This paper reviews the recent developments in the field of multiscale modelling of heterogeneous materials with emphasis on homogenization methods and strain localization problems. Among other topics, the following are discussed (i) numerical homogenization or unit cell methods, (ii) continuous computational homogenization for bulk modelling, (iii) discontinuous computational homogenization for adhesive/cohesive crack modelling and (iv) continuous-discontinuous computational homogenization for cohesive failures. Different boundary conditions imposed on representative volume elements are described. Computational aspects concerning robustness and computational cost of multiscale simulations are presented.
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Nguyen et al. (2011) studied this question.
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