The Mechanics and Mathematics of Biological Growth
Alain Goriely, Mathematics Department, Program in Applied Mathematics, and BIO5 Institute, University of Arizona, Tucson.

Growth is involved in many fundamental biological processes such as morphogenesis, physiological regulation, or pathological disorders.  It is, in general, a process of enormous complexity involving genetic, biochemical, and physical components at many different scales and with complex interactions. In this talk, I will consider the problem of modeling  growth in elastic materials and investigate its mechanical consequences. First, starting with simple system in one two and three dimensions, I will show how to generalize the classical theory of exact elasticity to include growth. Second, I will show how growth affects both the geometry of a body by changing typical length scales but also its mechanics by inducing incompatible residual stresses. The competition between these two effects can be used to regulate the physical properties of a material during regular physiological conditions. It can also lead to interesting phenomena such as cavitation and spontaneous instabilities in growing materials which can be observed in simple physical and biological systems.