Elasticity Moduli of Hexagonal Rhenium

Associated people

J. Schröder, P. Neff, V. Ebbing

Abstract

In order to guarantee the existence of minimizers of the underlying potential in finite elasticity, a suitable concept is the polyconvexity condition of the energy function in the sense of Ball 1977. Until recently, the construction of polyconvex energy functions for the description of anisotropic material behavior was a question yet to be answered. The first transversely isotropic and orthotropic polyconvex energy functions were presented by Schröder and Neff in the years 2001, 2003. In the present work a method for the construction of polyconvex, coordinate-invariant energy functions for the description of all existing anisotropic hyperelastic materials is proposed. The key idea is the introduction of so-called crystallographically motivated structural tensors. The applicability of this method is shown within several numerical examples.

References

Ebbing, V. [2010], "Design of Polyconvex Energy Functions for All Anisotropy Classes", Dissertation, Institut für Mechanik, Bericht Nr. 8, Universität Duisburg-Essen

Ebbing, V., Schröder, J., Neff, P. [2010], "Construction of Polyconvex Energies for Non-Trivial Anisotropy Classes", in Poly-, Quasi- and Rank-One Convexity in Applied Mechanics, CISM Courses and Lectures, Editors: J. Schröder and P. Neff, Springer, Vol. 516, 107-130

Schröder, J., Neff, P., Ebbing, V. [2008], "Anisotropic Polyconvex Energies on the Basis of Crystallographic Motivated Structural Tensors", Journal of the Mechanics and Physics of Solids, Vol. 56, 3486-3506