Enabling microstructure-based damage and localization analyses and upscaling

This paper presents a framework that enables microstructural modelling of complex microstructures involving damage, localization and fracture. Classical computational homogenization schemes hinge on the separation of scales and the existence of representative volume elements. Due to the accumulation of micro-damage, the microstructural volume elements gradually loose their representative character and evolve towards a unique volume with a developing strain localization band, rendering classical homogenization approaches inapplicable. The assumption that the representative nature of the microstructure along the strain localization band is preserved enables the definition of advance scale transition relations for both imposing the overall macroscale load and coarse graining the cohesive behaviour of the strain localization band. Newly developed strain percolation path aligned boundary conditions have been used for this purpose. It is shown that this enables the development and progressive evolution of a strain localization band with minimal interference of the imposed boundary conditions. In addition to classical homogenization of the stress–strain response, a coarse graining scheme for the effective cohesive behaviour of the strain localization band is proposed. This enables the assessment of the microstructural evolution within the strain localization band and simultaneously provides the effective cohesive response useful for macroscale failure models.