For the delamination and matrix crack prediction of composite laminated structures, the methods based on the damage mechanics and fracture mechanics are most commonly used. However, there are very few methods that can accurately simulate the delaminations together with matrix cracks, although the in-plane matrix cracks always exist alongside the delaminations under impact loading. In this work, an extended layerwise method is developed to model the composite laminated beam with multiple delaminations and matrix cracks. In the displacement field, the nodes in the thickness direction are located at the middle surface of each single layer, the top surface and the bottom surface of the composite beams. The displacement field contains the linear Lagrange interpolation functions, the one-dimensional weak discontinuous function and strong discontinuous function. The strong and weak discontinuous function are applied to model the displacement discontinuity induced by delaminations and the strain discontinuity induced by the interface between the layers, respectively. Because the nodes in the thickness direction are located at the middle surface of each single layer, the extended layerwise method can be conveniently employed to deal with the in-plane matrix cracks combined with the extend FEM. Copyright © 2014 John Wiley & Sons, Ltd.

An extended Layerwise method for composite laminated beams with multiple delaminations and matrix cracks

A polygonal XFEM with new numerical integration for linear elastic fracture mechanics

The extended isogeometric analysis method (XIGA) is further developed to study fracture of homogeneous and inhomogeneous materials under mechanical and thermo-mechanical loadings. The domain of the problem is discretized by the knot spans of the isogeometric analysis (IGA) and the same basis functions used for constructing the geometry are employed to discretize the solution. In addition, crack face discontinuity and tip enrichment functions of the extended finite element method (XFEM) are incorporated into the NURBS basis functions of IGA in order to reproduce crack face displacement discontinuity and tip singularity of the stress field. The proper form of the interaction integral method in inhomogeneous materials and thermal conditions is employed to evaluate the mixed mode stress intensity factors. In order to assess the efficacy of the proposed approach, a number of problems with different configurations and loadings are analyzed and the results are verified by comparing with the reference values.

Thermo-mechanical fracture study of inhomogeneous cracked solids by the extended isogeometric analysis method

An extended element free Galerkin method (XEFGM) has been adopted for fracture analysis of functionally graded materials (FGMs). Orthotropic enrichments functions are used along with the sub-triangle technique for enhancing the Gauss quadrature accuracy near the crack, and the incompatible interaction integral method is employed to calculate the stress intensity factors. Numerical simulations have proved that XEFGM provides more accurate results by less number of nodes (DOFs) in comparison with the unenriched EFGM and other conventional methods for several FGM problems with different crack locations and loadings. The results have been compared with the reference results, showing the reliability, stability, and efficiency of present XEFGM.Received 9 June 2014 Accepted 17 September 2014.

An extended element free Galerkin method for fracture analysis of functionally graded materials

Interaction integral method for computation of crack parameters K–T – A review

A computational method based on the extended finite element method (XFEM) is implemented for fracture analysis of isotropic and orthotropic functionally graded materials (FGMs) under mechanical and steady state thermal loadings. The aim is set to include the thermal effects in loading, governing equations, and the interaction integral for inhomogeneous materials with a complementary study on available crack propagation criteria in orthotropic FGMs under thermal loading conditions. The isotropic and orthotropic crack tip enrichments are applied to reproduce the singular stress field near crack tips. Mixed-mode stress intensity factors are evaluated in isotropic and orthotropic FGMs by means of the interaction integral. In addition, the mesh dependency and number of elements around the crack tip are substantially reduced in comparison with the standard finite element method with the same level of accuracy. Both mode-I and mixed-mode fracture problems with various types of mechanical and thermo-mechanical functionally graded material properties are simulated and discussed to assess the accuracy and efficiency of the proposed numerical method. Good agreements are observed between the predicted results and the reference results available in the literature with far lower degrees of freedom.

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S.S. Hosseini

Papers

Thermo-mechanical XFEM crack propagation analysis of functionally graded materials