On a system of independent arguments for constitutive tensor functions on the growing surface in micropolar continuum

Abstract

Abstract The present study is devoted to the boundary value problems statements for the growing materials with microstructural features. The general form of tensor relations on the propagating growing surface is derived as a consequence of the conservation laws of momentum and angular momentum. The necessary system of independent arguments of constitutive differential constraints on the growing surface in micropolar continuum is determined. A complete set of joint rational invariants of the system of tensors and vectors that determine the thermodynamics of the production process of a woven 3D material is given and discussed. An invariant-complete formulation of the constitutive relations on the growing surface is obtained.