Abstract
New advanced materials have received more attention from many scientists and engineers because of their outstanding chemical, electrical, thermal, optical, and mechanical properties. Since the design of advanced material by experiments requires high cost and time, numerical approaches have always been of great interest. In this paper, finite element analysis of anisotropic material behavior has been carried out based on a multiresolution continuum theory. Gurson-Tvergaard-Needleman (GTN) damage model has been applied as a constitutive model at macroscale. Effects of plastic anisotropy on deformation behavior are assessed using Hill’s 48 yield function for anisotropic material and von Mises yield function for isotropic material, respectively. The material parameters for both isotropic and anisotropic damage models have systematically been determined from microstructure through unit cell modeling. The newly proposed linear approximation of local velocity gradient resolved the underdetermined problem of the previous homogenization process. Anisotropic material behaviors of a tensile specimen have been investigated by the proposed multiresolution continuum theory.
Similar content being viewed by others
References
V. Tvergaard and A. Needleman, Nonlocal effects on localization in a void-sheet, International Journal of Solids and Structures, 34 (1997) 2221.
J. R. Brockenbrough, S. Suresh and H. A. Wienecke, Deformation of metal-matrix composites with continuous fibers: geometrical effects of fiber distribution and shape, Acta Metallurgica et Materialia, 39 (1991) 735.
P. E. McHugh, R. J. Asaro and C. F. Shin, Computational modeling of metal matrix composite materials — III. Comparison with phenomenological models, Acta Metallurgica et Materialia, 41 (1993) 1489.
J. M. Guedes and N. Kikuchi, Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods, Computer Methods in Applied Mechanics and Engineering, 83 (1990) 143.
R. J. M. Smit, Toughness of heterogeneous polymeric systems, Ph.D. thesis, indhoven University of Technology, Eindhoven, The Netherlands (1998).
F. Feyel and J. L. Chaboche, FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fiber SiC/Ti composite materials, Computer Methods in Applied Mechanics and Engineering, 183 (2000) 309–330.
H. T. Zhu, H. M. Zbib and E. C. Aifantis, Strain gradients and continuum modeling of size effect in metal matrix composites, Acta Mechanica, 121 (1997) 165.
V. Kouznetsova, M. G. D. Geers and W. A. M. Brekelmans, Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme, International Journal for Numerical Methods in Engineering, 54 (2002) 1235.
C. B. Hirschberger, A treatise on micromorphic continua. theory, computation, homogenization, Ph.D. thesis, Technische Universität Kaiserslautern (2008).
C. B. Hirschberger, N. Sukumar and P. Steinmann, Computational homogenization of material layers with micromorphic mesostructure, Philosophical Magazine, 88 (2008) 3603.
R. Janicke, Micromorphic media: Interpretation by homogenization, Ph.D. thesis, Universität des Saarlandes (2002).
C. McVeigh, F. Vernerey, W. K. Liu and L. C. Brinson, Multiresolution analysis for material design, Computer Methods in Applied Mechanics and Engineering, 195 (2006) 5053.
F. Vernerey, W. K. Liu and B. Moran, Multi-scale micromorphic theory for hierarchical materials, Journal of the Mechanics and Physics of Solids, 55 (2007) 2603–2651.
W. K. Liu, L. Siad, R. Tian, S. Lee, D Lee, X. Yin, W. Chen, S. Chan, G. B. Olson, L. E. Lindgen, M. F. Horstemeyer, Y. S. Chang, J. B. Choi and Y. J. Kim, Complexity science of multiscale materials via stochastic computations, International Journal for Numerical Methods in Engineering, 80 (2009) 932.
Z. Chen and X. Dong, The GTN damage model based on Hill’48 anisotropic yield criterion and its application in sheet metal forming, Computational Materials Science, 44 (2009) 1013.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Recommended by Associate Editor Heung Soo Kim
Moon Ki Kim received the B.S. and M.S. degrees in Mechanical Engineering from Seoul National University in 1997 and 1999, respectively, and the M.S.E. and Ph.D. degrees from the Johns Hopkins University in 2002 and 2004, respectively. He had been an Assistant Professor in the Department of Mechanical and Industrial Engineering at University of Massachusetts, Amherst from 2004 to 2008. He has worked for school of Mechanical Engineering at Sungkyungkwan University as an associate professor since 2009. His research interests are focused on computational structural biology based on robot kinematics, bioinstrumentations, and multiscale modeling and simulation.
Rights and permissions
About this article
Cite this article
Lee, D., Chang, YS., Choi, JB. et al. Prediction of anisotropic material behavior based on multiresolution continuum mechanics in consideration of a characteristic length scale. J Mech Sci Technol 26, 2863–2868 (2012). https://doi.org/10.1007/s12206-012-0728-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-012-0728-5