On rationally complete algebraic systems of finite strain tensors of complex continua

The paper is devoted to the mathematical description of complex continua and the systematic derivation of strain tensors by the notion of isometric immersion of complex continuum in a plane space of higher dimension. Problem of establishing of complete systems of irreducible objective strain and extra-strain tensors for complex continuum immersed in an external plane space is considered. The solution to the problem is given by methods of the field theory and the theory of algebraic invariants. Strain tensors are obtained as irreducible algebraic invariants of contravariant vectors of the external space emerging in the complex continuum action density. Considerations are restricted to rational algebraic invariants. Completeness criteria for systems of rational algebraic invariants and rational syzygies are discussed and applied to strain tensors of micropolar elastic continua. Objective strain tensors of micropolar continuum are alternatively obtained by combining multipliers of polar decompositions of strain and extra-strain gradients.