An Eulerian particle level set method for compressible deforming solids with arbitrary EOS. (English) Zbl 1176.74202
Summary: In this study, an Eulerian, finite-volume method is developed for the numerical simulation of elastic-plastic response of compressible solid materials with arbitrary equation of state (EOS) under impact loading. The governing equations of mass, momentum, and energy along with evolution equations for deviatoric stresses are solved in Eulerian conservation law form. Since the position of material boundaries is determined implicitly by Eulerian schemes, the solution procedure is split into two separate subproblems, which are solved sequentially at each time step. First, the conserved variables are evolved in time with appropriate boundary conditions at the material interfaces. In the present work a fourth-order central weighted essentially non-oscillatory shock-capturing method that was developed for gas dynamics has been extended to high strain rate solids problems. In this method fluxes are determined on a staggered grid at places where solution is smooth. As a result, the method does not rely on the solution of Riemann problems but enjoys the flexibility of using any type of EOS. Boundary conditions at material interfaces are also treated by a special ghost cell approach. Then in the second subproblem, the position of material interfaces is advanced to the new time using a particle level set method. A fifth-order Godunov-type central scheme is used to solve the Hamilton-Jacobi equation of level sets in two space dimensions. The capabilities of the proposed method are evaluated at the end by comparing numerical results with the experimental results and the reported benchmark solutions for the Taylor rod impact, spherical groove jetting, and void collapse problems.
MSC:
| 74S10 | Finite volume methods applied to problems in solid mechanics |
| 74C15 | Large-strain, rate-independent theories of plasticity (including nonlinear plasticity) |
| 74J40 | Shocks and related discontinuities in solid mechanics |
| 74M20 | Impact in solid mechanics |
Keywords:
impact; particle level set; central weighted essentially non-oscillatory (CWENO); Hamilton-Jacobi equation (HJ)References:
| [1] | Zukas, Introduction to Hydrocodes (2004) · Zbl 1058.74007 |
| [2] | 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 · doi:10.1016/S0045-7825(96)01134-6 |
| [3] | Zhu, Unified and mixed formulation of the 4-node quadrilateral elements by assumed strain method: application to thermomechanical problems, International Journal for Numerical Methods in Engineering 38 (4) pp 685– (1995) · Zbl 0823.73074 · doi:10.1002/nme.1620380411 |
| [4] | Udaykumar, An Eulerian method for computation of multimaterial impact with ENO shock capturing and sharp interfaces, Journal of Computational Physics 186 (1) pp 136– (2003) · Zbl 1047.76558 · doi:10.1016/S0021-9991(03)00027-5 |
| [5] | Tran, A particle-level set-based sharp interface cartesian grid method for impact, penetration, and void collapse, Journal of Computational Physics 193 (2) pp 469– (2004) · Zbl 1109.74376 · doi:10.1016/j.jcp.2003.07.023 |
| [6] | Aymone, Simulation of 3D metal-forming using an arbitrary Lagrangian-Eulerian finite element method, Journal of Materials Processing Technology 110 (2) pp 218– (2001) · doi:10.1016/S0924-0136(00)00886-4 |
| [7] | Donea, An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions, Computer Methods in Applied Mechanics and Engineering 33 (1-3) pp 689– (1982) · Zbl 0508.73063 · doi:10.1016/0045-7825(82)90128-1 |
| [8] | Harten, Uniformly high-order accurate essentially nonoscillatory schemes, III, Journal of Computational Physics 71 (2) pp 231– (1987) · Zbl 0652.65067 · doi:10.1016/0021-9991(87)90031-3 |
| [9] | Nessyahu, Non-oscillatory central differencing for hyperbolic conservation laws, Journal of Computational Physics 87 (2) pp 408– (1990) · Zbl 0697.65068 · doi:10.1016/0021-9991(90)90260-8 |
