On use of the thick level set method in 3D quasi-static crack simulation of quasi-brittle material

This work demonstrates the 3D capability of the thick level set (TLS) method, first introduced by Moës et al. (Int J Numer Methods Eng 86:358–380, 2011. doi:10.1002/nme.3069) and later in Stolz and Moës (Int J Fract 174(1):49–60, 2012. doi:10.1007/s10704-012-9693-3). The thick level set approach is a non-local damage method embedding fracture mechanics discontinuity. Enhanced numerical implementation for elastic quasi-brittle materials in 2D under quasi-static loading conditions was presented in Bernard et al. (Comput Methods Appl Mech Eng 233–236:11–27, 2012. doi:10.1016/j.cma.2012.02.020). The present work focuses on using this enhanced numerical implementation in a 3D context. This work adds a new way to construct the crack faces by use of a “double cut algorithm”. The regularization computation, part of the non-local feature of the model, is also reviewed to improve its accuracy. As 3D models are computationally intensive, CPU aspects are discussed. Five test cases are presented. The first one illustrates the capability of the method to deal with crack coalescence, which is quite unique for this kind of simulation. Three other cases point out a comparison with literature examples (numerical and experimental) and good agreement is observed. One is a more complex example, which deals with an engineering oriented application. This work confirms good performance of the thick level set method in 3D context. The use of the new “double cut” algorithm is giving well discretized crack path and allows for discontinuous displacement.