Prof. Reza Abedi
Department of Mechanical, Aerospace and Biomedical Engineering
University of Tennessee Space Institute / Knoxville

Statistical Fragmentation Analysis and Homogenization of Heterogeneous Quasi-Brittle Materials

ABSTRACT: Fracture response of materials is highly sensitive to microstructural details and defect distribution. Accordingly, in fragmentation analysis and some other fracture examples, the use of deterministic and homogeneous material properties results in a deterministic response, failing to capture the inherent variations of macroscopic Quantities of Interest (QoIs) such as dissipated energy, maximum stress, and fracture pattern. Moreover, these deterministic approaches can even fail to capture the mean response of the material, for example by under- or over-predicting the mean dissipated energy. In this talk, we discuss a few approaches that maintain certain level of material heterogeneity and randomness to address these shortcomings. For example, Statistical Volume Elements (SVEs) are discussed as an alternative to Representative Volume Elements (RVEs) for up-scaling effective elastic and fracture properties that are heterogeneous, random, and potentially anisotropic. The SVE size provides a gauge on the level of underlying details maintained in the up-scaling process. The effect of boundary condition and shape of SVE is discussed next. By analysis of the statistics of these up-scaled properties, random fields with consistent one- and two-point statistics can be generated for subsequent macroscale analysis. For the macroscale analysis with underlying random fields, the focus will be on 1D fragmentation problems of an expanding ring under an internal pressure. The results are presented for Traction-Separation Relation (TSR) and Phase Field (PF) fracture models, although the focus is mainly on TSR results. The input parameters include nondimensional elastic and fracture parameters such as fracture energy and displacement scales, a nondimensional loading rate that models quasi-static to high loading rate fracture, and parameters that represent the underlying random fields for material properties. Specifically, we use the range and correlation length of an underlying fracture strength field to investigate the effect of inherent material heterogeneity on fracture response. It will be demonstrated that low and high loading rates have very distinct responses in terms of the form of the probability distribution function of the macroscopic maximum fracture strength and its dependence on the weakest versus mean microscopic strength field. Moreover, the effects of key parameters of the underlying random field on such measures will be discussed. The talk will conclude with other analytical and computational results for fragmentation response of 1D and 2D quasi-brittle materials under high loading rate.

BIOGRAPHY: Reza Abedi received his B.S. in Civil Engineering and M.S. in Structural Engineering from Sharif University of Technology, Tehran, Iran, in 1999 and 2001, respectively. He obtained his M.S. in Mathematics and Ph.D. in Theoretical and Applied Mechanics from the University of Illinois at Urbana-Champaign in 2006 and 2010, respectively. He then joined the department of Mechanical Science and Engineering at the University of Illinois at Urbana-Champaign as a postdoctoral fellow. Since August 2012, he has been a professor in the department of Mechanical, Aerospace and Biomedical Engineering at the University of Tennessee Space Institute (UTSI) and the University of Tennessee Knoxville (UTK). Among his research interests are computational solid mechanics, electromagnetics, thermal mechanics, and stochastic fracture mechanics.