Scale-Dependent Homogenization and Scaling Laws in Random Polycrystals
Ranganathan, Shivakumar I.
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https://hdl.handle.net/2142/83921
Description
Title
Scale-Dependent Homogenization and Scaling Laws in Random Polycrystals
Author(s)
Ranganathan, Shivakumar I.
Issue Date
2008
Doctoral Committee Chair(s)
Ostoja-Starzewski, Martin
Department of Study
Mechanical Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Language
eng
Abstract
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.
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