A fracture-controlled path-following technique for phase-field modeling of brittle fracture

In the phase-field description of brittle fracture, the fracture-surface area can be expressed as a functional of the phase field (or damage field). In this work we study the applicability of this explicit expression as a (non-linear) path-following constraint to robustly track the equilibrium path in quasi-static fracture propagation simulations, which can include snap-back phenomena. Moreover, we derive a fracture-controlled staggered solution procedure by systematic decoupling of the path-following controlled elasticity and phase-field problems. The fracture-controlled monolithic and staggered solution procedures are studied for a series of numerical test cases. The numerical results demonstrate the robustness of the new approach, and provide insight in the advantages and disadvantages of the monolithic and staggered procedures. HighlightsThe phase-field fracture-surface area is used as a path-following control equation.A staggered path-following algorithm is derived from the monolithic formulation.A detailed comparison of the monolithic and staggered schemes is presented.The influence of phase-field tip enrichment on snap-back behavior is demonstrated.

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