Full Article - Open Access.

Idioma principal


Acton, K. A.;

Full Article:

Computational methods are developed to capture the macro-scale behavior of a heterogeneous composite material when the macro-scale is significantly larger than the scale of the heterogeneity. In this case, it may be computationally costly to model the material microstructure directly in a finite element analysis. Often a representative volume element (RVE) can be used with success; however, there are two main disadvantages of an RVE approach. First, when nonlinear behavior or damage initiation is considered, too much information is lost regarding the local variation in the microstructure. Second, an RVE approach effectively eliminates randomness in the meso-scale material representation, which is needed to statistically quantify structural reliability. As an alternative to the RVE approach, a moving windowing homogenization approach has been developed. This captures a degree of small scale material heterogeneity and randomness, and is suited to a priori implementation in a reduced-mesh large scale finite element analysis. However, non-unique solutions may exist for the homogenization of a window (or statistical volume element, SVE) that is below the scale of an RVE. At a scale smaller than the RVE, the inverse of the compliance tensor obtained by a statically uniform boundary condition (SUBC) test does not equal the stiffness tensor obtained by a kinematically uniform boundary condition (KUBC) test; these are lower and upper bonds on the effective behavior of the element, respectively. Mixed uniform boundary conditions and periodic boundary conditions, such as those used in the Generalized Method of Cells (GMC) predict apparent properties between the KUBC and SUBC upper and lower bounds. This work explores the assumption that accurately capturing effective behavior of a composite at the meso-scale and accurately predicting macro-scale behavior in a moving window analysis are equivalent considerations. A composite beam model with randomly varying inclusions is considered, and the deflection at midspan is used as a metric for macro-scale behavior. Homogenization methods including those described above are implemented. Results are compared to determine not only how well each homogenization technique approximates effective behavior, but also by how each predicts the macro-scale behavior of a structure in a finite element analysis.

Full Article:

