Multi-scale boundary element modelling of material degradation and fracture

In the present paper a multi-scale boundary element method for modelling damage is proposed. The constitutive behaviour of a polycrystalline macro-continuum is described by micromechanics simulations using averaging theorems. An integral non-local approach is employed to avoid the pathological localization of micro-damage at the macro-scale. At the micro-scale, multiple intergranular crack initiation and propagation under mixed mode failure conditions is considered. Moreover, a non-linear frictional contact analysis is employed for modelling the cohesive-frictional grain boundary interfaces. Both micro- and macro-scales are being modelled with the boundary element method. Additionally, a scheme for coupling the micro-BEM with a macro-FEM is also proposed. To demonstrate the accuracy of the proposed method, the mesh independency is investigated and comparisons with two macro-FEM models are made to validate the different modelling approaches. Finally, microstructural variability of the macro-continuum is considered to investigate possible applications to heterogeneous materials.