Reduced order homogenization models for failure of heterogeneous materials

This manuscript presents a new methodology for the identification of optimal reduced order models for the inelastic and failure response of heterogeneous materials. The proposed methodology employs the eigendeformation-based reduced order homogenization approach. The identification of the optimal reduced order model is posed as an integer optimization problem and the genetic algorithm method is used to evaluate the optimization problem. A second optimization problem is posed to ensure that the errors associated with the optimal reduced order model are minimized through scaling of the failure parameters. The performance and capabilities of the optimal reduced order models identified based on the proposed approach are demonstrated by comparing model predictions with the computational homogenization method with full resolution of the material microstructure. Numerical simulations conducted using unidirectional reinforced matrix microstructures reveal that the reduced order models accurately describe the response characteristics of the composite material for a wide range of loading regimes.

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