Doctoral Dissertations

Date of Award


Degree Type


Degree Name

Doctor of Philosophy


Mechanical Engineering

Major Professor

Reza Abedi

Committee Members

Katherine A. Acton, Stephanie C. TerMaath, Trevor M. Moeller


The effect of small-scale random defects such as microcracks or inclusions are critical to the prediction of material failure, yet including these in a fracture simulation can be difficult to perform efficiently. Typically, work has focused on implementing these through a statistical characterization of the micro- or meso-scales. This characterization has traditionally focused on the spatial distribution of faults, assuming the material is purely isotropic. At the macro-scale, many materials can be assumed to be fully isotropic and homogeneous, but at the small scale may show significant anisotropy or heterogeneity. Other materials may be effectively anisotropic in bulk, such as rock bedding planes.

Statistical volume elements (SVE) are one homogenization methodology used to retain this heterogeneity or anisotropy when characterizing a material. Unlike a Representative Volume Element (RVE), the choice of SVE including size, boundary conditions applied, shape, and type, may affect the given material properties. In addition, the size which an RVE exists is well-studied for homogeneity, but there is less study of the isotropic limit.

This work introduces a multi-scale methodology using SVEs to study material heterogeneity and anisotropy. Results are given for macroscopic fracture simulations using this SVE-based homogenization scheme. In addition, the rate of convergence to the RVE limit for both the homogeneous and isotropic limit of two types of SVE, Regular Square and Voronoi Square, are shown. This methodology shows promise for characterization of both isotropic and anisotropic materials.

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