Characterization of Random Heterogeneous Media
Andrew Goupee
Ph.D. Candidate
Department of Mechanical Engineering
University of Maine, Orono, ME 04469
Advisor: Senthil S. Vel
Abstract
A methodology is proposed for synthetically generating realistic microstructures of random heterogeneous media for use in numerical modeling. The microstructure morphologies, which closely resemble those found in actual composite materials with random microstructures, are created using a morphology description function. The proposed method is simple to implement and allows for the generation of microstructures that span the entire phase volume fraction range. The generated microstructures are analyzed using the homogenization method and finite element techniques to determine their homogenized thermoelastic properties as well as their failure behavior.
The first portion of the talk will focus on the major aspects of the morphology description function and other basic concepts central to the work being presented. These concepts include the mathematical techniques and finite element procedures involved in using the homogenization method, issues pertaining to choosing a proper microstructure sample size and its effect on the modeling process and requirements for convergence of the finite element model.
The second portion of the seminar will present results for the homogenized thermoelastic properties for a two-phase aluminum/silicon carbide random composite material. The thermoelastic properties of interest, namely the thermal conductivity, Young’s modulus, shear modulus and thermal expansion coefficient, are computed for the random composite material and compared against analytic bounds and common homogenization estimates for two-phase aluminum/silicon carbide random composites.
The last portion of the presentation will focus on characterizing the failure of aluminum/silicon carbide random media. Appropriate failure theories are employed in each material phase and a phase interface failure criterion is used to account for the fact that the phases are not perfectly bonded together. The computed factors of safety are regularized over the microstructure to ensure a mesh-independent finite element solution when sharp morphological features are present in the microstructure. Failure envelopes are presented for various phase volume fractions and the effect of varying the phase interface strength is also investigated.
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