Computational modelling of fracture with local maximum entropy approximations

The main aims of this research are to study fracture with a meshfree method, local maximum entropy (LME) approximations, and model fracture in thin shell structures with complex geometry and topology. The first part of this reseach was development of a method based on LME shape functions together with enrichment functions used in partition of unity methods. As extension of this method to 3D problems and complex thin shell structures with arbitrary crack growth is cumbersome, we developed a phase field model for fracture using LME. This approximation reduces considerably the implementation complexity because the crack is a natural outcome of the analysis and it does not require an explicit representation. Due to the higher order continuity of the LME approximation, we also present a fourth-order phase field model for fracture. In the last part of this research, we present a phase-field model for fracture in Kirchoff-Love thin shells using the LME meshfree method. The geometric description of the shell is based on statistical manifold learning techniques that allow dealing with general point set surfaces avoiding a global parametrization.