Coupling of mesh-free methods with finite elements: basic concepts and test results

• Published in: Communications in numerical methods in engineering Vol. 22; no. 10; pp. 1031 - 1065
• Main Authors: Rabczuk, T., Xiao, S. P., Sauer, M.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.10.2006; Wiley
• Subjects: adaptivity; Boundaries; Computational techniques; Consistency; Dynamic tests; EFG; Exact sciences and technology; Finite element method; Fundamental areas of phenomenology (including applications); Joining; Mathematical analysis; Mathematical methods in physics; mesh-free particle methods; Meshless methods; Physics; Shape functions; SPH; High strain; Smoothed particle hydrodynamics method; EFG; Master slave relationship; SPH; Experimental study; Finite element method; Crack bridging; Lagrange multiplier; Particle method; adaptivity; Granular materials; Meshless method; Modelling; Least square fit; mesh-free particle methods
• ISSN: 1069-8299; 1099-0887; 1099-0887
• DOI: 10.1002/cnm.871

This paper reviews several novel and older methods for coupling mesh‐free particle methods, particularly the element‐free Galerkin (EFG) method and the smooth particle hydrodynamics (SPH), with finite elements (FEs). We study master–slave couplings where particles are fixed across the FE boundary, coupling via interface shape functions such that consistency conditions are satisfied, bridging domain coupling, compatibility coupling with Lagrange multipliers and hybrid coupling methods where forces from the particles are applied via their shape functions on the FE nodes and vice versa. The hybrid coupling methods are well suited for large deformations and adaptivity and the coupling procedure is independent of the particle distance and nodal arrangement. We will study the methods for several static and dynamic applications, compare the results to analytical and experimental data and show advantages and drawbacks of the methods. Copyright © 2006 John Wiley & Sons, Ltd.