Biological materials are complex hierarchical systems subjected to external stimuli like mechanical forces, chemical potentials and electrical signals. A deeper understanding of the behavior of these materials is required for the response characterization of healthy and diseased conditions. The primary aim of this dissertation is to study the mechanics of biological materials like cells and tissues from a computational perspective and relate its behavior with experimental works, so as to provide a framework for the identification and treatment of pathological conditions like cancer and vascular diseases.

The first step towards understanding the behavior of a biological cell is to comprehend its response to external mechanical stimuli. Experimentally derived material properties of cells have found to vary by orders of magnitude even for the same cell type. The primary cause of such disparity is attributed to the stimulation process, and the theoretical models used to interpret the experimental data. The variations in mechanical properties obtained from the experimental and theoretical studies can be overcome only through the development of a sound mathematical framework correlating the derived mechanical property with the cellular structure. Such a formulation accounting for the inhomogeneity of the cytoplasm due to stress fibers and actin cortex is developed in this work using Mori-Tanaka method of homogenization. Mechanical modeling of single cells would be extremely useful in understanding its behavior in an experimental setup.

Characterization of in-vivo response of cells requires mathematical modeling of the embedding environment like fibers and fluids, which forms the extra cellular matrix. Studies on fluid-tissue interactions in biomechanics have primarily relied on either an iterative solution of the individual solid or tissue phases or a sequential solution of the entire domain using a coupled algorithm. In this dissertation, a new computational methodology for the analysis of fluid-tissue interaction problem is presented. The modeling procedure is based on a biphasic representation of fluid and tissue domain, consisting of fluid and solid phases. The biphasic-fluid interaction model is also implemented to study the transfer of low-density lipoprotein from the blood to the arterial wall, and also the nutrient transfer in the tissue scaffolds of a bioreactor.