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A level set enhanced natural kernel contact algorithm for impact and penetration modeling. (English) Zbl 1352.74139

Summary: A natural kernel contact (NKC) algorithm under the framework of the semi-Lagrangian reproducing kernel particle method (semi-Lagrangian RKPM) is proposed to model multi-body contact with specific consideration for impact and penetration modeling. The NKC algorithm utilizes the interaction of the semi-Lagrangian kernel functions associated with contacting bodies to serve as the non-penetration condition. The effects of friction are represented by introducing a layer of the friction-like elasto-plasticity material between contacting bodies. This approach allows the frictional contact conditions and the associated kinematics to be naturally embedded in the semi-Lagrangian RKPM inter-particle force calculation. The equivalence in the Karush-Kuhn-Tucker conditions between the proposed NKC algorithm and the conventional contact kinematic constraints as well as the associated state variable relationships are identified. A level set method is further introduced in the NKC algorithm to represent the contact surfaces without pre-defined potential contact surfaces. The stability analysis performed in this work shows that temporal stability in the semi-Lagrangian RKPM with NKC algorithms is related to the velocity gradient between contacting bodies. The proposed methods have been verified by several benchmark problems and applied to the simulation of impact and penetration processes.

MSC:

74H55 Stability of dynamical problems in solid mechanics
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[1] Johnson, Eroding interface and improved tetrahedral element algorithms for high-velocity impact computations in three dimensions, International Journal of Impact Engineering 5 pp 411– (1987)
[2] Belytschko, A three-dimensional impact-penetration algorithm with erosion, International Journal of Impact Engineering 5 pp 111– (1987) · Zbl 0603.73078
[3] Camacho, Adaptive Lagrangian modelling of ballistic penetration of metallic targets, Computer Methods in Applied Mechanics and Engineering 142 (3-4) pp 269– (1997) · Zbl 0892.73056
[4] Belytschko, Elastic crack growth in finite elements with minimal remeshing, International Journal for Numerical Methods in Engineering 45 (5) pp 601– (1999) · Zbl 0943.74061
[5] Moes, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering 46 (1) pp 131– (1999) · Zbl 0955.74066
[6] Wriggers, Finite element algorithms for contact problems, Archives of Computational Methods in Engineering 2 (4) pp 1– (1995) · Zbl 0840.73067
[7] Wriggers, Computational Contact Mechanics (2006) · Zbl 1104.74002
[8] Kikuchi, A smoothing technique for reduced integration penalty methods in contact problems, International Journal for Numerical Methods in Engineering 18 (3) pp 343– (1982) · Zbl 0479.73086
[9] Oden, Finite-element methods for constrained problems in elasticity, International Journal for Numerical Methods in Engineering 18 (5) pp 701– (1982) · Zbl 0486.73068
[10] Campos, A numerical-analysis of a class of contact problems with friction in elastostatics, Computer Methods in Applied Mechanics and Engineering 34 (1-3) pp 821– (1982) · Zbl 0504.73050
[11] Hughes, A finite element method for a class of contact-impact problems, Computer Methods in Applied Mechanics and Engineering 8 (3) pp 28– (1976) · Zbl 0367.73075
[12] Jones, A yield-limited Lagrange multiplier formulation for frictional contact, International Journal for Numerical Methods in Engineering 48 (8) pp 1127– (2000) · Zbl 0980.74064
[13] Simo, A perturbed Lagrangian formulation for the finite-element solution of contact problems, Computer Methods in Applied Mechanics and Engineering 50 (2) pp 163– (1985) · Zbl 0552.73097
[14] Simo, An augmented Lagrangian treatment of contact problems involving friction, Computers & Structures 42 (1) pp 97– (1992) · Zbl 0755.73085
[15] Pietrzak, Large deformation frictional contact mechanics: continuum formulation and augmented Lagrangian treatment, Computer Methods in Applied Mechanics and Engineering 177 (3-4) pp 351– (1999) · Zbl 0991.74047
[16] Johnson, Symmetric contact and sliding interface algorithms for intense impulsive loading computations, Computer Methods in Applied Mechanics and Engineering 190 (35-36) pp 4531– (2001) · Zbl 1002.74095
[17] Yang, A large deformation mortar formulation of self contact with finite sliding, Computer Methods in Applied Mechanics and Engineering 197 (6-8) pp 756– (2008) · Zbl 1169.74513
[18] Zeng, Numerical simulation method for elastic-plastic dynamic response for hypervelocity impact phenomena, International Journal of Impact Engineering 17 (4-6) pp 763– (1995)
[19] Benson, A single surface-contact algorithm for the post-buckling analysis of shell structures, Computer Methods in Applied Mechanics and Engineering 78 (2) pp 141– (1990) · Zbl 0708.73079
[20] Hallquist, Sliding interfaces with contact-impact in large-scale Lagrangian computations, Computer Methods in Applied Mechanics and Engineering 51 (1-3) pp 107– (1985) · Zbl 0567.73120
