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Abstract: This study offers novel progresses for a semianalytical method to simulate 2D propagation of cracks based on linear elastic fracture mechanics. For this purpose, a new algorithm is proposed on the basis of the linear elastic fracture mechanics for crack propagation in single‐mode and mixed mode. Herein, discretization is only performed on the boundaries of the problem by using specific subparametric elements and higher‐order Chebyshev polynomials as mapping functions. Implementing the weighted residual method and by taking Clenshaw‐Curtis numerical quadrature, diagonal Euler's differential equations are obtained. Consequently, once the local coordinate origin is assumed at the tip of the crack, the stress intensity factors can be derived directly. In accordance with the rate of maximum energy release as a propagation criterion and by proposing a new quasi‐automatic remeshing procedure based on domain division, the crack propagation is applied here. Based on the new presented algorithm, application of the new semianalytical method to crack propagation analysis is more flexible and efficient. By taking this advantage, relatively coarse and simple discretization compared with other computational methods may be used. By modelling 4 benchmark problems with a few numbers of degrees of freedom, the validity and accuracy of the current method is illustrated. Results show that the presented algorithm is applicable for efficient and precise prediction of crack trajectories. [ABSTRACT FROM AUTHOR]

The existence of crack and notch is a considerable and serious subject in the failure study of solids and structures. As most of cracked domain problems do not have closed-form solutions, numerical methods are dominant approaches dealing with fracture mechanics problems. In fracture mechanics and failure analysis, cracked media energy and consequently stress intensity factors (SIFs) play a crucial and significant role. Based on linear elastic fracture mechanics, the SIFs may be estimated using the energy release rate, as an indirect approach. This study presents the development of a new semi-analytical method to model cracked media. In this method, only the boundaries of problems are discretized using specific higher-order subparametric elements and higher-order Chebyshev mapping functions. Implementing the weighted residual method and using Clenshaw-Curtis quadrature yield diagonal Euler's differential equations. Therefore, when the local coordinate origin is located at the crack tip, the geometry of crack problems is implemented directly without further processing. In order to present crack boundary conditions, a modified form of nodal force function is presented. Validity and accuracy of the proposed method is fully illustrated by four benchmark problems, whose results agree very well with those of other numerical and/or analytical solutions existing in the literature. [ABSTRACT FROM AUTHOR]

This study presents a novel development of a new semi-analytical method with diagonal coefficient matrices to model crack issues. Accurate stress intensity factors based on linear elastic fracture mechanics are extracted directly from the semi-analytical method. In this method, only the boundaries of problems are discretized using specific subparametric elements and higher-order Chebyshev mapping functions. Implementing the weighted residual method and using Clenshaw-Curtis numerical integration result in diagonal Euler's differential equations. Consequently, when the local coordinates origin is located at the crack tip, the stress intensity factors can be determined directly without further processing. In order to present infinite stress at the crack tip, a new form of nodal force function is proposed. Validity and accuracy of the proposed method is fully demonstrated through four benchmark problems, which are successfully modeled using a few numbers of degrees of freedom. The numerical results agree very well with the analytical solution, experimental outcomes and the results from existing numerical methods available in the literature. [ABSTRACT FROM AUTHOR]