For an isotropic hyperelastic material, the free energy per unit reference volume, ψ, may be expressed in terms of an isotropic function ψ =ψ(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 √ 2|E 0 | (with E 0 the deviatoric part of E) is small but not infinitesimal:, withThis 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 (µr, ǫr, ǫc), 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 √ 2|E 0 | 0.05 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.