Modeling fracture problems by the local mesh refinement NMM with variable-midside-node elements

Abstract

Uniform finite element meshes are usually used to discrete problem domain in the numerical manifold method. This strategy provides high interpolation accuracy but is ineffective when dealing with cases involving steep deformation gradients or singularities. The major objective of this research is to develop a local multilevel mesh refinement strategy on the basis of the numerical manifold method, in which the determination of mathematical elements to be refined and the multilevel refinement to the target region can be performed automatically. To accurately capture the singularity while saving computational cost during crack growth, a follow-up refinement scheme is implemented to realize real-time refinement for the crack tip region. The variable-midside-node elements with conforming shape functions are integrated into the present formulation to solve the mismatching problem induced by different different-sized elements in an effective way. A special subdivision algorithm is proposed for appropriately and accurately treating numerical integration of manifold elements in the transition elements. The numerical performance of the proposed method is first validated by a linear elastic example. Next, six fracture problems involving multiple and branched cracks are simulated. The obtained results indicate high accuracy, low computational cost, and good performance of the proposed method in fracture analysis.