Treatment of material discontinuity in the element-free Galerkin method. (English) Zbl 0918.73331

Summary: A method is presented for application of the element-free Galerkin method (EFG) to solid mechanics problems containing material discontinuities. By using the EFG method, the trial and test functions for the weak form are constructed with moving least-square interpolants in each material domain. Additional constraints are imposed at the variational level to ensure satisfaction of interface conditions. As a result, only nodal data (no elemental connectivity) is needed. Given \(C^1\) continuity of the interpolant weighting function, the dependent variable and its gradient are continuous in each material domain. Two linear elastic bi-material examples are presented to illustrate the effectiveness of the method.


74S30 Other numerical methods in solid mechanics (MSC2010)
74B05 Classical linear elasticity
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[1] Belytschko, T.; Lu, Y.Y.; Gu, L., Element-free Galerkin methods, Int. J. numer. methods engrg., 37, 229-256, (1994) · Zbl 0796.73077
[2] Lancaster, P.; Salkauskas, K., Surfaces generated by moving least squares methods, Math. comput., 37, 155, 141-158, (1992) · Zbl 0469.41005
[3] Lu, Y.Y.; Belytschko, T.; Gu, L., A new implementation of the element free Galerkin method, Comput. methods appl. mech. engrg., 115, 227-286, (1994) · Zbl 0847.73064
[4] Belytschko, T.; Gu, L.; Lu, Y.Y., Fracture and crack growth by element-free Galerkin methods, Modeling simul. mater. sci. engrg., 2, 519-534, (1994)
[5] Terry, T.G., Fatigue crack propagation modeling using element free Galerkin method, ()
[6] MacKinnon, R.J.; Carey, G.F., Treatment of material discontinuities in finite element computations, Int. J. numer. methods engrg., 24, 393-417, (1987) · Zbl 0602.73065
[7] Chu, Y.A.; Moran, B., Application of the element-free Galerkin method to nucleation of solid-solid phase transformations, (), 135-149
[8] Chu, Y.A.; Moran, B., A computational model for nucleation of solid-solid phase transformations, Modeling simul. mater. sci. engrg., 3, 445-471, (1995)
[9] Beissel, S.R., Nodal integration of the element-free Galerkin method and related topics in the stability of computational mechanics, ()
[10] Y.A. Chu, Personal communications, 1994.
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