Vector-based damage-driven computational homogenization with localized gradient enhanced boundary conditions for multi-scale modelling of quasi-brittle materials

Abstract

Although a lot of progress has been made in computational homogenization, it is still a difficult challenge to emerge and evolve localization bands robustly and to tackle the size dependency issue for brittle and quasi-brittle materials. In this paper, a vector-based damage-driven computational homogenization with localized gradient enhanced boundary conditions is proposed. In the homogenization, the crack band theory is used to up-scale the damage at the micro level to the macro level based on the unit cell size and element size. The vector-based homogenization introduces damage in the principal direction based on the smeared crack model. The updated localized displacement gradients are introduced in the boundary conditions of unit cells to localize crack propagation between adjacent unit cells. The localized displacement gradients are updated iteratively to consider crack open and closure as well as the influences of surrounding elements. Incremental sequentially linear analysis is used to guarantee computational robustness. Size objectivity and localization have been demonstrated for different unit cell sizes and element sizes compared with the direct simulation method (DSM). In addition, an array of voids is considered in the notched beam test for further validation.