Computational homogenisation of phase-field fracture

In this manuscript, the computational homogenisation of phase-field fractures is addressed. To end, a variationally consistent two-scale fracture framework developed, which formulates coupled momentum balance and evolution equations at macro-scale as well Representative Volume Element (RVE1) scale. The variable represent RVE scale, however, macro-scale, it treated an auxiliary variable. latter interpretation follows from through volume or surface-average. For either choices, set sub-scale equations, pertinent macro-homogeneity satisfying boundary conditions are established. As special case, concept selective introduced, where chosen to live only in domain, thereby eliminating equation. Numerical experiments demonstrate local material behaviour based model, while its non-selective counterpart yields non-local behaviour.