Claudia Grabs (UP)
There are many elastic moduli for isotropic elastic materials, such as the bulk modulus and the Youngs modulus, but they all are related to two basic material parameters, namely the Lamé parameters, that arise in the Taylor expansion of the Second Piola Kirchhoff stress tensor for deformations close to a relaxed reference configuration of the elastic material. All the various elasic moduli can be considered theoretically in arbitrary dimension, in practice they are considered mainly in three dimensions. But when using them in simulations for deformations of elastic shells, thought of as two dimensional elastic bodies, we need a link between the 3D values that can be found in the literature and the 2D elastic moduli. This is what we want to present here, after a short introduction to the mathematical foundations of elasticity.