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A new approach to defining the effective fracture toughness for heterogeneousmaterials is proposed. This temporal averaging approach is process-dependent,incorporating the crack velocity and material toughness. The effectiveness ofthe new technique is investigated in the context of hydraulic fracture throughheterogeneous rock with a periodic material toughness. The plane strain modelis considered without fluid leak-off, to more easily investigate differentregimes (toughness/viscosity). Numerical simulations are used to examine theeffectiveness of the new homogenisation strategy, with comparison against therecently-proposed maximum toughness strategy. Simulations are conducted usingan extremely effective (in house-built) time-space adaptive solver. The regimesin which each strategy is effective are determined.

A temporal-averaging based approach to toughness homogenisation in heterogeneous material