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 modeling of elastic 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, we
will see that growth affects the geometry of a body by changing
typical length scales but also its mechanics by inducing 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 spontaneous
instabilities in growing materials as observed in simple physical
systems.