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

For an isotropic hyperelastic material, the free energy per unit reference volume, ψ, may be expressed in terms of an isotropic function ψ = ψ̄(E) of the logarithmic elastic strain E = lnV. 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 trE, but the shear strain √ 2|E0| (with E0 the deviatoric part of E) is small but not infinitesimal: ψ(E) = μ(trE) |E0| + g(trE), with μ(trE) = μr − (μr − μ0) exp „