Study on Coupling of Smooth Particle Method with Finite Elements Based on Mesh–Particle Matching Degree

Study on Coupling of Smooth Particle Method with Finite Elements Based on Mesh–Particle Matching Degree

Jun Liu Pei Wang Anmin He

Institute of Applied Physics and Computational Mathematics, Beijing, China.

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| Citation



In this paper, a new algorithm coupling the finite element and smooth particle methods is proposed. It is an improved algorithm based on the hybrid coupling method. By calculating the mesh–particle matching degree, the new method can better deal with a poor mesh–particle matching relationship. The coupling algorithm can also ensure the transmission of tension and shear stress and the natural discon-nection of the contact surface. The comparison of impact simulation shows that the algorithm can deal with mesh–particle separation and re-compaction better, and the coupling interface force is smooth and non-oscillatory. Finally, the new coupling algorithm is applied to the detonation driving problem,  and the calculated results are in good agreement with the experimental results.


coupling method, finite element, smooth particle method, virtual particle.


[1] Attaway, S.W., Heinstein, M.W. & Swegle, J.W., Coupling of smoothed particle hydrodynamics with the finite element method. Post-SMIRT Impact IV Seminar, Berlin, Nuclear Engineering and Design, 150(2–3), pp. 199–205, 1994.

[2] Johnson, G.R., Linking of Lagrangian particle methods to standard finite element methods for high velocity impact computations. Nuclear Engineering & Design, 150(2–3), pp. 265–274, 1994.

[3] Johnson, G.R. & Holmquist, T.J., Evaluation of cylinder‐impact test data for constitu-tive model constants. Journal of Applied Physics, 64(8), pp. 3901–3910, 1988.

[4] Belytschko, T. & Xiao, S.P., A bridging domain method for coupling continua with molecular dynamic. Computer Methods in Applied Mechanics and Engineering, 193, pp. 17–20, 2004.

[5] Wagner, G.J. & Liu, W.k., Coupling of atomistic and continuum simulations using a bridging scale decomposition. Journal of Computational Physics, 190(1), pp. 249–274,

[6] Rabczuk, T., Xiao, S.P. & Sauer, M., Coupling of mesh-free methods with finite elements: basic concepts and test results. International Journal for Numerical Methods in Biomed- ical Engineering, 22(10), pp. 1031–1065, 2006.

[7] Gui, Y.L., Bui, H.H., kodikara, J., Zhang, Q.B., Zhao, J. & Rabczuk, T., Modelling the dynamic failure of brittle rocks using a hybrid continuum-discrete element method with a mixed-mode cohesive fracture model. International Journal of Impact Engineering, 87, pp. 146–155, 2016.

[8] Zhang, Z.C., Qiang, H.F. & Gao, W.A., A new SPH-FEM coupling method and Its application in impact dynamics. Explosion and Shock, 31(3), pp. 243–249, 2011.

[9] Menouillard, T. & Belytschko, T., Dynamic fracture with meshfree enriched XFEM. Acta Mechanica, 213(1–2), pp. 53–69, 2010.

[10] Zhang, C.Y., Gu, Y., Zhang S.W. & et al., Expansion and deformation characteristics of metal tubes driven by impact of detonation waves. Explosion and Shock Waves, 25(3), pp. 222–226, 2005.