Among the different approaches proposed to study the mechanical response of heterogeneous composite materials, multiscale procedures are the most modern and have proved to be efficient and accurate both in the linear and nonlinear framework. This talk will focus on the so-called FE2 multiscale models relying on computational homogenization techniques to investigate the damaging response of heterogeneous microstructured materials. Both a first-order nonlocal homogenization procedure and an enriched approach, adopting the Cosserat continuum model, will be presented. Moreover, a reduced order model based on the Transformation Field Analysis (TFA) will be introduced allowing a considerable computational savings. Structural examples on masonry structures and reinforced concrete beams will be illustrated.
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