A computational homogenization framework with enhanced localization criterion for macroscopic cohesive failure in heterogeneous materials

Abstract

Computational homogenization allows to let the macroscopic constitutive behavior of materials emerge from microscale simulations without loss of generality with respect to microstructure and microscale constitutive response. Although computationally demanding, computational homogenization works very well for the hardening response of materials where the macroscopic stress and strain fields are smooth. However, in case of softening materials, when localization of deformation takes place, special care is needed to ensure objectivity of the method. In this paper, a generic multiscale computational homogenization approach for modeling onset and propagation of cracks in heterogeneous materials that is capable of considering various microscale mechanisms is presented. The common acoustic tensor bifurcation criterion is reinforced by an additional condition to help detect the localization mode more robustly. After the onset of macroscale localization, a key scale transition parameter is needed to translate the macroscopic displacement jump to an averaged strain over the micromodel domain. Then the macroscale crack is governed by a homogenized traction-separation relation evaluated from the underlying micromodel in which micro-failure accumulates. The scale transition parameter is studied for a range of different scenarios and endowed with a geometrical interpretation. Various numerical tests have been performed to confirm the objectivity and validity of the framework. The framework is generic in the sense that no assumptions on the microscale constitutive or kinematic representation of material failure are made in the scale transition. The framework is also highly compatible with the first order computational homogenization, which minimizes the additional complexity of adding macroscopic crack growth to the computational implementation.