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oai:www.ideals.illinois.edu:2142/31024 2023-07-10 col_2142_5131 col_2142_14787 com_2142_5130 com_2142_9630 com_2142_234

Ostoja-Starzewski, Martin Sena, Michael 2012-05-22T00:22:23Z 2012-05-22T00:22:23Z 2012-05 2012-05-22T00:22:23Z 2012-05 Unique effective material properties are not possible for random heterogeneous materials at intermediate length scales, which is to say at some mesoscale above the microscale yet prior to the attainment of the representative volume element (RVE). Focusing on elastic moduli in particular, a micromechanical analysis based on the Hill-Mandel condition leads to the conclusion that two fields, stiffness and compliance, are required to bound the response of the material. Continuing the work of M. Ostoja-Starzewski, in this thesis we analyze variations of a random planar material with a two-phase microstructure. We employ micromechanics, in what can be viewed as a smoothing procedure using the concept of a mesoscale ``window'', and random field theory to compute the correlation structure of 4th-rank tensor fields of stiffness and compliance for a given mesoscale. Results are presented for various correlation distances, volume fractions, and contrasts in stiffness between phases. The main contribution of this research is to provide the data for developing analytical correlation functions, which can then be used at any mesoscale to generate stochastic finite elements (SFE) with an authentic micromechanical-basis. Item withdrawn by Rebecca Bryant (rabryant@illinois.edu) on 2012-04-26T19:46:54Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 0_thesis-FINAL.zip: 22279655 bytes, checksum: 6ac963aca2d49938e8b54ee54fd8b8d0 (MD5) Sena_Michael.pdf: 3745184 bytes, checksum: d1ac37c02e38b9cda78ce4c121e851fd (MD5) Made available in DSpace on 2012-05-22T00:22:23Z (GMT). No. of bitstreams: 3 Sena_Michael.pdf: 3745184 bytes, checksum: d1ac37c02e38b9cda78ce4c121e851fd (MD5) 0_thesis-FINAL.zip: 22279655 bytes, checksum: 6ac963aca2d49938e8b54ee54fd8b8d0 (MD5) license.txt: 4060 bytes, checksum: 593771afae2a07aabbfd548effd708c8 (MD5) http://hdl.handle.net/2142/31024 en Copyright 2012 Michael P. Sena random media heterogeneous materials random fields mesoscale effective properties elastic modulus stiffness anisotropy stochastic finite elements statistical volume element multiscale methods Mesoscale random fields of stiffness for in-plane elasticity text Mechanical Sci & Engineering 1917 Mechanical Engineering 0133 University of Illinois at Urbana-Champaign Thesis M.S. MS:Mechanical Engineerng -UIUC 10KS0133MS