Contorsion of Material Connection in Growing Solids

The subject of the present paper is a material connection that describes the sources of incompatibility in growing solids. There are several possibilities to introduce such a connection on the body manifold, which provides formal description of a body as a continuous collection of material particles. Two of them are discussed in detail. The first sets the geometry of Riemannian manifold, while the second sets Weitzenbock geometry. To derive particular connection functions, related with given evolutionary problem for growing solid, one has to use some intermediate configurations, whose choice is also uncertain. The purpose of this study is to find out how the ambiguity affects on the stress-strain state modelling. The main results are the following. It is proven that the geometrical invariants of considered material connections, namely the invariants of torsion and curvature, are independent on particular choice of intermediate configuration. It is shown that Weitzenbock connection contains all metric information that completely defines Riemannian ones, but, except it, provides additional description for contorsion, which characterizes inhomogeneity by specific term in balance of momentum. Thus, the two connections do not contradict each other. To describe the body’s response to deformation it is sufficient to construct more simpler Riemannian connection, while to completely describe balance laws it is advisable to obtain more complete Weitzenbock connection.