Abstract: Phase field models for fracturing approximate the crack as a globally diffused scalar field.The crack nucleation and propagation are simulated by solving partial differential equations, which avoids the numerical challenges in describing and tracking cracks in the discontinuous displacement field, and exhibits several advantages in modeling conventionally challenging problems, such as crack bifurcation, multiple cracks, fracture problems within heterogeneous materials and three-dimensional cases.However, fracture modeling based on the phase field method requires a refined finite element mesh near the crack, resulting in enormous computational costs.With substructuring and damage identification, this work proposes a highly efficient phase field method for brittle fracturing simulation of periodic structures.Firstly, the structure is partitioned into identical substructures according to its periodicity, and their internal nodes are statically condensed by means of substructuring.Secondly, an elastic strain energy threshold is identified by representative off-line tests of the substructure.Moreover, only the internal displacement and crack phase field of the substructures whose strain energies are above the threshold are further analyzed during the on-line fracturing simulation.Therefore, not only the structural periodicity contributes to the reduction of computational costs through sbustructuring, but the non-crack propagation substructures are prevented from repetitive FE analysis by virtue of damage identification.

Key words: phase field, fracture modeling, computation reduction, substructuring, damage identification