Incorporation of microstructural geometry in material modelling

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Abstract
Detailed numerical simulations of the deformation of measured microstructures are reviewed, analysing grain interactions in a polycrystal, flow localization between holes in a sheet and particle cracking in a reinforced material. The analyses employ two-dimensional models, but the results demonstrate the necessity of considering the three-dimensional microstructural geometry in accurate predictions of crystallographic orientation evolution, strain localization and fracture. Several methods of characterizing the three-dimensional microstructures from planar sections of the material are described. The importance of the size and distribution of the microstructural features is discussed in relation to the size of the volume elements utilized in numerical simulations, and the impact of this relative size on the formulation of constitutive relations by homogenization techniques is explored.