Growing Solids and Thin-Walled Structures

The present paper provides a systematic treatment of modern differential-geometrical methods for modeling of incompatible finite deformations in solids and thin walled structures. The incompatibility of deformations may be caused by a variety of physical phenomena; among them are: growth, non-uniform thermal fields, shrinkage, etc. Incompatible deformations results in residual stresses and distortion of geometrical shape. These factors are associated with critical parameters in modern high-precision technologies, particularly, in additive manufacturing, and considered to be essential constituents in corresponding mathematical models. The methods in question are based on the representation of a body and physical space in terms of differentiable manifolds, namely material manifold and physical manifold. These manifolds are equipped with specific metrics and connections, non-Euclidian in general.