journal article·2026-06

A dual-mesh virtual element particle method for simulating extreme deformation problems

Ruopu Zhou, Zhixin Zeng, Xiong Zhang

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OpenAlex topics: Fluid Dynamics Simulations and Interactions · Advanced Numerical Methods in Computational Mathematics · Composite Material Mechanics

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References (54)

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1. Aldakheel, F., Hudobivnik, B., Hussein, A., Wriggers, P.: Phase-field modeling of brittle fracture using an efficient virtual element scheme. Comput. Methods Appl. Mech. Eng. 341, 443–466 (2018). https://doi.org/10.1016/j.cma.2018.07.00810.1016/j.cma.2018.07.008 ↗
2. Artioli, E., da Veiga, L.B., Lovadina, C., Sacco, E.: Arbitrary order 2D virtual elements for polygonal meshes: part II, inelastic problem. Comput. Mech. 60(4), 643–657 (2017). https://doi.org/10.1007/s00466-017-1429-910.1007/s00466-017-1429-9 ↗
3. Beir, L., Brezzi, F., Arabia, S.: Basic principles of virtual element methods. Math. Models Methods Appl. Sci. 23, 199–214 (2013)10.1142/S0218202512500492 ↗
4. Beirão da Veiga, L., Brezzi, F., Cangiani, A., Manzini, G., Marini, L.D., Russo, A.: Basic principles of virtual element methods. Math. Models Methods Appl. Sci. 23(01), 199–214 (2013). https://doi.org/10.1142/S021820251250049210.1142/S0218202512500492 ↗
5. Beirão da Veiga, L., Brezzi, F., Marini, L.D., Russo, A.: The hitchhiker’s guide to the virtual element method. Math. Models Methods Appl. Sci. 24(08), 1541–1573 (2014). https://doi.org/10.1142/S021820251440003X10.1142/S021820251440003X ↗
6. Beirão da Veiga, L., Lovadina, C., Russo, A.: Stability analysis for the virtual element method. Math. Models Methods Appl. Sci. 27(13), 2557–2594 (2017). https://doi.org/10.1142/S021820251750052X10.1142/S021820251750052X ↗
7. Benvenuti, E., Chiozzi, A., Manzini, G., Sukumar, N.: Extended virtual element method for two-dimensional linear elastic fracture. Comput. Methods Appl. Mech. Eng. 390, 114352 (2022). https://doi.org/10.1016/j.cma.2021.11435210.1016/j.cma.2021.114352 ↗
8. Böhm, C., Munk, L., Hudobivnik, B., Aldakheel, F., Korelc, J., Wriggers, P.: Virtual elements for computational anisotropic crystal plasticity. Comput. Methods Appl. Mech. Eng. 405, 115835 (2023)10.1016/j.cma.2022.115835 ↗
9. Bui, H.H., Fukagawa, R., Sako, K., Ohno, S.: Lagrangian meshfree particles method (sph) for large deformation and failure flows of geomaterial using elastic-plastic soil constitutive model. Int. J. Numer. Anal. Meth. Geomech. 32(12), 1537–1570 (2008). https://doi.org/10.1002/nag.68810.1002/nag.688 ↗
10. Chen, D., Huang, W., Sloan, S.W.: An alternative updated Lagrangian formulation for finite particle method. Comput. Methods Appl. Mech. Eng. 343, 490–505 (2019). https://doi.org/10.1016/j.cma.2018.09.00110.1016/j.cma.2018.09.001 ↗
11. Chi, H., da Veiga, L.B., Paulino, G.: Some basic formulations of the virtual element method (VEM) for finite deformations. Comput. Methods Appl. Mech. Eng. 318, 148–192 (2017). https://doi.org/10.1016/j.cma.2016.12.02010.1016/j.cma.2016.12.020 ↗
