Two-dimensional tensor function representation for all kinds of material symmetry

Abstract
All kinds of physically possible material symmetry in two-dimensional space were investigated in a recent work of Q.-S. Zheng and J. P. Boehler. In this paper, we establish the complete and irreducible representations with respect to every kind of material symmetry for scalar-, vector-, and second-order tensor-valued functions in two-dimensional space of any finite number of vectors and second-order tensors. These representations allow general invariant forms of physical and constitutive laws of anisotropic materials to be developed in plane problems.