The general theme of the project is the study of growth, structure, and function in physical and biological systems through the use, and development of, nonlinear elasticity theory and the associated methods of applied mathematics. The project is divided into three main lines of interconnected research: (i) the analysis and modeling of elastic growth in soft materials, such as biological tissue; (ii) the biomechanics of microbial systems including the study of force-driven penetration mechanisms, such as those arising in fungi that destroy crops; and (iii) the dynamics and stability of various elastic rods, cables, and pipes having important engineering applications. For the first theme, the investigators and their students study the mechanical consequences of growth and its potential to either generate instabilities through changes in geometry and stresses, or to act as a mechanism to stabilize and regulate physical properties. The goal of these studies is to gain insight into the fundamental coupling between growth and stress in many biological systems. The second theme of microbial biomechanics involves the mathematical modeling of both bacterial and fungal systems. The investigators formulate and analyze mechanical models of growing micro-organisms in order to understand their overall structure (e.g. the formation of appressoria in the rice-blast fungus) and their ability to invade host tissues by penetration (as found in many fungi), as well as the growth and structural changes exhibited by filamentary bacteria, such as those that are a natural source of antibiotics. The description of these organisms combines a general formulation of membrane growth (based on the first research theme), the elastic modeling of cell walls undergoing large deformations, and the use of plasticity and fracture theory to describe penetration processes. The third theme of elastic rod dynamics involves the study of elastic tubes conveying fluids, and the dynamics of rods with constitutive coupling between twist and tension (hemitropic rods) -- a functionality that is relevant to the design of crane cable and other braided structures. The analysis of filament instabilities is carried out through the use and extension of the nonlinear analysis techniques developed by the investigators in their previous work.
The project concerns the dynamics of filamentary structures such as pipes and rods and the physical analysis of growth mechanisms and invasion appearing in biological systems. It is highly interdisciplinary in nature, cutting across the fields of applied mathematics, mechanical engineering, microbiology, and biomechanics, and addresses questions of both practical importance and mathematical interest. The themes have a broad range of applicability in biology (morphogenesis), in biomedical engineering (analysis of soft tissues, their mechanical regulation and function), in understanding fundamental processes in biological invasion such as fungal penetration of tissues, and in classical engineering problems (pipes conveying fluids, instabilities in drilling). The project also provides many attractive training experiences at different levels suitable for graduate and undergraduate students from diverse backgrounds. These include opportunities to synthesize mathematical modeling with hands-on experimentation through the use of the Applied Mathematics Program's unique experimental facilities.
