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A mesh-grading material point method and its parallelization for problems with localized extreme deformation. (English) Zbl 1423.74901

Summary: As a kind of meshless method, material point method (MPM) applies an Eulerian background grid served as a finite element mesh in each time step, and therefore its accuracy and efficiency are mainly dependent on the cell size setting of background grid. However, the conventional MPM commonly uses a regular background grid with uniform cells, which is not apposite for localized extreme deformation problems from the view point of computation efficiency, where, in fact, a local refined background grid is preferable. Hence, a mesh-grading material point method (MGMPM) is proposed here for such problems to supply MPM with the ability for local refinement simulation. The edge displacement continuity associated with mesh grading is embedded in the nodal shape functions. Besides, the truss element is incorporated into MGMPM to model the steel reinforcement bars in reinforced concrete impacting problems, based on our previous work. Furthermore, the proposed method is parallelized using OpenMP (Open Multi-Processing) to take advantage of PC power with multi-core and hyper threading technologies for large scale engineering problems, where both loop-level parallelism and code-block parallelism are used. Several numerical examples including stress wave propagation, Taylor bar impact, and penetration problems, are studied, which show that the efficiency of MGMPM is much higher than that of conventional MPM, and with lower memory requirement.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65Y05 Parallel numerical computation

Software:

MPM3D; MPM3DMP
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Monaghan, J. J., An introduction to SPH, Comput. Phys. Comm., 48, 89-96 (1988) · Zbl 0673.76089
[2] Liu, M. B.; Liu, G. R., Smoothed particle hydrodynamics (SPH): an overview and recent developments, Arch. Comput. Methods Eng., 17, 25-76 (2010) · Zbl 1348.76117
[3] Rafiee, A.; Thiagarajan, K. P., An SPH projection method for simulating fluid-hypoelastic structure interaction, Comput. Methods Appl. Mech. Engrg., 198, 33-36, 2785-2795 (2009) · Zbl 1228.76117
[4] Belytschko, T.; Lu, Y. Y.; Gu, L., Element free Galerkin methods, Internat. J. Numer. Methods Engrg., 37, 229-256 (1994) · Zbl 0796.73077
[5] Pan, X. F.; Yuan, H., Computational algorithm and application of element-free Galerkin methods for nonlocal damage models, Eng. Fract. Mech., 77, 2640-2653 (2010)
[6] Liu, W. K.; Chen, Y. J., Wavelet and multiple scale reproducing kernel methods, Internat. J. Numer. Methods Fluids, 21, 10, 901-931 (1995) · Zbl 0885.76078
[7] Chen, J. S.; Pan, C.; Roque, C. M.O. L.; Wang, H. P., A Lagrangian reproducing kernel particle method for metal form analysis, Comput. Mech., 22, 3, 289-307 (1998) · Zbl 0928.74115
[8] Sulsky, D.; Chen, Z.; Schreyer, H. L., A particle method for history-dependent materials, Comput. Methods Appl. Mech. Engrg., 118, 1-2, 179-196 (1994) · Zbl 0851.73078
[9] Bardenhagen, S. G.; Kober, E. M., The generalized interpolation material point method, CMES Comput. Model. Eng. Sci., 5, 6, 477-495 (2004)
[10] Silling, S. A.; Epton, M.; Weckner, O.; Xu, J.; Askari, E., Peridynamic states and constitutive modeling, J. Elasticity, 88, 151-184 (2007) · Zbl 1120.74003
