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Shear-strain and shear-stress fluctuations in generalized Gaussian ensemble simulations of isotropic elastic networks

Abstract : Shear-strain and shear-stress correlations in isotropic elastic bodies are investigated both theoretically and numerically at either imposed mean shear-stress tau (lambda - 0) or shear-strain gamma (lambda - 1) and for more general values of a dimensionless parameter. characterizing the generalized Gaussian ensemble. It allows to tune the strain fluctuations mu(gamma gamma) beta V = (1 - lambda)/G(eq) with beta being the inverse temperature, V the volume, gamma the instantaneous strain and G(eq) the equilibrium shear modulus. Focusing on spring networks in two dimensions we show, e.g., for the stress fluctuations mu(tau tau) beta V (tau being the instantaneous stress) that mu(tau tau)|(lambda) = mu A - lambda G(eq) with mu A = mu(tau tau)vertical bar(lambda= 0) being the affine shear-elasticity. For the stress autocorrelation function C-tau tau(t) beta V this result is then seen (assuming a sufficiently slow shear-stress barostat) to generalize to C-tau tau(t)|(lambda) = G(t) - lambda G(eq) with G(t) = C-tau tau(t)|(lambda= 0) being the shear-stress relaxation modulus.
Keywords : Constants
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https://hal.univ-lorraine.fr/hal-01515450
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Submitted on : Thursday, April 27, 2017 - 3:02:21 PM
Last modification on : Thursday, May 7, 2020 - 1:37:56 AM

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Joachim Paul Wittmer, Ivan Kriuchevskyi, Joerg Baschnagel, Hong Xu. Shear-strain and shear-stress fluctuations in generalized Gaussian ensemble simulations of isotropic elastic networks. European Physical Journal B: Condensed Matter and Complex Systems, Springer-Verlag, 2015, 88 (9), ⟨10.1140/epjb/e2015-60506-6⟩. ⟨hal-01515450⟩

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