An Elastic Interface Model for the Delamination of Bending-Extension Coupled Laminates

The paper addresses the problem of an interfacial crack in a multi-directional laminated beam with possible bending-extension coupling. A crack-tip element is considered as an assemblage of two sublaminates connected by an elastic-brittle interface of negligible thickness. Each sublaminate is modeled as an extensible, flexible, and shear-deformable laminated beam. The mathematical problem is reduced to a set of two differential equations in the interfacial stresses. Explicit expressions are derived for the internal forces, strain measures, and generalized displacements in the sublaminates. Then, the energy release rate and its Mode I and Mode II contributions are evaluated. As an example, the model is applied to the analysis of the double cantilever beam test with both symmetric and asymmetric laminated specimens.

S-FEM FOR FRACTURE PROBLEMS, THEORY, FORMULATION AND APPLICATION

This paper briefs some of recent works on applications of the smoothed finite element method (SFEM) to fracture problems. In the SFEM formulation for simulating the singular filed near the crack-tip, it is known that one can directly enrich the filed by adding in proper terms needed to simulate the singularity, which can be done in a number of ways (see the SFEM book). In this work a generalized technique called the "enriched linear PIM" for constructing shape functions is used to formulate a special "five-node (T5) singular crack-tip element" that can produce a proper order of stress singularity near the crack-tip. One layer of T5 crack-tip singular elements are used in a basic mesh of linear elements leading to a very simple model that can be crated automatically for complicated geometry. Because the SFEM uses weakened weak formulations, such a simple model does not require transition elements and the compatibility is ensured. In addition, the singular terms of functions as well as mapping procedures are no longer necessary to compute the stiffness matrix. Thus, the singular SFEM method is straightforward and can be easily implemented in the existing codes. The stress intensity factors of mix-modes can also be easily evaluated by an appropriate treatment during the domain form of the interaction integral, due to the use of simple triangular mesh. The effectiveness of the present singular T5 element is demonstrated via benchmark examples.

A New Scheme for Crack Growth Modeling by Coupling Modified Quarter Point Crack-Tip Element and the Level Set Method

In this paper, an efficient, numerical procedure is presented to track crack growth modeling without remeshing. The method's key feature is the coupling of a modified quarter-point crack tip element (MQPE) with the level set method (LSM) for crack growth problems. The LSM was used to represent the crack location, including the location of crack tips. The MQPE was used to compute the stress and displacement fields necessary for determining the rate of crack growth. Numerical test cases including various geometrical exceptions (the center-crack plate specimen, the single edge-crack plate specimen, and the double-edge crack plate) demonstrate the accuracy, robustness, and efficiency of the MQPE/LSM coupling. The extrapolation technique was used to estimate numerically the calibration factor for various specimens. This work confirms the feasibility of the MQPE/LSM to model accurately the singularity existing in the vicinity of the cracks. It allows an economic and adequate calculation of the stress intensity factors, which can be introduced into the various criteria of fracture or laws of propagation of the crack. The new method reduces the need for remeshing, and results agree well with reference data.

A NOVEL GENERAL FORMULATION FOR SINGULAR STRESS FIELD USING THE ES-FEM METHOD FOR THE ANALYSIS OF MIXED-MODE CRACKS

This paper presents a general formulation for simulating the singular stress field at the vicinity of the crack-tip for linear fracture mechanics problems, based on the edge-based smoothed finite element method (ES-FEM) settings. This novel "singular ES-FEM" makes use of the unique feature offered by the ES-FEM that only the assumed displacement values (not the derivatives) are required to compute the stiffness matrix of the discretized system. The present singular ES-FEM method uses a basic mesh of linear triangular elements and a layer of novel "five-noded crack-tip elements" sharing the crack-tip node. The five-noded crack-tip element has one additional node on each of the edges connected to the crack-tip, and the locations of the "edge-node" can be arbitrary. A number of examples are analyzed and the results demonstrate that the present singular ES-FEM is generally softer and much more accurate than the existing FEM. The stress intensity factors obtained using the singular ES-FEM are very stable for different area-integration paths designed around the crack-tip. The present singular ES-FEM is found an excellent alternative to the standard FEM for fracture problems.