| [10] | Cooper, A numerical exploration of the role of void geometry on void collapse and hot spot formation in ductile materials, International Journal of Plasticity 16 (5) pp 525– (2000) · Zbl 1043.74519 · doi:10.1016/S0749-6419(99)00072-8 |
| [11] | Youngs, Numerical Methods for Fluid Dynamics pp 273– (1982) |
| [12] | Fedkiw, A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the Ghost fluid method), Journal of Computational Physics 152 (2) pp 457– (1999) · Zbl 0957.76052 · doi:10.1006/jcph.1999.6236 |
| [13] | Liu, Convex ENO high order multi-dimensional schemes without field by field decomposition or staggered grids, Journal of Computational Physics 142 (2) pp 304– (1998) · Zbl 0941.65082 · doi:10.1006/jcph.1998.5937 |
| [14] | Levy, Fourth-order central WENO scheme for multidimensional hyperbolic systems of conservation laws, SIAM Journal on Scientific Computing (SISC) 24 (2) pp 480– (2002) · Zbl 1014.65079 · doi:10.1137/S1064827501385852 |
| [15] | Enright, A hybrid particle level set method for improved interface capturing, Journal of Computational Physics 183 (1) pp 83– (2002) · Zbl 1021.76044 · doi:10.1006/jcph.2002.7166 |
| [16] | Johnson, Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, Engineering Fracture Mechanics 21 (1) pp 31– (1985) · doi:10.1016/0013-7944(85)90052-9 |
| [17] | Ponthot, An extension of the radial return algorithm to account for rate-dependent effects in frictional contact and visco-plasticity, Journal of Materials Processing Technology 80-81 pp 628– (1998) · doi:10.1016/S0924-0136(98)00125-3 |
| [18] | Zennaro, Natural continuous extensions of Runge-Kutta methods, Mathematics of Computation 46 (173) pp 119– (1986) · Zbl 0608.65043 · doi:10.2307/2008218 |
| [19] | Bryson, High-order central WENO schemes for multidimensional Hamilton-Jacobi equations, SIAM Journal on Numerical Analysis (SINUM) 41 (4) pp 1339– (2003) · Zbl 1050.65076 · doi:10.1137/S0036142902408404 |
| [20] | Gravouil, Non-planar 3D crack growth by the extended finite element and level sets-Part II: level set update, International Journal for Numerical Methods in Engineering 53 pp 2569– (2002) · Zbl 1169.74621 · doi:10.1002/nme.430 |
| [21] | Osher, The Level Set Methods and Dynamic Implicit Surfaces (2002) |
| [22] | Sethian, Level Set Methods and Fast Marching Methods (1999) · Zbl 0929.65066 |
| [23] | Sussman, A level set approach for computing solutions to incompressible two-phase flow, Journal of Computational Physics 114 (1) pp 146– (1994) · Zbl 0808.76077 · doi:10.1006/jcph.1994.1155 |
| [24] | Shu, Efficient implementation of essentially non-oscillatory shock-capturing schemes, Journal of Computational Physics 77 (2) pp 439– (1988) · Zbl 0653.65072 · doi:10.1016/0021-9991(88)90177-5 |
| [25] | Brunig, Numerical simulation of Taylor impact tests, International Journal of Plasticity 23 pp 1979– (2007) · Zbl 1134.74010 · doi:10.1016/j.ijplas.2007.01.012 |
| [26] | Chapman, Shock induced void nucleation during Taylor impact, International Journal of Fracture 134 (1) pp 41– (2005) · doi:10.1007/s10704-005-7151-1 |
| [27] | Lu, Taylor impact test for ductile porous materials-Part 1: theory, International Journal of Impact Engineering 25 (10) pp 981– (2001) · doi:10.1016/S0734-743X(01)00027-6 |
| [28] | Wang, Taylor impact test for ductile porous materials-Part 2: experiments, International Journal of Impact Engineering 28 (5) pp 499– (2003) · doi:10.1016/S0734-743X(02)00105-7 |
| [29] | Mali, Flow of metals with a hemispherical indentation under the action of shock waves, Combustion, Explosion, and Shock Waves 9 (2) pp 241– (1973) · doi:10.1007/BF00814821 |
| [30] | Deribas, Investigation of the shock damping process in metals under contact explosion loading, Combustion, Explosion, and Shock Waves 15 (2) pp 220– (1979) · doi:10.1007/BF00790449 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