[21] Belytschko, Contact-impact by the pinball algorithm with penalty and Lagrangian-methods, International Journal for Numerical Methods in Engineering 31 (3) pp 547– (1991) · Zbl 0825.73984
[22] Belytschko, The splitting pinball method for contact-impact problems, Computer Methods in Applied Mechanics and Engineering 105 (3) pp 375– (1993) · Zbl 0774.73081
[23] Rabczuk, A three-dimensional large deformation meshfree method for arbitrary evolving cracks, Computer Methods in Applied Mechanics and Engineering 196 (29-30) pp 2777– (2007) · Zbl 1128.74051
[24] Chen, Large deformation analysis of rubber based on a reproducing kernel particle method, Computational Mechanics 19 (3) pp 211– (1997) · Zbl 0888.73073
[25] Chen, Reproducing kernel particle methods for large deformation analysis of non-linear structures, Computer Methods in Applied Mechanics and Engineering 139 (1-4) pp 195– (1996) · Zbl 0918.73330
[26] Chen, New boundary condition treatments in meshfree computation of contact problems, Computer Methods in Applied Mechanics and Engineering 187 (3-4) pp 441– (2000) · Zbl 0980.74077
[27] Guan, Semi-Lagrangian reproducing kernel particle method for fragment-impact problems, International Journal of Impact Engineering 38 (12) pp 1033– (2011)
[28] Chen, A Lagrangian reproducing kernel particle method for metal forming analysis, Computational Mechanics 22 (3) pp 289– (1998) · Zbl 0928.74115
[29] Randles, Smoothed particle hydrodynamics: some recent improvements and applications, Computer Methods in Applied Mechanics and Engineering 139 (1-4) pp 375– (1996) · Zbl 0896.73075
[30] Swegle, Smoothed particle hydrodynamics stability analysis, Journal of Computational Physics 116 (1) pp 123– (1995) · Zbl 0818.76071
[31] Monaghan, SPH without a tensile instability, Journal of Computational Physics 159 (2) pp 290– (2000) · Zbl 0980.76065
[32] Seo, Application of an improved contact algorithm for penetration analysis in SPH, International Journal of Impact Engineering 35 (6) pp 578– (2008)
[33] Belytschko, Element-free Galerkin methods, International Journal for Numerical Methods in Engineering 37 (2) pp 229– (1994) · Zbl 0796.73077
[34] Liu, Reproducing kernel particle methods, International Journal for Numerical Methods in Fluids 20 (8-9) pp 1081– (1995) · Zbl 0881.76072
[35] Chen, A stabilized conforming nodal integration for Galerkin mesh-free methods, International Journal for Numerical Methods in Engineering 50 (2) pp 435– (2001) · Zbl 1011.74081
[36] Chen, Non-linear version of stabilized conforming nodal integration for Galerkin mesh-free methods, International Journal for Numerical Methods in Engineering 53 (12) pp 2587– (2002) · Zbl 1098.74732
[37] Chen, Strain smoothing for stabilization and regularization of Galerkin meshfree method, Lecture Notes in Computational Science and Engineering 57 pp 57– (2006)
[38] Chen, An arbitrary order variationally consistent integration for Galerkin meshfree methods, International Journal for Numerical Methods in Engineering 95 (5) pp 387– (2013) · Zbl 1352.65481
[39] Kikuchi, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods (1988) · Zbl 0685.73002
[40] Osher, Fronts propagating with curvature-dependent speed-algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics 79 (1) pp 12– (1988) · Zbl 0659.65132
[41] Osher, Level Set Methods and Dynamic Implicit Surface (2002)
[42] Slawson TR Chen JS Chi SW Lee CH Roth MJ Nonlinear Meshfree Analysis Program (NMAP) Version 1.0 2012
[43] Parreira, Efficient algorithms and data structures for element-free Galerkin method, IEEE Transactions on Magnetics 42 (4) pp 659– (2006)
[44] Cartwright, Parallel support set searches for meshfree methods, SIAM Journal on Scientific Computing 28 (4) pp 1318– (2006) · Zbl 1120.65021
[45] Hughes, Finite rotation effects in numerical-integration of rate constitutive-equations arising in large-deformation analysis, International Journal for Numerical Methods in Engineering 15 (12) pp 1862– (1980) · Zbl 0463.73081
[46] Han, Error analysis of the reproducing kernel particle method, Computer Methods in Applied Mechanics and Engineering 190 (46-47) pp 6157– (2001) · Zbl 0992.65119
[47] Chen JS Chi SW Lee CH Lin SP Marodon C Roth MJ Slawson TR A multiscale meshfree approach for modeling fragment penetration into ultra high-strength concrete 2011
[48] Timoshenko, Theory of Elasticity (1934)
[49] Wilkins, Impact of cylinders on a rigid boundary, Journal of Applied Physics 44 (3) pp 1200– (1973)
[50] Unosson, Projectile penetration and perforation of high performance concrete: experimental results and macroscopic modelling, International Journal of Impact Engineering 32 (7) pp 1068– (2006)
[51] Adley MD Frank AO Danielson KT Akers SA O’Daniel JL The Advanced Fundamental Concrete (AFC) model Vicksburg, MS 2010
[52] Roth MJ Chen JS Slawson TR Boone RN Ren X Chi SW Lee CH Guan PC Multiscale RKPM formulation for modeling penetration of an ultra high-strength concrete materials Corfu, Greece 2011 125 134
[53] Unosson M Numerical simulations of penetration and perforation of high performance concrete with 75 mm steel projectile 2000
[54] Chen, Plasticity for Structural Engineers (1988)
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