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

Abstract

This paper presents a novel numerical procedure based on the combination of an edge-based smoothed finite element (ES-FEM) with a phantom-node method for 2D linear elastic fracture mechanics. In the standard phantom-node method, the cracks are formulated by adding phantom nodes, and the cracked element is replaced by two new superimposed elements. This approach is quite simple to implement into existing explicit finite element programs. The shape functions associated with discontinuous elements are similar to those of the standard finite elements, which leads to certain simplification with implementing in the existing codes. The phantom-node method allows modeling discontinuities at an arbitrary location in the mesh. The ES-FEM model owns a close-to-exact stiffness that is much softer than lower-order finite element methods (FEM). Taking advantage of both the ES-FEM and the phantom-node method, we introduce an edge-based strain smoothing technique for the phantom-node method. Numerical results show that the proposed method achieves high accuracy compared with the extended finite element method (XFEM) and other reference solutions.

A coupled SPH-DEM model for fluid-structure interaction problems with free-surface flow and structural failure

“…The interaction forces between SPH particles and DEM particles follow Eq. (34). The density and the pressure for DEM particles stay unchanged at all times, and only their velocity and position evolve with time.…”

“…Phantom-Node method [34] was also incorporated into FEM through integration of overlapped elements in order to handle crack kinematics, but the crack-tip enrichment is still challenging and its flexibility is comprised when crack growth is the only focus. Therefore coupling FEM with SPH for modelling fluid induced structural failure during the FSI process would become even more challenging.…”

Numerical Investigation of Influence of In-Situ Stress Ratio, Injection Rate and Fluid Viscosity on Hydraulic Fracture Propagation Using a Distinct Element Approach

“…Numerical simulation [17][18][19][20][21][22][23][24][25][26][27][28] would avoid some of the randomness in laboratory experiments and could reflect the effect of critical parameters on hydraulic fracturing characteristics. Many works have been carried out to investigate the influence of some important parameters on hydraulic fracturing by numerical simulation.…”

Phase-field modeling of fracture in linear thin shells

“…To get a better understanding of the proposed methodology, we consider a well studied benchmark example of 2D solid under plane stress state [51,52]. The plane is a square of edge length L = 1 mm, under pure tension with initial crack (see sketch in Fig.…”