Yongxing Shen

TL;DR: In this paper, a phase-field model for fracture in Kirchoff-love thin shells using the local maximum-entropy (LME) mesh-free method is presented, which does not require an explicit representation and tracking, which is advantage over techniques as the extended finite element method that requires tracking of the crack paths.

TL;DR: In this article, a finite element-based algorithm is presented to simulate plane-strain, straight hydraulic fractures in an impermeable elastic medium, which accounts for the nonlinear coupling between the fluid pressure and the crack opening.

TL;DR: A massively parallel algorithm on the graphical processing unit (GPU) to alleviate the difficulty in the case of dynamic brittle fracture by adopting the standard finite element method on an unstructured mesh combined with second order explicit integrators.

TL;DR: In this paper, the authors formulate a class of delicately controlled problems to model the kink-free evolution of quasistatic cracks in brittle, isotropic, linearly elastic materials in two dimensions.

TL;DR: In this article, a variant of the extended finite element method (XFEM) rendering an optimally convergent scheme was introduced. But the method is provably stable for any positive value of a stabilization parameter, and by weakly enforcing the continuity between the two regions it eliminates "blending elements" partly responsible for the suboptimal convergence of some early XFEMs.