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Topology evolution of composite structures based on a phase field model

The composition of fibers and matrix is of great importance in several fields of engineering, such as steel reinforcement in concrete for civil engineering or lightweight applications in the automotive and aviation industry, as it allows combining the advantages of both materials. If the bond between fibers and matrix is ideally strong enough, the mechanical deformation can be assumed to be equal in both materials. With this assumption we set up a phase field model evolving the topology of reinforcement. The phase field parameter represents regions of reinforcement in the sense of averaged increased stiffness since we do not intend to simulate single fibers. A similar model but for topology optimization based on equivalent stresses was introduced by Muench et al. [1]. In many matrix materials, viscoelastic behavior is observed. Therefore, we also consider viscoelasticity in our model for the matrix.