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Hierarchical Framework for the Multiscale Modeling of Microstructure Evolution in Heterogeneous Materials

机译：非均匀材料微观组织演化多尺度建模的层次框架

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All materials are heterogeneous at various scales of observation. The influence of material heterogeneity on nonuniform response and microstructure evolution can have profound impact on continuum thermomechanical response at macroscopic engineering scales. In many cases, it is necessary to treat this behavior as a multiscale process thus integrating the physical understanding of material behavior at various physical (length and time) scales in order to more accurately predict the thermomechanical response of materials as their microstructure evolves. The intent of the dissertation is to provide a formal framework for multiscale hierarchical homogenization to be used in developing constitutive models. This research developed a hierarchical multiscale approach for modeling microstructure evolution. A theoretical framework for the hierarchical homogenization of inelastic response of heterogeneous materials was developed with a special focus on scale invariance principles needed to assure physical consistency across scales. Within this multiscale framework, the second gradient is used as a nonlocal kinematic link between the response of a material point at the coarse scale and the response of a neighborhood of material points at the fine scale. Kinematic consistency between two scales results in specific requirements for constraints on the fluctuation field. A multiscale internal state variable (ISV) constitutive theory is developed that is couched in the coarse scale intermediate configuration and from which an important new concept in scale transitions emerges, namely scale invariance of dissipation.

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