically degenerate as well as non-degenerate materials. Behaviour around the crack front is modeled with quarter-point elements for the extended displacements (elastic displacements, electric potential and magnetic potential) and singular quarter-point elements for the extended stresses (mechanical stresses, electric displacements and magnetic inductions) which allow for the direct extrapolation of the extended stress intensity factors (the mechanical stress intensity factors in the three classical modes KI, KII and KIII, the electric displacement intensity factor KIV and the magnetic induction intensity factor KV) from the computed nodal values at the singular quarter-point elements. Some benchmark examples are presented and discussed in order to validate this simple and robust approach for the assessment of multifield fracture parameters.