Microstructural Modeling and Computational Homogenization of the Physically Linear and Nonlinear Constitutive Behavior of Micro-Heterogeneous Materials

Most engineering materials show a pronounced heterogeneity on a smaller scale that influences the macroscopic constitutive behavior. In order to examine this relation, the concept of model microstructures is introduced. Algorithms for the periodic discretization are presented for use in thermomechanical homogenization based on the finite element method. Polycrystalline metals, metal ceramic composites and porous materials are investigated. The microstructures are used in the Nonuniform Transformation Field Analysis (NTFA). The NTFA is an order reduction based nonlinear homogenization method with micro-mechanical background. Theoretical and numerical aspects of the method are discussed and its efficiency is validated. Further, Monte Carlo type simulations on periodic porous aggregates are performed in order to predict the macroscopic yield surface of such materials. The thereby generated yield curves are compared to existing models.

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