Dynamics, Instability, and Bifurcation in the Mechanics of Biological Growth
Biological growth is at the heart of many developmental, physiological, and pathological processes. Growth relies on the fine tuning of different genetic and biochemical processes but, ultimately, expresses itself through a change of geometry mediated by physical forces. These forces generated by growth also influence growth itself, creating a complex feedback mechanism. The coupling between geometry, stresses, and growth in elastic tissues can be modeled within the framework of nonlinear anelasticity, a theory which includes both reversible and irreversible deformations. The consequences of growth can then be studied on simple geometries or reduced models. I will explain the basic foundational principles of nonlinear anelasticity and, motivated by the behavior of biological systems, I will describe generic instabilities and bifurcations occurring in the growth dynamics.
Alain Goriely, University of Arizona