Palavras-chave: Multi-scale modeling, homogenization, composites,


DOI: 10.5151/meceng-wccm2012-19337

Referências bibliográficas
  • [1] Aboudi, J., "The Generalized Method of Cells and High-Fidelity Generalized Method of Cells Micromechanical Models-A Review," Mechanics of Advanced Materials and Structures, vol. 11, pp. 329-366, 2004.
  • [2] Acton, K. and Graham-Brady, L., "Elastoplastic Mesoscale Homogenization of Composite Materials," Journal of Engineering Mechanics, vol. 136, pp. 613-624, 2010.
  • [3] Acton, K. and Graham-Brady, L., "Fitting an Anisotropic Yield Surface Using the Generalized Method of Cells," in Advances in Mathematical Modeling and Experimental Methods for Materials and Structures. vol. 168, R. Gilat and L. Banks- Sills, Eds., ed: Springer Netherlands, 2009, pp. 27-41.
  • [4] Acton, K. and Graham-Brady, L., "Meso-scale modeling of plasticity in composites," Computer Methods in Applied Mechanics and Engineering, vol. 198, pp. 920-932, 2009.
  • [5] Bensoussan, A., Lions, J.-L., Papanicolaou, G., and Caughey, T. K., "Asymptotic Analysis of Periodic Structures," Journal of Applied Mechanics, vol. 46, p. 477, 1979.
  • [6] Bohm, H. J., "A Short Introduction to Basic Aspects of Continuum Micromechanics," CDL–FMD Report, 1998.
  • [7] Chung, P. W., Tamma, K. K., and Namburu, R. R., "Asymptotic expansion homogenization for heterogeneous media: computational issues and applications," Composites Part a-Applied Science and Manufacturing, vol. 32, pp. 1291-1301, 2001.
  • [8] Drago, A. and Pindera, M.-J., "Micro-macromechanical analysis of heterogeneous materials: Macroscopically homogeneous vs periodic microstructures," Composites Science and Technology, vol. 67, pp. 1243-1263, 2007.
  • [9] Drugan, W. J. and Willis, J. R., "A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites," Journal of the Mechanics and Physics of Solids, vol. 44, pp. 497-524, 1996.
  • [10] Ferrante, F. J. and Graham-Brady, L. L., "Stochastic simulation of non-Gaussian/nonstationary properties in a functionally graded plate," Computer Methods in Applied Mechanics and Engineering, vol. 194, pp. 1675-1692, 2005.
  • [11] Fish, J., "Multiscale Modeling and Simulation of Composite Materials and Structures," in Lecture Notes in Applied and Computational Mechanics. vol. 55, R. de Borst and E. Ramm, Eds., ed: Springer Berlin / Heidelberg, 2011, pp. 215-231.
  • [12] Fish, J., Shek, K., Pandheeradi, M., and Shephard, M. S., "Computational plasticity for composite structures based on mathematical homogenization: Theory and practice," Computer Methods in Applied Mechanics and Engineering, vol. 148, pp. 53-73, 1997.
  • [13] Fish, J. and Wagiman, A., "Multiscale finite element method for a locally nonperiodic heterogeneous medium," Computational Mechanics, vol. 12, pp. 164-180, 1993.
  • [14] Ghosh, S., Bai, J., and Paquet, D., "Homogenization-based continuum plasticitydamage model for ductile failure of materials containing heterogeneities," Journal of the Mechanics and Physics of Solids, vol. 57, pp. 1017-1044, 2009.
  • [15] Ghosh, S., Lee, K., and Moorthy, S., "Multiple scale analysis of heterogeneous elastic structures using homogenization theory and voronoi cell finite element method," International Journal of Solids and Structures, vol. 32, pp. 27-62, 1995.
  • [16] Ghosh, S., Lee, K., and Raghavan, P., "A multi-level computational model for multiscale damage analysis in composite and porous materials," International Journal of Solids and Structures, vol. 38, pp. 2335-2385, 2001.
  • [17] Gitman, I. M., Askes, H., and Sluys, L. J., "Representative volume: Existence and size determination," Engineering Fracture Mechanics, vol. 74, pp. 2518-2534, 2007.
  • [18] Graham, L. L. and Baxter, S. C., "Simulation of local material properties based on moving-window GMC," Probabilistic Engineering Mechanics, vol. 16, pp. 295-305, 2001.
  • [19] Guedes, J. M. and Kikuchi, N., "Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods," Computer Methods in Applied Mechanics and Engineering, vol. 83, pp. 143-198, 1990.
  • [20] Hazanov, S. and Amieur, M., "On overall properties of elastic heterogeneous bodies smaller than the representative volume," International Journal of Engineering Science, vol. 33, pp. 1289-1301, 1995.
  • [21] Hazanov, S. and Huet, C., "Order relationships for boundary conditions effect in heterogeneous bodies smaller than the representative volume," Journal of the Mechanics and Physics of Solids, vol. 42, pp. 1995-2011, 1994.
  • [22] Hersum, T., "Phase change and melt dynamics in partially molten rock " Ph.D., Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD, 2006.
  • [23] Hill, R., "Elastic properties of reinforced solids: Some theoretical principles," Journal of the Mechanics and Physics of Solids, vol. 11, pp. 357-372, 1963.
  • [24] Hollister, S. J. and Kikuchi, N., "A comparison of homogenization and standard mechanics analyses for periodic porous composites," Computational Mechanics, vol. 10, pp. 73-95, 1992.
  • [25] Huet, C., "Application of variational concepts to size effects in elastic heterogeneous bodies," Journal of the Mechanics and Physics of Solids, vol. 38, pp. 813-841, 1990.
  • [26] Huet, C., "Coupled size and boundary-condition effects in viscoelastic heterogeneous and composite bodies," Mechanics of Materials, vol. 31, pp. 787-829, 1999.
  • [27] Jiang, M., Alzebdeh, K., Jasiuk, I., and Ostoja-Starzewski, M., "Scale and boundary conditions effects in elastic properties of random composites," Acta Mechanica, vol. 148, pp. 63-78, 2001.
  • [28] Jiang, M., Ostoja-Starzewski, M., and Jasiuk, I., "Scale-dependent bounds on effective elastoplastic response of random composites," Journal of the Mechanics and Physics of Solids, vol. 49, pp. 655-673, 2001.
  • [29] Ju, J. and Chen, T., "Micromechanics and effective moduli of elastic composites containing randomly dispersed ellipsoidal inhomogeneities," Acta Mechanica, vol. 103, pp. 103-121, 1994.
  • [30] Khisaeva, Z. F. and Ostoja-Starzewski, M., "Mesoscale bounds in finite elasticity and thermoelasticity of random composites," Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, vol. 462, pp. 1167-1180, April 8, 2006 2006.
  • [31] Lewis, A. C. and Geltmacher, A. B., "Image-based modeling of the response of experimental 3D microstructures to mechanical loading," Scripta Materialia, vol. 55, pp. 81-85, 2006.
  • [32] Michel, J. C., Moulinec, H., and Suquet, P., "Effective properties of composite materials with periodic microstructure: a computational approach," Computer Methods in Applied Mechanics and Engineering, vol. 172, pp. 109-143, 1999.
  • [33] Ostoja-Starzewski, M., "Material spatial randomness: From statistical to representative volume element," Probabilistic Engineering Mechanics, vol. 21, pp. 112-132, 2006.
  • [34] Ostoja-Starzewski, M., "Random field models of heterogeneous materials," International Journal of Solids and Structures, vol. 35, pp. 2429-2455, 1998.
  • [35] Yuan, Z. and Fish, J., "Toward realization of computational homogenization in practice," International Journal for Numerical Methods in Engineering, vol. 73, pp. 361-380, Jan 15 2008.
  • [36] Zohdi, T. I., Oden, J. T., and Rodin, G. J., "Hierarchical Modeling of Heterogeneous Bodies," Computer Methods in Applied Mechanics and Engineering, vol. 138, pp. 273-298, 1996.
  • [37] Zohdi, T. I. and Wriggers, P., Introduction to Computational Micromechanics vol. 20. Berlin: Springer, 2005.
  • [38] Zohdi, T. I., Wriggers, P., and Huet, C., "A method of substructuring large-scale computational micromechanical problems," Computer Methods in Applied Mechanics and Engineering, vol. 190, pp. 5639-5656, 2001.
Como citar:

Acton, K. A.; "MESO-SCALE HOMOGENIZATION METHODS FOR MOVING WINDOW ANALYSIS", p. 3326-3337 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-19337

últimos 30 dias | último ano | desde a publicação