A MMALE Method Based on Interface Reconstruction for Three-dimensional Elastic-Plastic Multi-material Flow

doi:10.19596/j.cnki.1001-246x.8799

Abstract

Abstract:

The MMALE (multi-material Arbitrary Lagrangian Eulerian method) is an effective method for the simulation of multi-material flow with large deformation. Traditional MMALE methods are mainly used in pure fluids and focus on two-dimensional problems. In this paper, we propose a three-dimensional MMALE algorithm for elastic-plastic fluids by developing three key technologies: a closure model for elastic-plastic flow, an interface reconstruction method adapted to three-dimensional grids with large deformation, and a physical property preserving remapping method for elastic-plastic quantities. Firstly, to solve the pressure imbalance problem caused by elastic-plastic fluids using traditional bulk modulus weighted closure models, a relaxation mechanism is introduced in our new closure model to achieve the balance of the pressure. At the same time, this model does not require iterations, avoiding the difficulties of non convergence that may be encountered during the iteration process; Secondly, in order to address the conservation issues caused by distorted three-dimensional polyhedral grids, a step-by-step surface triangulation algorithm is introduced to preserve the conservation during the interface reconstruction process. Thirdly, in the aspect of the remapping of elastic-plastic quantities, aiming at the problem that the tensor property is destroyed and the strain energy is not conserved after the deviator stress is remapped component by component, the remapping of invariants of the stress tensor is introduced to preserve the tensor property and maintain the conservation of the strain energy. Finally, the MMALE method is used to simulate several typical examples, and its correctness and robustness are verified.

Key words: elastic-plastic, multiple material, interface reconstruction, MMALE

CLC Number:

Shaodong GUO, Haibing ZHOU, Jun XIONG. A MMALE Method Based on Interface Reconstruction for Three-dimensional Elastic-Plastic Multi-material Flow[J]. Chinese Journal of Computational Physics, 2024, 41(5): 607-618.

Figures/Tables 21

Fig.1 Flow chart of elastic-plastic MMALE method

Fig.2 Progressive surface triangulation

Fig.3 Interface reconstruction on non convex polyhedral grid

Fig.4 Initial distribution of vacuum Riemann problem(t=0)

Fig.5 Density and pressure of MMALE simulation and analytical solution with t=2.5

Fig.6 Pressure with time by two mixed closure models (a) bulk modulus weighted model; (b) our model

Fig.7 Equivalent plastic strain by two methods

Fig.8 Pressure by two methods

Fig.9 Pressure by two mixed closure models at t=2.0 (a) bulk modulus weighted model; (b) our model

Fig.10 (a) Stress; and (b) equivalent plastic strain with different mesh sizes at t=4.0

Fig.11 Plastic collapse of Be shell under the first calculation mode

Fig.12 Equivalent plastic strain at final time (a) Lagrange; (b)MMALE

Fig.13 Interface at final time (a) Lagrange; (b)MMALE

Fig.14 Plastic collapse problem of Be shell under the second calculation mode

Fig.15 Equivalent plastic strain at final time (a) Lagrange; (b)MMALE

Fig.16 Interface at final time (a) Lagrange; (b)MMALE

Fig.17 Variation of interface location by the MMALE method with time

Fig.18 Variation of energy by the MMALE method with time

Fig.19 The initial material interface of 3D R-T instability problem

Fig.20 Variation of the interfaces of 3D R-T stability problem (a) Ref. [26]; (b) our method

Fig.21 Simulation of high-speed impact of the target on the thin target plate by our MMALE method

