Strain orthogonal decomposition implemented within the phase field method with interfacial damage to model fracture in multi-phase heterogeneous materials

Abstract

In recent times, the phase field method is a robust simulation tool that can predict crack formation and propagation in structures. In brittle and quasi-brittle materials, the strain tensor is decomposed into negative and positive parts corresponding to the compression and tension behaviors when the structure is loaded. In the previous studies related to the phase field method, the strain tensor decompositions do not satisfy the orthogonal condition of these two parts, even if the elastic stiffness tensor is isotropic. This problem leads to inaccuracies in the mechanical behavior of the materials. In this paper, the strain tensor orthogonal condition is applied to the bulk strain tensor parts representing the internal strain of the component phases. This orthogonal condition is implemented into the phase field method with interfacial damage to simulate crack propagation in a sample containing multi-phase heterogeneous materials. Furthermore, the shape and area fraction of these phases are recognized by a supplemental sub-function which was studied in our recent paper from image formats. Through several examples, the obtained results are compared with the relevant numerical ones to demonstrate the correctness and effectiveness of the proposed method.