Handbook of bi-dimensional tensors: Part I: Harmonic decomposition and symmetry classes

To investigate complex physical phenomena, bi-dimensional models are often an interesting option. It allows spatial couplings to be produced while keeping them as simple as possible. For linear physical laws, constitutive equations involve the use of tensor spaces. As a consequence the different types of anisotropy that can be described are encoded in tensor spaces involved in the model. In the present paper, we solve the general problem of computing symmetry classes of constitutive tensors in ℝ 2 using mathematical tools coming from representation theory. The power of this method is illustrated through the tensor spaces of Mindlin strain-gradient elasticity.