Numerical solutions to dynamic fracture problems using the element-free Galerkin method.

摘要

Application of the element-free Galerkin method to dynamic fracture problems is described. This meshless method facilitates the modeling of arbitrary crack growth because it does not require remeshing; crack propagation is modeled by extending the crack surfaces. The essential feature of the method is the use of moving least square approximations, where the dependent variable is obtained at any point by minimizing a weighted discrete error norm involving the nodal variables within a small domain surrounding the point. The governing equations are solved by a Galerkin method.; A procedure is developed for coupling meshless methods and finite element methods, allowing the use of efficient finite elements in regions without cracks, while a meshless method is used in crack growth regions. The coupling is constructed using interface elements in which continuity and consistency are preserved. Results are presented for both elastostatic and elastodynamic problems.; Continuous meshless approximations near nonconvex boundaries, such as crack tips, are constructed by the diffraction method. Approximations by the diffraction method are compared to the visibility criterion in which the approximations are discontinuous in the vicinity of nonconvex boundaries. The continuous approximations show moderate improvement in accuracy over the discontinuous approximations when a linear basis is used, but yield significant improvements for enhanced bases.; Fracture modeling is described for meshless methods. The accurate computation of fracture parameters, the propagation criterion, and modeling arbitrary crack growth are presented.; A series of dynamic fracture examples illustrates the performance of the techniques developed, ranging from a stationary crack under impact loading to multiple cracks growing in arbitrary directions at arbitrary speeds. The EFG solutions compare well with analytical solutions and experimental results for stationary cracks and arbitrary crack growth at constant as well as variable crack velocities.