We investigate the effective elastic properties of disordered heterogeneous materials whose Young's modulus varies spatially as a lognormal random field. For one-, two-, and three-dimensional (1D, 2D, and 3D) rectangular blocks, we decompose the spatial fluctuations of the Young's log-modulus into first- and higher-order terms and find the joint distribution of the effective elastic tensor by multiplicatively combining the term-specific effects. The analytical results are in good agreement with Monte Carlo simulations. Through parametric analysis of the analytical solutions, we gain insight into the effective elastic properties of this class of heterogeneous materials. The results have applications to structural/mechanical reliability assessment and design.
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January 2015
Research-Article
Random Bulk Properties of Heterogeneous Rectangular Blocks With Lognormal Young's Modulus: Effective Moduli
Leon S. Dimas,
Leon S. Dimas
Laboratory for Atomistic and Molecular
Mechanics (LAMM),
Department of Civil and
Environmental Engineering,
Mechanics (LAMM),
Department of Civil and
Environmental Engineering,
Massachusetts Institute of Technology
,77 Massachusetts Avenue
,Cambridge, MA 02139
Department of Civil and
Environmental Engineering,
Environmental Engineering,
Massachusetts Institute of Technology
,77 Massachusetts Avenue
,Cambridge, MA 02139
Search for other works by this author on:
Daniele Veneziano,
Daniele Veneziano
Department of Civil and
Environmental Engineering,
Environmental Engineering,
Massachusetts Institute of Technology
,77 Massachusetts Avenue
,Cambridge, MA 01239
Search for other works by this author on:
Tristan Giesa,
Tristan Giesa
Laboratory for Atomistic and Molecular
Mechanics (LAMM),
Department of Civil and
Environmental Engineering,
Mechanics (LAMM),
Department of Civil and
Environmental Engineering,
Massachusetts Institute of Technology
,77 Massachusetts Avenue
,Cambridge, MA 02139
Department of Civil and
Environmental Engineering,
Environmental Engineering,
Massachusetts Institute of Technology
,77 Massachusetts Avenue
,Cambridge, MA 02139
Search for other works by this author on:
Markus J. Buehler
Markus J. Buehler
1
Laboratory for Atomistic and Molecular
Mechanics (LAMM),
Department of Civil and
Environmental Engineering,
Mechanics (LAMM),
Department of Civil and
Environmental Engineering,
Massachusetts Institute of Technology
,77 Massachusetts Avenue
,Cambridge, MA 02139
Department of Civil and
Environmental Engineering,
e-mail: mbuehler@MIT.EDU
Environmental Engineering,
Massachusetts Institute of Technology
,77 Massachusetts Avenue
,Cambridge, MA 02139
e-mail: mbuehler@MIT.EDU
1Corresponding author.
Search for other works by this author on:
Leon S. Dimas
Laboratory for Atomistic and Molecular
Mechanics (LAMM),
Department of Civil and
Environmental Engineering,
Mechanics (LAMM),
Department of Civil and
Environmental Engineering,
Massachusetts Institute of Technology
,77 Massachusetts Avenue
,Cambridge, MA 02139
Department of Civil and
Environmental Engineering,
Environmental Engineering,
Massachusetts Institute of Technology
,77 Massachusetts Avenue
,Cambridge, MA 02139
Daniele Veneziano
Department of Civil and
Environmental Engineering,
Environmental Engineering,
Massachusetts Institute of Technology
,77 Massachusetts Avenue
,Cambridge, MA 01239
Tristan Giesa
Laboratory for Atomistic and Molecular
Mechanics (LAMM),
Department of Civil and
Environmental Engineering,
Mechanics (LAMM),
Department of Civil and
Environmental Engineering,
Massachusetts Institute of Technology
,77 Massachusetts Avenue
,Cambridge, MA 02139
Department of Civil and
Environmental Engineering,
Environmental Engineering,
Massachusetts Institute of Technology
,77 Massachusetts Avenue
,Cambridge, MA 02139
Markus J. Buehler
Laboratory for Atomistic and Molecular
Mechanics (LAMM),
Department of Civil and
Environmental Engineering,
Mechanics (LAMM),
Department of Civil and
Environmental Engineering,
Massachusetts Institute of Technology
,77 Massachusetts Avenue
,Cambridge, MA 02139
Department of Civil and
Environmental Engineering,
e-mail: mbuehler@MIT.EDU
Environmental Engineering,
Massachusetts Institute of Technology
,77 Massachusetts Avenue
,Cambridge, MA 02139
e-mail: mbuehler@MIT.EDU
1Corresponding author.
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 21, 2014; final manuscript received October 9, 2014; accepted manuscript posted October 13, 2014; published online November 14, 2014. Editor: Yonggang Huang.
J. Appl. Mech. Jan 2015, 82(1): 011003 (9 pages)
Published Online: January 1, 2015
Article history
Received:
September 21, 2014
Revision Received:
October 9, 2014
Accepted:
October 13, 2014
Online:
November 14, 2014
Citation
Dimas, L. S., Veneziano, D., Giesa, T., and Buehler, M. J. (January 1, 2015). "Random Bulk Properties of Heterogeneous Rectangular Blocks With Lognormal Young's Modulus: Effective Moduli." ASME. J. Appl. Mech. January 2015; 82(1): 011003. https://doi.org/10.1115/1.4028783
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