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Multimaterial structural topology optimization with a generalized Cahn-Hilliard model of multiphase transition. (English) Zbl 1245.74077
Summary: We describe a phase field method for the optimization of multimaterial structural topology with a generalized Cahn-Hilliard model. Similar to the well-known simple isotropic material with penalization method, the mass concentration of each material phase is considered a design variable. However, a variational approach is taken with the Cahn-Hilliard theory to define a thermodynamic model, taking into account the bulk energy and interface energy of the phases and the elastic strain energy of the structure. As a result, the structural optimization problem is transformed into a phase transition problem defined by a set of nonlinear parabolic partial differential equations. The generalized Cahn-Hilliard model regularizes the original ill-posed topology optimization problem and provides the flexibility of topology changes with interface coalescence and break-up due to phase separation and coarsening. We employ a powerful multigrid algorithm and extend it to include four material phases for numerical solution of the Cahn-Hilliard equations. We demonstrate our approach through several 2-D and 3-D examples to minimize mean compliance of the multimaterial structures.

74P15 Topological methods for optimization problems in solid mechanics
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74G65 Energy minimization in equilibrium problems in solid mechanics
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