Phase field modelling combined with optimization algorithm for maximizing the resistance in two-phase composites

Abstract

Recently, the phase field modelling is widely used to model and simulate material damage. In present work, we present a framework of the topology optimization combined with the phase-field modelling with/ without interfacial damage for optimizing the damage resistance of the inclusion-matrix composites. The first phase field method with the interfacial damage described by the phase field variable d(x) and an interfacial phase field variable β(x), thus the crack occurs in the interaction between the bulk fracture and the interfacial one; the second phase field method without the interfacial damage describes the crack by using only a damage variable d(x), thus the crack initiates at the points where stress concentration occurs (damage only occurring in the phases). Extended bi-directional evolutionary structural optimization algorithm (BESO) is used to optimize the inclusion distribution in order to reduce its volume while keeping the fracture resistance value of the initial design unchanged. Moreover, the strain tensor orthogonal decompositions are implemented into the phase field methods to improve the inaccuracy in the mechanical behavior of the materials. We compare the inclusion optimal distribution, the crack propagation and the fracture resistance between the proposed models through several numerical examples.