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oai:www.ideals.illinois.edu:2142/83921 2023-07-11 col_2142_5131 col_2142_14787 com_2142_5130 com_2142_9630 com_2142_234

Ostoja-Starzewski, Martin Ranganathan, Shivakumar I. 2015-09-25T21:12:43Z 2015-09-25T21:12:43Z 10000-01-01 2008 2008 The framework of stochastic mechanics is employed to obtain scale-dependent bounds on the response of multifarious random polycrystals. In doing so, one infers the approach to the Representative Volume Element (RVE), the cornerstone of the separation of scales in continuum mechanics. The RVE is approached by setting up and solving stochastic Dirichlet and Neumann boundary value problems consistent with the Hill(-Mandel) macrohomogeneity condition. Further, the concept of a scaling function is introduced to establish unifying scaling laws. It turns out that the scaling function depends on a mesoscale (scale of observation relative to grain size) and an appropriate universal anisotropy index quantifying the single crystal anisotropy. Based on the scaling function, a material selection diagram is constructed that clearly separates the microscale from the macroscale. Using such a diagram, one can determine the size of RVE for a whole range of polycrystals made of various crystal classes. Application problems include the scaling of the fourth-rank elasticity and the second-rank thermal conductivity tensors. Made available in DSpace on 2015-09-25T21:12:43Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3347501.pdf: 1379272 bytes, checksum: 9b40559513d1637b0892bcb28aef7f10 (MD5) Previous issue date: 2008 Embargo set by: Seth Robbins for item 85202 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 83 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008. http://hdl.handle.net/2142/83921 (MiAaPQ)AAI3347501 eng Applied Mechanics Scale-Dependent Homogenization and Scaling Laws in Random Polycrystals text Mechanical Engineering Mechanical Engineering University of Illinois at Urbana-Champaign Dissertation Ph.D.