High order boundary and finite elements for 3D fracture propagation in brittle materials

The quasi-static propagation of fracture in brittle materials was studied in several recent publications. A variational formulation (Salvadori, 2008; Salvadori and Carini, 2011; Salvadori and Fantoni, 2013) led to three-dimensional crack tracking strategies (Salvadori and Fantoni, 2014 [2,3]; Salvadori and Fantoni, 2016). One of the complexities of this new class of algorithms is the evaluation of high-order terms of the expansion of the crack opening and sliding. In this paper, new types of finite and boundary elements are formulated that capture the near crack-front asymptotical displacement behavior up to the order 3/2. The use of these elements with the quasi-static crack propagation algorithms of the above references is demonstrated for a simple crack configuration.