Shear-stress relaxation and ensemble transformation of shear-stress autocorrelation functions

Abstract : We revisit the relation between the shear-stress relaxation modulus G(t), computed at finite shear strain 0 < gamma << 1, and the shear-stress autocorrelation functions C(t)vertical bar(gamma) and C(t)vertical bar(tau) computed, respectively, at imposed strain gamma and mean stress tau. Focusing on permanent isotropic spring networks it is shown theoretically and computationally that in general G(t) = C(t)vertical bar(tau) = C(t)vertical bar(gamma) + G(eq) for t > 0 with G(eq) being the static equilibrium shear modulus. G(t) and C(t)vertical bar(gamma) thus must become different for solids and it is impossible to obtain G(eq) alone from C(t)vertical bar(gamma) as often assumed. We comment briefly on self-assembled transient networks where G(eq)(f) must vanish for a finite scission-recombination frequency f. We argue that G(t) = C(t)vertical bar(tau) = C(t)vertical bar(gamma) should reveal an intermediate plateau set by the shear modulus G(eq)(f = 0) of the quenched network.
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Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2015, 91 (2), 〈10.1103/PhysRevE.91.022107〉
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J. P. Wittmer, Hong Xu, J. Baschnagel. Shear-stress relaxation and ensemble transformation of shear-stress autocorrelation functions. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2015, 91 (2), 〈10.1103/PhysRevE.91.022107〉. 〈hal-01515835〉

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