12. Chi, H., Pereira, A., Menezes, I.F., Paulino, G.H.: Virtual element method (VEM)-based topology optimization: an integrated framework. Struct. Multidiscip. Optim. 62(3), 1089–1114 (2020)10.1007/s00158-019-02268-w ↗
13. Cihan, M., Hudobivnik, B., Aldakheel, F., Wriggers, P.: 3D mixed virtual element formulation for dynamic elasto-plastic analysis. Comput. Mech. 68(3), 1–18 (2021). https://doi.org/10.1007/s00466-021-02010-810.1007/s00466-021-02010-8 ↗
14. Cihan, M., Hudobivnik, B., Korelc, J., Wriggers, P.: A virtual element method for 3D contact problems with non-conforming meshes. Comput. Methods Appl. Mech. Eng. 402, 115385 (2022). A Special Issue in Honor of the Lifetime Achievements of J. Tinsley Oden. https://doi.org/10.1016/j.cma.2022.11538510.1016/j.cma.2022.115385 ↗
15. Dassi, F., Mascotto, L.: Exploring high-order three dimensional virtual elements: bases and stabilizations. Comput. Math. Appl. 75(9), 3379–3401 (2018)10.1016/j.camwa.2018.02.005 ↗
16. De Bellis, M., Wriggers, P., Hudobivnik, B.: Serendipity virtual element formulation for nonlinear elasticity. Comput. Struct. 223, 106094 (2019). https://doi.org/10.1016/j.compstruc.2019.07.00310.1016/j.compstruc.2019.07.003 ↗
17. Drucker, D.C., Prager, W.: Soil mechanics and plastic analysis or limit design. Q. Appl. Math. 10(2), 157–65 (2013)10.1090/qam/48291 ↗
18. Einav, I.: The unification of hypo-plastic and elasto-plastic theories. Int. J. Solids Struct. 49(11), 1305–1315 (2012). https://doi.org/10.1016/j.ijsolstr.2012.02.00310.1016/j.ijsolstr.2012.02.003 ↗
19. Fish, J., Shek, K.: Computational aspects of incrementally objective algorithms for large deformation plasticity. Int. J. Numer. Methods Eng. 44(6), 839–851 (1999)10.1002/(SICI)1097-0207(19990228)44:6<839::AID-NME533>3.0.CO;2-C ↗
20. Gain, A.L., Talischi, C., Paulino, G.H.: On the virtual element method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes. Comput. Methods Appl. Mech. Eng. 282, 132–160 (2014)10.1016/j.cma.2014.05.005 ↗
21. Gain, A.L., Paulino, G.H., Duarte, L.S., Menezes, I.F.: Topology optimization using polytopes. Comput. Methods Appl. Mech. Eng. 293, 411–430 (2015). https://doi.org/10.1016/j.cma.2015.05.00710.1016/j.cma.2015.05.007 ↗
22. Gu, Y.: An adaptive local meshfree updated Lagrangian approach for large deformation analysis of metal forming. Adv. Mater. Res. 97–101, 2664–2667 (2010)10.4028/www.scientific.net/AMR.97-101.2664 ↗
23. Harlow, F.: The particle-in-cell computing method for fluid dynamics. Methods Comput. Phys. 3, 319–343 (1964)
24. Hut, P., Makino, J., McMillan, S.L.W.: Building a better leapfrog. Astrophys. J. 443 (1995)10.1086/187844 ↗
25. Johnson, G.R., Holmquist, T.J.: Evaluation of cylinder-impact test data for constitutive model constants. J. Appl. Phys. 64(8), 3901–3910 (1988)10.1063/1.341344 ↗
26. Kury, J., Hornig, H., Lee, E., McDonnel, J., Ornellas, D., Finger, M., Strange, F., Wilkins, M.: Metal acceleration by chemical explosives, in: fourth symposium (International) on Detonation, US Government Printing Office Washington, DC, pp. 3–13 (1965)
