Abstract
The modelling and understanding of crack propagation for elastic–plastic materials is critical in various engineering applications, such as safety analysis of concrete structures and stability analysis of rock slopes. In this paper, the local radial basis point interpolation method (LRPIM) combined with elastic–plastic theory and fracture mechanics is employed to analyse crack propagation in elastic–plastic materials. Crack propagation in elastic–plastic materials is compared using the LRPIM and eXtended finite-element method (XFEM). The comparative investigation indicates that: (i) the LRPIM results are close to the model test results, which indicates that it is feasible for analysing the crack growth of elastic–plastic materials; (ii) compared with the LRPIM, the XFEM results are closer to the experimental results, showing that the XFEM has higher accuracy and computational efficiency; and (iii) compared with the XFEM, when the LRPIM method is used to analyse crack propagation, the propagation path is not smooth enough, which can be explained as the crack tip stress and strain not being accurate enough and still needing further improvement.
Highlights
The modelling and understanding of crack propagation for elastic–plastic materials is critical in various engineering applications, such as safety analysis of concrete structures and stability analysis of rock slopes
The local radial basis point interpolation method (LRPIM) combined with elastic–plastic theory and fracture mechanics is employed to analyse crack propagation in elastic–plastic materials
The comparative investigation indicates that: (i) the LRPIM results are close to the model test results, which indicates that it is feasible for analysing the crack growth of elastic–plastic materials; (ii) compared with the LRPIM, the XFEM results are closer to the experimental results, showing that the XFEM has higher accuracy and computational efficiency; and (iii) compared with the XFEM, when the LRPIM method is used to analyse crack propagation, the propagation path is not smooth enough, which can be explained as the crack tip stress and strain not being accurate enough and still needing further improvement
Summary
Many meshless methods have been proposed by scholars Their main differences lie in the approximation method and form of the system equation. The approximation method of LRPIM is radial basis point interpolation, and the system equation is obtained using the local weighted residual method:. The combination of a polynomial basis function [26] and compactly supported radial basis function [27] in a meshless method is used to construct the radial basis point interpolation shape function. Considering the solid mechanics problem defined in domain Ω, the local weighted residual method is used for node I to satisfy the governing equation and the local weak equation of the node is obtained. The form of the locally weighted residuals is defined on the local integral domain Ωq and the corresponding boundary Γq in the following form: ð. After assembling the total rigid matrix, a penalty function is used to apply the displacement boundary conditions
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