The macroscale mechanical and physical properties of materials are inherently linked to the underlying microstructure. Traditional continuum mechanics theories have focused on approximating the heterogeneous microstructure as a continuum, which is conducive to a partial differential equation mathematical description. Although this makes large scale simulation of material much more efficient than modeling the detailed microstructure, the relationship between microstructure and macroscale properties becomes unclear. In order to perform computational materials design, material models must clearly relate the key underlying microstructural parameters (cause) to macroscale properties (effect).; In this thesis, microstructure evolution and instability events are related to macroscale mechanical properties through a new multiresolution continuum analysis approach. The multiresolution nature of this theory allows prediction of the evolving magnitude and scale of deformation as a direct function of the changing microstructure. This is achieved via a two-pronged approach: (a) Constitutive models which track evolving microstructure are developed and calibrated to direct numerical simulations (DNS) of the microstructure. (b) The conventional homogenized continuum equations of motion are extended via a virtual power approach to include extra coupled microscale stresses and stress couples which are active at each characteristic length scale within the microstructure.; The multiresolution approach is applied to model the fracture toughness of a cemented carbide, failure of a steel alloy under quasi-static loading conditions and the initiation and velocity of adiabatic shear bands under high speed dynamic loading. In each case the multiresolution analysis predicts the important scale effects which control the macroscale material response. The strain fields predicted in the multiresolution continuum analyses compare well to those observed in direct numerical simulations of the microstructure. However much less computational effort is required because the detailed microstructure does not have to be modeled (unlike the direct numerical simulations). Furthermore the characteristic length scale of inhomogeneous deformation is predicted to change as a function of the evolving microstructure. As such the predicted scale of inhomogeneous deformation which controls the macroscale response is a function of the underlying microstructural instability events. This provides an important link between macroscale properties and microstructure which is useful for materials design.
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