Chapter 13: Multiscale Design: From Theory to Practice

We present a practical multiscale approach that possesses computational efficiency of phenomenological models for heterogeneous media with accuracy inherent to generalized and nonlocal continua models. The method introduces no scale separation, makes no assumption about infinitesimality of the fine-scale structure, does not require higher order continuity, introduces no new degrees-of-freedom, is free of higher order boundary conditions and exploits a pre-computed material database to effectively solve a unit cell (representative volume) problem. It features four building blocks: (i) the nonlocal quadrature scheme, (ii) the coarse-scale stress function, (iii) the residual-free fields and (iv) identification of the overall microstructural properties from the coarse-scale observations.