On Theories of Growing Bodies

A general setting for a continuum kinematics and force theory for bodies whose material structure may evolve is presented. The body object of continuum mechanics is replaced by two distinct objects: the growing body and the material manifold. The configuration space of the growing body is given the structure of an infinite dimensional fiber bundle over the manifold containing the collection of material struc-tures that the growing body may possess. A connection on this fiber bundle allows the decomposition of generalized velocities and forces into components pertaining to growth and mechanical power. A num-ber of examples of growing body theories is given.