Prediction of macroscopic material failure based on microscopic cohesive laws

A three-dimensional finite element formulation is applied to the process of determination of macroscopic material properties based on constitutive relationships characterising a microscale. More specifically, a macroscopic failure criterion is computed numerically. The adopted finite element model captures the localised fully nonlinear kinematics associated with the failure on the microscale by means of the Strong Discontinuity Approach (SDA). In contrast to classical continuum mechanics, the deformation gradient is additively decomposed into a conforming part corresponding to a smooth deformation mapping and an enhanced part reflecting the final failure kinematics of the microscale. The implementation of the Enhanced-Assumed-Strain (EAS) concept leads to the elimination of the additional degrees of freedom (displacement jump) on the material point level. More precisely, the applied numerical implementation is similar to that of standard (finite) plasticity. The model does not require any assumption regarding neither the type of the finite elements, nor the constitutive behaviour. Any traction-separation law, connecting the displacement jump to the traction vector, can be chosen. Based on the proposed finite element formulation, microscopic material properties (traction-separation laws) are then used for the computation of the macroscopic material failure. The applicability of the presented numerical model is demonstrated by means of rather academic examples.