References 29

1	HIRT C W , AMSDEN A A , COOK J L . An arbitrary Lagrangian-Eulerian computing method for all flow speeds[J]. Journal of Computational Physics, 1974, 14 (3): 227- 253. DOI
2	PEERY J S , CARROLL D E . Multi-Material ALE methods in unstructured grids[J]. Computer Methods in Applied Mechanics and Engineering, 2000, 187 (3/4): 591- 619.
3	BENSON D J . Computational methods in Lagrangian and Eulerian hydrocodes[J]. Computer Methods in Applied Mechanics and Engineering, 1992, 99 (2/3): 235- 394.
4	BENSON D J . A mixture theory for contact in multi-material Eulerian formulations[J]. Computer Methods in Applied Mechanics and Engineering, 1997, 140 (1/2): 59- 86.
5	MILLER D S , ZIMMERMAN G B . An algorithm for time evolving volume fractions in mixed zones in Lagrangian hydrodynamics calculations[J]. Russian Journal of Physical Chemistry B, 2009, 3 (1): 117- 121. DOI
6	DESPRES B , LAGOUTIERE F . Numerical resolution of a two-component compressible fluid model with interfaces[J]. Progress in Computational Fluid Dynamics, An International Journal, 2007, 7 (6): 295- 310. DOI
7	田保林, 刘妍, 申卫东, 等. 可压缩多介质流动的整体ALE方法(GALE)[J]. 北京理工大学学报, 2010, 30 (5): 622- 625.
8	SHASHKOV M . Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes[J]. International Journal for Numerical Methods in Fluids, 2008, 56 (8): 1497- 1504. DOI
9	KAMM J R , SHASHKOV M J . A pressure relaxation closure model for one-dimensional, two-material Lagrangian hydrodynamics based on the Riemann problem[J]. Communications in Computational Physics, 2010, 7, 927- 976. DOI
10	ROBINSON A, BRUNNER T, CARROLL S, et al. ALEGRA: An arbitrary Lagrangian-Eulerian multimaterial, multiphysics code[C]//46th AIAA Aerospace Sciences Meeting and Exhibit. Reno: AIAA, 2008: AIAA2008-1235.
11	HIRT C W , NICHOLS B D . Volume of fluid (VOF) method for the dynamics of free boundaries[J]. Journal of Computational Physics, 1981, 39 (1): 201- 225. DOI
12	YOUNGS D. Time-dependent multi-material flow with large fluid distortion[M]//MORTON K W, BAINES M J. Numerical methods for fluid dynamics. New York: Academic Press, 1982: 273-285.
13	RUDMAN M . Volume-tracking methods for interfacial flow calculations[J]. International Journal for Numerical Methods in Fluids, 1997, 24 (7): 671- 691. DOI
14	DYADECHKO V, SHASHKOV M. Moment-of-fluid interface reconstruction[Z]. Los Alamos National Laboratory Report, 2005.
15	DYADECHKOV , SHASHKOV M . Reconstruction of multi-material interfaces from moment data[J]. Journal of Computational Physics, 2008, 227 (11): 5361- 5384. DOI
16	AHN H T , SHASHKOV M . Multi-material interface reconstruction on generalized polyhedral meshes[J]. Journal of Computational Physics, 2007, 226 (2): 2096- 2132. DOI
17	KUCHARIK M , SHASHKOV M , WENDROFF B . An efficient linearity-and-bound-preserving remapping method[J]. Journal of Computational Physics, 2003, 188 (2): 462- 471. DOI
18	MARGOLIN L G , SHASHKOV M . Second-order sign-preserving conservative interpolation (remapping) on general grids[J]. Journal of Computational Physics, 2003, 184 (1): 266- 298. DOI
19	熊俊, 周海兵, 张树道. SALE速度重映算法的改进[J]. 计算物理, 2006, 23 (1): 37- 42.
20	GRANDY J . Conservative remapping and region overlays by intersecting arbitrary polyhedra[J]. Journal of Computational Physics, 1999, 148 (2): 433- 466.
21	KUCHARIK M , SHASHKOV M . Conservative multi-material remap for staggered multi-material arbitrary Lagrangian-Eulerian methods[J]. Journal of Computational Physics, 2014, 258, 268- 304.
22	MARBŒUF A , CLAISSE A , LE TALLEC P . Conservative and entropy controlled remap for multi-material ALE simulations with space-staggered schemes[J]. Journal of Computational Physics, 2019, 390, 66- 92.
23	GALERA S , MAIRE P H , BREIL J . A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface Reconstruction[J]. Journal of Computational Physics, 2010, 229 (16): 5755- 5787.
24	GALERA S , BREIL J , MAIRE P H . A 2D unstructured multi-material cell-centered arbitrary Lagrangian-Eulerian (CCALE) scheme using MOF interface Reconstruction[J]. Computers & Fluids, 2011, 46 (1): 237- 244.
25	JIA Zupeng , LIU Jun , ZHANG Shudao . An effective integration of methods for second-order three-dimensional multi-material ALE method on unstructured hexahedral meshes using MOF interface Reconstruction[J]. Journal of Computational Physics, 2013, 236, 513- 562.
26	CHEN Xiang , ZHANG Xiong , JIA Zupeng . A robust and efficient polyhedron subdivision and intersection algorithm for three-dimensional MMALE remapping[J]. Journal of Computational Physics, 2017, 338, 1- 17.
27	CARAMANA E J , BURTON D E , SHASHKOV M J , et al. The construction of compatible hydrodynamics algorithms utilizing conservation of total energy[J]. Journal of Computational Physics, 1998, 146 (1): 227- 262.
28	CARAMANA E J , ROUSCULP C L , BURTON D E . A compatible, energy and symmetry preserving lagrangian hydrodynamics algorithm in Three-Dimensional cartesian geometry[J]. Journal of Computational Physics, 2000, 157 (1): 89- 119.
29	BARLOW A , HILL R , SHASHKOV M . Constrained optimization framework for interface-aware sub-scale dynamics closure model for multimaterial cells in Lagrangian and arbitrary Lagrangian-Eulerian hydrodynamics[J]. Journal of Computational Physics, 2014, 276, 92- 135.

