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. •We developed a novel approach in modeling crack propagation that requires high order COD terms.•We developed finite and boundary elements to this purpose.•We implemented and tested the novel finite and boundary elements.•We evaluated performances of the new elements.•We solved benchmark problems of parameters evaluation and crack growth.