A Large Strain Isotropic Elasticity Model Based on Molecular Dynamics Simulations of a Metallic Glass
Author(s)Henann, David Lee; Anand, Lallit
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For an isotropic hyperelastic material, the free energy per unit reference volume, ψ [psi], may be expressed in terms of an isotropic function ψ = ¯ ψ(E) [psi = psi overscore (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 trE, but the shear strain √2|E0| [square root 2 pipe E subscript 0 pipe] (with E0 [E supscript 0] the deviatoric part of E) is small but not infinitesimal: ψ(E) = μ(trE) |E0|2 [psi (E)= mu (trE pipe E subscript 0 pipe superscript 2] + g(trE) , with μ(trE) = μr − (μr − μ0) exp„trE ǫr « [mu (trE) = mu subscript x - (mu subscript x - mu subscript 0) exp (trE divided by epsilon subscript x)], and g(trE) = κ0 (ǫc)2 »1 − „1 + trE ǫc «exp„− trE ǫc «– [g(trE) = kappa subscript 0 (epsilon subscript c) superscript 2 [1-(1 + trE divided by epsilon subscript c) exp (-trE divided by epsilon subscript c)]]. This free energy has five material constants — the two classical positive-valued shear and bulk moduli μ0 [mu subscript 0] and κ0 [kappa subscript 0] of the infinitesimal theory of elasticity, and three additional positive-valued material constants (μr, ǫr, ǫc) [(mu subscript r, epsilon subscript r, epsilon subscript c)], which are used to characterize the nonlinear response at large values of trE. In the large volumetric strain range −0.30 ≤ trE ≤ 0.15 but small shear strain range √2|E0| [square root 2 pipe E subscript 0 pipe < or about] 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. D. L.
DepartmentMassachusetts Institute of Technology. Department of Mechanical Engineering
Journal of Elasticity
Henann, David L., and Lallit Anand. “A Large Strain Isotropic Elasticity Model Based on Molecular Dynamics Simulations of a Metallic Glass.” Journal of Elasticity 104.1-2 (2011) : 281-302. Copyright © 2011, Springer Science+Business Media B.V.
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