Marc Duflot

TL;DR: This manuscript is to give a practical overview of meshless methods (for solid mechanics) based on global weak forms through a simple and well-structured MATLAB code, to illustrate the discourse.

TL;DR: In this article, the shape of the level set functions around a crack in two dimensions that is propagating with a sharp kink, obtained both with level set update methods found in the literature and with several innovative update methods developed by the author.

TL;DR: In this paper, an extended finite element method (XFEM) is applied to the simulation of thermally stressed, cracked solids, where both thermal and mechanical fields are enriched in the XFEM way to represent discontinuous temperature, heat flux, displacement, and traction across the crack surface, as well as singular heat flux and stress at the crack front.

TL;DR: In this article, the fatigue growth of cracks in two-dimensional bodies is considered based upon Paris' equation and new enriched weight functions are introduced in the meshless method formulation to capture the singularity at the crack tip.

TL;DR: In this paper, a simple and effective local a posteriori error estimate for partition of unity enriched finite element methods such as the extended finite element method (XFEM) is proposed, in which near-tip asymptotic functions are added to the MLS basis.