On Volumetric Growth and Material Frames

A theory of volumetric growth on differentiable manifolds is presented. A balance law for an extensive property, that includes a source term, induces material structure and bodies. Transformation rules for the basic variables that represent growth, under a change of frame in the physical event space, are examined and the material frame, where the volumetric growth has a simple canonical form, is defined. Finally, we give a frame-invariant variational version of volumetric growth.