[1]	Xiao LI, Zhijun SHEN, Hongping GUO, Jun FANG, Hongping ZHANG. Analyse and Suppression Method of Wall Heating Error for Elastic-Plastic Problem [J]. Chinese Journal of Computational Physics, 2024, 41(5): 569-581.
[2]	LI Xiao, SUN Chen, SHEN Zhijun. Numerical Simulation of One-dimensional Elastic-Perfectly Plastic Flow and Suppression of Wall Heating Phenomenon [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(5): 539-550.
[3]	HE Anmin, LIU Jun, SHAO Jianli, LIU Chao, WANG Pei. Theoretical Ejecta Model for Elastic-Plastic Solids Based on Richtmyer-Meshkov Instability [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 35(5): 505-514.
[4]	GUO Shaodong, JIA Zupeng, XIONG Jun, ZHOU Haibing. MMALE Method Based on Interface Capture for Three-Dimensional Multi-Material Radiation Hydrodynamics Equation [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 35(2): 127-137.
[5]	JIA Zupeng, SUN Yutao. A 2D Cell-centered MMALE Method Based on MOF Interface Reconstruction [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(5): 523-538.
[6]	LIANG Xianhong. Second Order Volume of Fluid Interface Reconstruction Method in Three Dimensions [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 30(3): 353-360.
[7]	ZHANG Deliang, WANG Jingtao, WANG Gang. High-order CE/SE Method and Applications [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 26(2): 211-220.
[8]	WANG Jingtao, ZHANG Deliang, LIU Kaixin. A Eulerian Approach Based on CE/SE Method for 2D Multimaterial Elastic-Plastic Flows [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 24(4): 395-401.
[9]	WANG Tie-liang, ZHANG Jian-xin, HAN Xue-an. NUMERICAL SIMULATION OF THE STRESS PRODUCED BY CHEMICAL EXPLOSION IN ROCK [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2000, 17(S1): 126-130.
[10]	Zhou Nan, Cheng Shuyu, Chen Yusheng, Ding Sheng. A NEW AND ACCURATE FREE SURFACE SCHEME IN 1-D AND 2-D NUMERICAL CALCULATIONS OF ELASTIC-PLASTIC FLOW [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1998, 15(4): 385-392.
[11]	Gui Xingen. THE DYNAMIC ELASTIC-PLASTIC DEFORMATION OF THE FREE CONICAL SHELL [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1992, 9(4): 375-376.