A mesh generation procedure to simulate bimaterials

Document Type : Research Paper


1 School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran,

2 Mechanical Engineering Department, University of Kashan, Kashan, Iran


It is difficult to develop an algorithm which is able to generate the appropriate mesh around the interfaces in bimaterials. In this study, a corresponding algorithm is proposed for this class of unified structures made from different materials with arbitrary shapes. The non-uniform mesh is generated adaptively based on advancing front technique available in Abaqus software. Implementing several preliminary analyses, the output of each step prepared data source for the next step of mesh generation. After examining several criteria, the mean elemental stress derivative is selected as a suitable criterion to evaluate the performance of current mesh. The convergence indicates non-isometric final mesh with appropriate and optimum distribution. In general, automatic mesh generators determine the mesh density only based on the geometry of the model; however, the developed algorithm modifies mesh after sensing the stress intensity due to various reasons including loading condition and any change in material and geometry. In addition, the proposed algorithm converges to accurate result fast enough if considering the numbers of remeshing steps. An adaptive mesh generator code can be programmed based on the developed procedure to automatically generate mesh if implementing in Abaqus as a subroutine.


Main Subjects

[1]. Abaqus, User's Manual, Dassault Systèmes Simulia Corp, 2012.
[2]. Ansys, Tutorial Release 14.5, SAS IP, Inc., 2012.
[3]. C. Gonza´lez and J. LLorca, "Mechanical behavior of unidirectional fiber-reinforced polymers under transverse compression: Microscopic mechanisms and modeling," Composites Science and Technology, vol. 67, p. 2795–2806, 2007.
[4]. Laurent Van Miegroet, Pierre Duysinx, Stress concentration minimization of 2D filets using X-FEM and level set description, Struct Multidisc Optim (2007) 33:425–438.
[5]. C. Lee and R. Hobbs, "Automatic adaptive ®nite element mesh generation over arbitrary two-dimensional domain using advancing front technique," Computers and Structures, no. 71, pp. 9-34, 1999.
[6]. R. Montenegro, J. Cascón, J. Escobar, E. Rodríguez and G. Montero, "An automatic strategy for adaptive tetrahedral mesh generation," Applied Numerical Mathematics, no. 59, p. 2203–2217, 2009.
[7]. S. Phongthanapanich, "Delaunay Adaptive Remeshing Technique for Finite Element/Finite Volume Methods," Thailand, 2010.
[8]. S. Lo, "Dynamic grid for mesh generation by the advancing front method," Computers and Structures, no. 123, p. 15–27, 2013.
[9]. G. H. Paulino, I. F. M. Menezes, J. B. Cavalcante Neto, L. F. Martha, A methodology for adaptive finite element analysis: Towards an integrated computational environment, Computational Mechanics 23 (1999) 361-388.
[10]. K.S.R.K. Murthy and M. Mukhopadhyay, Adaptive finite element analysis of mixed-mode fracture problems containing multiple crack-tips with an automatic mesh generator, International Journal of Fracture 108: 251–274, 2001.
[11]. Guoqun Zhao, Hongmei Zhang, Lianjun Cheng, Geometry-adaptive generation algorithm and boundary match method for initial hexahedral element mesh, Engineering with Computers (2008) 24:321–339
[12]. Xinghua Liang , Yongjie Zhang, An octree-based dual contouring method for triangular and tetrahedral mesh generation with guaranteed angle range, Engineering with Computers (2014) 30:211–222
[13]. Lu Sun, Guoqun Zhao, Adaptive hexahedral mesh generation and quality optimization for solid models with thin features using a grid-based method, Engineering with Computers, DOI 10.1007/s00366-015-0399-9, Published online, 14 Feb 2015.
[14]. Alshoaibi, Abdulnaser M., Ariffin, Ahmad Kamal, Finite element simulation of stress intensity factors in elastic-plastic crack growth, Journal of Zhejiang University SCIENCE A, 2006 7(8):1336-1342.
[15]. E. Ruiz-Girones, X. Roca, J. Sarrate, Size-preserving size functions and smoothing procedures for adaptive quadrilateral mesh generation, Engineering with Computers (2015) 31:483–498
[16]. A. Rajagopal, S. M. Sivakumar, A combined r-h adaptive strategy based on material forces and error assessment for plane problems and bimaterial interfaces, Comput Mech (2007) 41:49–72.
[17]. James P. Carson, Andrew P. Kuprat, Xiangmin Jiao, Volodymyr Dyedov, Facundo del Pin, Julius M. Guccione, Mark B. Ratcliffe, Daniel R. Einstein, Adaptive generation of multimaterial grids from imaging data for biomedical Lagrangian fluid–structure simulations, Biomech Model Mechanobiol (2010) 9:187–201.
[18]. C. Li, C. Song, H. Man, E.T. Ooi, W. Gao, " HYPERLINK "http://www.sciencedirect.com/science/article/pii/S0020768314000626" 2D dynamic analysis of cracks and interface cracks in piezoelectric composites using the SBFEM ," International Journal of Solids and Structures, vol. 51, no. 11–12, P. 2096-2108, 2014.
[19]. M. H. Sadd, Elasticity: Theory, Applications, and Numerics, Burlington: Elsevier Inc, 2005.
[20]. J. D. Hoffman, Numerical methods for engineers and scientists, 2nd edition, New York: Marcel Dekker, Inc., 2001.
  • Receive Date: 01 May 2014
  • Revise Date: 03 August 2015
  • Accept Date: 12 September 2014