On a Differential Constraint in Asymmetric Theories of the Mechanics of Growing Solids

The article deals with the problem on setting boundary conditions for asymmetric problems in the mechanics of growing solids. Firstly, we study the conditions on the growing surface that are most important from the point of view of the theory completeness. When deriving relations on the growing surface, we use the results known from the algebra of rational invariants. Geometrically and mechanically consistent differential constraints that are valid for a very wide range of materials and metamaterials are obtained on the growing surface. Several variants of constitutive equations on the growing surface of different levels of complexity are investigated. The formulated differential constraints imply the experimental identification of several defining functions. Thus, the results obtained can serve as a general basis in applied research on the mechanics of growing solids with an asymmetric stress tensor.