A Large Strain Isotropic Elasticity Model Based on Molecular Dynamics Simulations of a Metallic Glass

摘要

For an isotropic hyperelastic material, the free energy per unit reference volume, ψ, may be expressed in terms of an isotropic function y = [`(y)](E)psi=bar{psi}(mathbf{E}) of the logarithmic elastic strain E=ln V. We have conducted numerical experiments using molecular dynamics simulations of a metallic glass to develop the following simple specialized form of the free energy for circumstances in which one might encounter a large volumetric strain tr E, but the shear strain Ö2|E₀|sqrt{2}|mathbf{E}_{0}| (with E ₀ the deviatoric part of E) is small but not infinitesimal: Ö2|E₀|lessapprox0.05sqrt {2}|mathbf{E}_{0}|lessapprox0.05 numerically explored in this paper, this simple five-constant model provides a very good description of the stress-strain results from our molecular dynamics simulations.