Computational homogenisation of phase-field fracture

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

Automated summary

In this study, a computational homogenisation method for phase-field fractures is developed, leading to a two-scale phase-field fracture framework. The concept of selective homogenisation is introduced, showing local macro-scale material behavior in numerical experiments. Non-selective homogenisation yields a non-local macro-scale material behavior.