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This article addresses two topics on multiscale modeling of heterogeneous metals and alloys. The first topic focuses on developing an adaptive hierarchical-concurrent multilevel modeling framework for ductile fracture. The microstructure of aluminum alloys, for example, is characterized by a dispersion of heterogeneities such as silicon and intermetallics in a ductile aluminum matrix. The multilevel model invokes two-way coupling, viz. hierarchical models for homogenized constitutive modeling and concurrent models with scale transition in regions of localization and damage. Adaptivity is necessary for evolving microstructural deformation and damage. A macroscopic analysis in regions homogeneity incorporates homogenization-based continuum plasticity-damage models. A microscopic analysis using locally enhanced-Voronoi cell finite-element method is required for regions of high macroscopic gradients caused by underlying localized plasticity and damage. Coupled macroscopic and microscopic analysis is conducted concurrently. Physics-based level change criteria are developed to improve accuracy and efficiency. The second topic discusses a nested dual-stage homogenization method for microstructure-based homogenized continuum plasticity models for cast aluminum alloys with large secondary dendrite arm spacing. Two distinct statistically equivalent representative volume elements are identified and used in the asymptotic expansion-based homogenization and self-consistent homogenization processes, respectively. The two-stage homogenization enables an evaluation of the overall homogenized model of a cast alloy from limited experimental data, as well as material properties of constituents like interdendritic phase and pure aluminum matrix.

Adaptive Hierarchical-Concurrent Multiscale Modeling of Ductile Failure in Heterogeneous Metallic Materials