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Application of meshfree method to elastic-plastic fracture mechanics parameter analysis. (English) Zbl 1184.74058
Summary: The element-free Galerkin (EFG) method is applied to the calculation of elastic-plastic fracture mechanics parameters such as the J-integral and T${}^{*}$-integral. The fields of displacement, strain and stress for a crack problem are obtained using the elastic-plastic EFG method. Then the elastic-plastic fracture mechanics parameters J-integral and T${}^{*}$-integral are calculated from path and domain integrals. In the finite element analysis, paths for the path integral and domains for the domain integral are selected depending on finite element mesh division. On the other hand, they can be arbitrarily selected in the EFG method, and we can use a simple integral path and domain such as a circular shape surrounding a crack tip, which can provide efficient numerical integral formulae for the path and domain integrals. In a crack growth problem, the simple integral path and domain can easily move together with the crack tip, as the crack tip advances. This paper presents a method for calculating the J-integral and T${}^{*}$-integral in a framework of the EFG method. The proposed method is applied to both a stationary crack problem and a stable crack growth problem. The results obtained from the EFG method are compared with those of the finite element method and experiments to show the effectiveness of the EFG method to the elastic-plastic fracture mechanics parameter analysis.
##### MSC:
 74R99 Fracture and damage 74S30 Other numerical methods in solid mechanics 65N99 Numerical methods for BVP of PDE