[11] Foster, J. T.; Silling, S. A.; Chen, W. W., Visoplasticity using peridynamics, Internat. J. Numer. Methods Engrg., 81, 1242-1258 (2010) · Zbl 1183.74035
[12] Bessa, M. A.; Foster, J. T.; Belytschko, T.; Liu, W. K., A meshfree unification: reproducing kernel peridynamics, Comput. Mech., 53, 1251-1264 (2014) · Zbl 1398.74452
[13] Ma, S.; Zhang, X.; Qiu, X. M., Comparison study of MPM and SPH in modeling hypervelocity impact problems, Int. J. Impact. Eng., 36, 272-282 (2009)
[14] Hu, W. Q.; Chen, Z., Model-based simulation of the synergistic effects of blast and fragmentation on a concrete wall using the MPM, Int. J. Impact. Eng., 32, 12, 2066-2096 (2006)
[15] Lian, Y. P.; Zhang, X.; Zhou, X.; Ma, S.; Zhao, Y. L., Numerical simulation of explosively driven metal by material point method, Int. J. Impact. Eng., 38, 237-245 (2011)
[16] Nairn, J. A., On the calculation of energy release rates for cracked laminates with residual stresses, Int. J. Fract., 139, 267-293 (2006) · Zbl 1197.74119
[17] Yang, P. F.; Liu, Y.; Zhang, X.; Zhou, X.; Zhao, Y. L., Simulation of fragmentation with material point method based on Gurson model and random failure, CMES Comput. Model. Eng. Sci., 85, 3, 207-236 (2012) · Zbl 1356.74013
[18] Guilkey, J. E.; Hoying, J. B.; Weiss, J. A., Computational modeling of multicellular constructs with the material point method, J. Biomech., 39, 2074-2086 (2006)
[19] Zhou, S. Z.; Zhang, X.; Ma, H. L., Numerical simulation of human head impact using the material point, Int. J. Comput. Methods, 10, 04, 1350014 (2013) · Zbl 1359.92072
[20] Guillkey, J. E.; Harman, T. B.; Banerjee, B., An Eulerian-Lagrangian approach for simulating explosions of energetic devices, Comput. Struct., 85, 660-674 (2007)
[21] Gan, Y.; Chen, Z.; Smith, S. M., Improved material point method for simulating the zona failure response in piezo-assisted intracytoplasmic sperm injection, CMES Comput. Model. Eng. Sci., 73, 1, 45-76 (2011) · Zbl 1223.74046
[22] Liu, Y.; Wang, H. K.; Zhang, X., A multiscale framework for high-velocity impact process with combined material point method and molecular dynamics, Int. J. Mech. Mater. Des., 9, 127-139 (2013)
[23] Chen, Z.; Jiang, S.; Gan, Y.; Liu, H. T.; Sewell, T. D., A particle-based multiscale simulation procedure within the material point method framework, Comp. Part. Mech. (2014)
[24] Andersen, S.; Andersen, L., Modelling of landslides with the material-point method, Comput. Geosci., 14, 137-147 (2010) · Zbl 1185.76898
[25] Ma, J.; Wang, D.; Randolph, M. F., A new contact algorithm in the material point mehtod for geotechnical simulations, Int. J. Numer. Anal. Methods Geomech. (2014)
[26] Sadeghirad, A.; Brannon, R. M.; Burghardt, J., A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive de-formations, Internat. J. Numer. Methods Engrg., 86, 1435-1456 (2011) · Zbl 1235.74371
[27] Zhang, D. Z.; Ma, X.; Giguere, P. T., Material point method enhanced by modified gradient of shape function, J. Comput. Phys., 230, 6379-6398 (2011) · Zbl 1419.76513
[28] Bardenhagen, S. G.; Brackbill, J. U.; Sulsky, D., The material-point method for granular materials, Comput. Methods Appl. Mech. Engrg., 187, 3-4, 529-541 (2000) · Zbl 0971.76070
[29] Bardenhagen, S. G.; Guilkey, J. E.; Roessig, K. M.; Brackbill, J. U.; Witzel, W. M.; Foster, J. C., An improved contact algorithm for the material point method and application to stress propagation in granular material, CMES Comput. Model. Eng. Sci., 2, 4, 509-522 (2001) · Zbl 1147.74375
