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

Nicolas Auffray (1) , Boris Kolev (2) , Marc Olive (2)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
2 I2M - Institut de Mathématiques de Marseille

To investigate complex physical phenomena, bi-dimensional models are often an interesting option. It allows spatial couplings to produce 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.

Mots clés: Anisotropy; Symmetry classes; Constitutive laws; Higher-order tensors

Domaines: Mécanique des solides [physics.class-ph]

Nicolas Auffray, Boris Kolev, Marc Olive. Handbook of bi-dimensional tensors: Part I: Harmonic decomposition and symmetry classes. Mathematics and Mechanics of Solids, 2017, 9 (22), pp.1847-1865. ⟨10.1177/1081286516649017⟩. ⟨hal-01303964⟩