An isogeometric-meshfree collocation approach for two-dimensional elastic fracture problems with contact loading. (January 2020) - Li, Weidong; Nguyen-Thanh, Nhon; Zhou, Kun
Highlights: An isogeometric-meshfree collocation approach is developed for elastic fracture problems. The present approach achieves automatic adaptive mesh refinement by utilizing the gradient-based error estimator. The present approach models a crack by the visibility criterion without using Heaviside or tip-enrichment functions. Advantages in the high convergence rate and computational efficiency are demonstrated. Adaptive crack analysis considering contact conditions is conducted. Abstract: A strong form-based isogeometric-meshfree moving least-squares collocation (IMMLS-C) approach is developed for two-dimensional linear elastic fracture problems with contact loading. The IMMLS-C approach uses reproducing conditions to establish an equivalence between MLS shape functions and isogeometric basis functions. The advantages of this approach include the exact geometry representation, convenient crack modeling and flexible adaptive refinement. The IMMLS-C approach focuses on solving fracture problems based on strong formulations without requiring the numerical integration of Galerkin weak forms. Traction-free boundary conditions are enforced over a set of collocation points located on both sides of a crack surface. The displacement discontinuity along the crack surface is modeled by the visibility criterion and the singularity of near-tip stress fields is captured by adaptive mesh refinement without adding tip-enrichment functions, thereby reducing the degrees of freedom compared with the extended finite element method. Moreover, contact constraints are enforced by introducing a penalty algorithm to the strong formulations. The numerical results demonstrate that the adaptive refinement is able to achieve a high convergence rate at a low computational cost.