27. Lamperti, A., Cremonesi, M., Perego, U., Russo, A., Lovadina, C.: A hu-washizu variational approach to self-stabilized virtual elements: 2d linear elastostatics. Comput. Mech. 71(5), 935–955 (2023)10.1007/s00466-023-02282-2 ↗
28. Lee, B., Tarng, Y., Ma, S.: Modeling of the process damping force in chatter vibration. Int. J. Mach. Tools Manuf. 35(7), 951–962 (1995). https://doi.org/10.1016/0890-6955(94)00046-M10.1016/0890-6955(94)00046-M ↗
29. Lian, Y., Zhang, X.: A Coupled Finite Element Material Point Method for Large Deformation Problems, 7, 251–288 (2018). https://doi.org/10.1142/9781786344786_000710.1142/9781786344786_0007 ↗
30. Lian, Y., Zhang, X., Zhou, X., Ma, Z.: A FEMP method and its application in modeling dynamic response of reinforced concrete subjected to impact loading. Comput. Methods Appl. Mech. Eng. 200(17), 1659–1670 (2011). https://doi.org/10.1016/j.cma.2011.01.01910.1016/j.cma.2011.01.019 ↗
31. Liu, C., Sun, Q., Zhou, G.G.: Coupling of material point method and discrete element method for granular flows impacting simulations. Int. J. Numer. Methods Eng. 115(2), 172–188 (2018). https://doi.org/10.1002/nme.580010.1002/nme.5800 ↗
32. Liu, T.-R., Aldakheel, F., Aliabadi, M.: Virtual element method for phase field modeling of dynamic fracture. Comput. Methods Appl. Mech. Eng. 411, 116050 (2023). https://doi.org/10.1016/j.cma.2023.11605010.1016/j.cma.2023.116050 ↗
33. Ma, S., Zhang, X., Qiu, X.: Comparison study of mpm and sph in modeling hypervelocity impact problems. Int. J. Impact Eng. 36(2), 272–282 (2009). https://doi.org/10.1016/j.ijimpeng.2008.07.00110.1016/j.ijimpeng.2008.07.001 ↗
34. Ma, Z.T., Zhang, X., Huang, P.: An object-oriented MPM framework for simulation of large deformation and contact of numerous grains. CMES-Comput. Model. Eng. Sci. 55, 61–88 (2010)
35. Marino, M., Hudobivnik, B., Wriggers, P.: Computational homogenization of polycrystalline materials with the virtual element method. Comput. Methods Appl. Mech. Eng. 355, 349–372 (2019). https://doi.org/10.1016/j.cma.2019.06.00410.1016/j.cma.2019.06.004 ↗
36. Nguyen, V.P., de Vaucorbeil, A., Nguyen-Thanh, C., Mandal, T.K.: A generalized particle in cell method for explicit solid dynamics. Comput. Methods Appl. Mech. Eng. 371, 113308 (2020). https://doi.org/10.1016/j.cma.2020.11330810.1016/j.cma.2020.113308 ↗
37. Park, K., Chi, H., Paulino, G.H.: On nonconvex meshes for elastodynamics using virtual element methods with explicit time integration. Comput. Methods Appl. Mech. Eng. 356, 669–684 (2019). https://doi.org/10.1016/j.cma.2019.06.03110.1016/j.cma.2019.06.031 ↗
38. Park, K., Chi, H., Paulino, G.H.: Numerical recipes for elastodynamic virtual element methods with explicit time integration. Int. J. Numer. Methods Eng. 121(1), 1–31 (2020)10.1002/nme.6173 ↗
39. Raftenberg, M.N.: Modeling RHA plate perforation by a shaped charge jet, Tech. Rep. BRL-TR-3363, U.S. Army Ballistic Research Laboratory (1992). https://api.semanticscholar.org/CorpusID:136896888
40. Sulsky, D., Chen, Z., Schreyer, H.L.: A particle method for history-dependent materials. Comput. Methods Appl. Mech. Eng. 118(1–2), 179–196 (1994)10.1016/0045-7825(94)90112-0 ↗