[30] Huang, P.; Zhang, X.; Ma, S.; Huang, X., Contact algorithms for the material point method in impact and penetration simulation, Internat. J. Numer. Methods Engrg., 85, 4, 498-517 (2011) · Zbl 1217.74145
[31] Lian, Y. P.; Zhang, X.; Liu, Y., Coupling of finite element method with material point method by local multi-mesh contact method, Comput. Methods Appl. Mech. Engrg., 200, 3482-3494 (2011) · Zbl 1230.74187
[32] Lian, Y. P.; Zhang, X.; Liu, Y., An adaptive finite element material point method and its application in extreme deformation problems, Comput. Methods Appl. Mech. Engrg., 241-244, 1, 275-285 (2012) · Zbl 1353.74072
[33] Cui, X. X.; Zhang, X.; Zhou, X.; Liu, Y.; Zhang, F., A coupled finite difference material point mehtod and its application in explosion simulation, CMES Comput. Model. Eng. Sci., 98, 565-599 (2014) · Zbl 1356.80062
[34] Lian, Y. P.; Zhang, X.; Zhang, F.; Cui, X. X., Tied interface grid material point method for problems with localized extreme deformation, Int. J. Impact Eng., 70, 50-61 (2014)
[35] Huang, P.; Zhang, X.; Ma, S., Shared memory OpenMP parallelization of explicit mpm and its application to hypervelocity impact, CMES Comput. Model. Eng. Sci., 38, 119-147 (2008) · Zbl 1357.74082
[36] Zhang, Y. T.; Zhang, X.; Liu, Y., An alternated grid updating parallel algorithm for material point method using OpenMP, CMES Comput. Model. Eng. Sci., 69, 2, 143-165 (2010)
[37] Lian, Y. P.; Zhang, X.; Zhou, X.; Ma, Z. T., A FEMP method and its application in modeling dynamic response of reinforced concrete subjected to impact loading, Comput. Methods Appl. Mech. Engrg., 200, 17-20, 1659-1670 (2011) · Zbl 1228.74116
[38] McDill, J. M.; Goldak, J. A.; Oddy, A. S.; Bibby, M. J., Isoparametric quadrilaterals and hexahedrons for mesh-grading algorithms, Int. J. Numer. Methods Bio., 3, 2, 155-163 (1987) · Zbl 0605.73069
[39] Bardenhagen, S. G., Energy conservation error in the material point method for solid mechanics, J. Comput. Phys., 180, 383-403 (2002) · Zbl 1061.74057
[40] Johnson, G. R.; Holmquist, T. J., Evaluation of cylinder-impact test data for constitutive model constants, J. Appl. Phys., 64, 8, 3901-3910 (1988)
[41] Hanchak, S. J.; Forrestal, M. J.; Young, E. R.; Ehrgott, J. Q., Perforation of concrete slabs with 48 MPa (7ksi) and 140 MPa (20ksi) unconfined compressive strengths, Int. J. Impact Eng., 12, 1, 1-7 (1992)
[42] T.J. Holmquist, G.R. Johnson, W.H. Cook, A computational constitutive model for concrete subjected to large strains, high strain rates, and high pressures, in: 14th International Symposium on Ballistics Quebec, Candan, 26-29 September 1993, 1993.; T.J. Holmquist, G.R. Johnson, W.H. Cook, A computational constitutive model for concrete subjected to large strains, high strain rates, and high pressures, in: 14th International Symposium on Ballistics Quebec, Candan, 26-29 September 1993, 1993.
[43] Ma, Z.; 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, 1, 61-87 (2010)
[44] Piekutowski, A. J.; Forrestal, M. J.; Poormon, K. L.; Warren, T. L., Perforation of aluminum plates with ogive-nose steel rods at normal and oblique impacts, Int. J. Impact Eng., 18, 877-887 (1996)
[45] Meyers, M. A., Dynamic Behavior of Materials, 133 (1994), John Wiley & Sons: John Wiley & Sons New York
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