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

Abstract

For an isotropic hyperelastic material, the free energy per unit reference volume, ψ, may be expressed in terms of an isotropic function $\psi=\bar{\psi}(\mathbf{E})$ 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 $\sqrt{2}|\mathbf{E}_{0}|$ (with E ₀ the deviatoric part of E) is small but not infinitesimal:

This free energy has five material constants—the two classical positive-valued shear and bulk moduli μ ₀ and κ ₀ of the infinitesimal theory of elasticity, and three additional positive-valued material constants (μ _r,ε _r,ε _c), which are used to characterize the nonlinear response at large values of tr E. In the large volumetric strain range −0.30≤tr E≤0.15 but small shear strain range $\sqrt {2}|\mathbf{E}_{0}|\lessapprox0.05$ 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.