41. Sun, Z., Zeng, Z., Li, J., Zhang, X.: An immersed multi-material arbitrary Lagrangian–Eulerian finite element method for fluid-structure-interaction problems. Comput. Methods Appl. Mech. Eng. 432, 117398 (2024a). https://doi.org/10.1016/j.cma.2024.11739810.1016/j.cma.2024.117398 ↗
42. Sun, Z., Ni, R., Zeng, Z., Zhang, X.: A localized subdomain smoothing mmale particle method for efficient modeling fsi problems. Comput. Methods Appl. Mech. Eng. 419, 116676 (2024b). https://doi.org/10.1016/j.cma.2023.11667610.1016/j.cma.2023.116676 ↗
43. Tang, T., Gu, Y., Li, Q., Hua, J., Sun, X.: Expanding fracture of steel cylinder shell by detonation driving. Explosion Shock Waves (06) (2003) 529–533
44. Truesdell, C., Noll, W.: The Non-Linear Field Theories of Mechanics. Springer, Berlin (1992)10.1007/978-3-662-13183-1 ↗
45. van Huyssteen, D., Reddy, B.: A virtual element method for transversely isotropic hyperelasticity. Comput. Methods Appl. Mech. Eng. 386, 114108 (2021). https://doi.org/10.1016/j.cma.2021.11410810.1016/j.cma.2021.114108 ↗
46. Wriggers, P., Rust, W.T., Reddy, B.D.: A virtual element method for contact. Comput. Mech. 58(6), 1039–1050 (2016). https://doi.org/10.1007/s00466-016-1331-x10.1007/s00466-016-1331-x ↗
47. Xiao, M., Liu, C., Sun, W.: Dp-mpm: Domain partitioning material point method for evolving multi-body thermal-mechanical contacts during dynamic fracture and fragmentation. Comput. Methods Appl. Mech. Eng. 385, 114063 (2021). https://doi.org/10.1016/j.cma.2021.11406310.1016/j.cma.2021.114063 ↗
48. Xu, B.-B., Peng, F., Junker, P., Wriggers, P.: Virtual element method with non-matching and adaptive meshes for phase field fracture. Comput. Mech. 1–14 (2025)10.1007/s00466-025-02665-7 ↗
49. Xu, B.-B., Peng, F., Wriggers, P.: Stabilization-free virtual element method for 3d hyperelastic problems. Comput. Mech. 1–15 (2024)10.1002/nme.7490 ↗
50. Xu, B.-B., Wriggers, P.: 3D stabilization-free virtual element method for linear elastic analysis. Comput. Methods Appl. Mech. Eng. 421, 116826 (2024). https://doi.org/10.1016/j.cma.2024.11682610.1016/j.cma.2024.116826 ↗
51. Xu, B.-B., Peng, F., Wriggers, P.: Stabilization-free virtual element method for finite strain applications. Comput. Methods Appl. Mech. Eng. 417, 116555 (2023). https://doi.org/10.1016/j.cma.2023.11655510.1016/j.cma.2023.116555 ↗
52. Yang, P., Liu, Y., Zhang, X., Zhou, X., Zhao, Y.: Simulation of fragmentation with material point method based on Gurson model and random failure. Comput. Model. Eng. Sci. 85(3), 207–238 (2012). https://doi.org/10.3970/cmes.2012.085.20710.3970/cmes.2012.085.207 ↗
53. Zhang, X., Chen, Z., Liu, Y.: The Material Point Method: A Continuum-Based Particle Method for Extreme Loading Cases. Academic Press, New York (2016)10.1016/B978-0-12-407716-4.00003-X ↗
54. Zhou, R., Zeng, Z., Zhang, X.: Explicit dual-mesh virtual element method for 2d nonlinear dynamic problems. Comput. Methods Appl. Mech. Eng. 439, 117893 (2025). https://doi.org/10.1016/j.cma.2025.11789310.1016/j.cma.2025.117893 ↗