On a differential constraint in the continuum theory of growing solids

The present paper is devoted to the problem of boundary conditions formulation for asymmetric problems in the mechanics of growing solids (MGS). The boundary conditions on the propagating growing surface (PGS) is the fundamental problem of this branch of mechanics. Results from the algebra of rational invariants are used for deriving constitutive equations on PGS. Geometrically and mechanically consistent differential constraints are obtained on PGS. Those are valid for a wide range of materials and metamaterials. A number of constitutive equations on PGS of different complexity levels are proposed. The boundary conditions simultaneously can be treated as differential constraints within the frameworks of variational formulations. The differential constraints imply an experimental identification of constitutive functions. For this reason, the obtained results furnish a general ground in applied problems of the MGS.