Date of Award

Spring 11-8-2014

Document Type


Degree Name

Doctor of Philosophy (PhD)

First Advisor

Franck J. Vernerey

Second Advisor

Richard Regueiro

Third Advisor

Alireza Doostan

Fourth Advisor

Yunping Xi

Fifth Advisor

Mark Stoykovich


An adaptive concurrent multiscale methodology (ACM$^2$) is introduced to enable strong interaction between both macroscopic and microscopic deformation fields. The method is formulated in finite element framework and is based on the balance between two sources of error, namely, numerical and homogenization errors. In finite element framework, the first type of error dictates element refinement in regions that are characterized by high deformation gradient, to improve the accuracy of numerical solution. In contrary, the second type of error indicates that the refining procedure should not exceed a critical level, that is determined by the size of the unit cell and represents the scale of material's microstructure. The method then aims at embedding unit cells in continuum region and through appropriate boundary conditions couple the deformation field in both regions. Upon this, the method is able to adequately combine different descriptions of material to assure accuracy with low computational cost. We will then show that our computational technique, in conjunction with the extended finite element method, is ideal to study the strong interactions between a macroscopic crack and the microstructure of heterogeneous media. In particular, the method enables an explicit description of micro-structural features near the crack tip, while a computationally inexpensive coarse scale continuum description is used in the rest of the domain. The present work also aim at investigating several examples of crack propagation in materials with random microstructures, and discussing the potential of the multiscale technique in relating microstructural details to material strength and toughness, and capturing the size effect.