Computational homogenisation of phase-field fracture. (English) Zbl 1475.74105
Summary: 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 (RVE\(^1\)) 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.
MSC:
| 74R10 | Brittle fracture |
| 74Q05 | Homogenization in equilibrium problems of solid mechanics |
| 74E05 | Inhomogeneity in solid mechanics |
Keywords:
phase-field fracture; homogenisation; macro-homogeneity; multi-scale method; representative volume elementReferences:
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