A Phantom-Node Method with Edge-Based Strain Smoothing for Linear Elastic Fracture Mechanics

摘要

This paper presents a novel numerical procedure based on thecombination of an edge-based smoothed finite element (ES-FEM) witha phantom-node method for 2D linear elastic fracture mechanics. Inthe standard phantom-node method, the cracks are formulated byadding phantom nodes, and the cracked element is replaced by twonew superimposed elements. This approach is quite simple toimplement into existing explicit finite element programs. Theshape functions associated with discontinuous elements are similarto those of the standard finite elements, which leads to certainsimplification with implementing in the existing codes. Thephantom-node method allows modeling discontinuities at anarbitrary location in the mesh. The ES-FEM model owns aclose-to-exact stiffness that is much softer than lower-orderfinite element methods (FEM). Taking advantage of both the ES-FEMand the phantom-node method, we introduce an edge-based strainsmoothing technique for the phantom-node method. Numerical resultsshow that the proposed method achieves high accuracy compared withthe extended finite element method (XFEM) and other referencesolutions.