Field-enriched finite element method for simulating complex cracks in brittle solids

Abstract

A field-enriched finite element method (FE-FEM) is proposed to simulate cracking behaviors of brittle solids containing cracks of complex geometries. Three different coalescence types, i.e. the coalescence of crack tip and crack tip, crack tip and crack segment, crack tip and free boundary, are considered by employing reasonable strategies. Moreover, a predictor-and-corrector algorithm is developed to solve problem of competing crack growth. Three benchmark examples containing cracks of complex geometries are performed to validate the accuracy and correctness of the proposed numerical method. Finally, the evolution of complex cracks, including a tree-shaped crack, regularly distributed intersecting cracks, and randomly distributed intersecting cracks, are simulated and investigated. All numerical results show that the proposed numerical method can effectively handle complex cracks without any special treatment around junction points.