2015/08/15 by J. P. Wittmer, Ivan Kriuchevskyi, I. Kriuchevskyi +3 · 8 citations
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Composite Material Mechanics #Dimensionless quantity #Elasticity and Material Modeling #Geometry #Inverse #Isotropy #Lambda #Material Dynamics and Properties #Mathematical physics #Mathematics #Physics #Quantum mechanics #Shear modulus #Shear stress #Thermodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1140/epjb/e2015-60506-6
published in The European Physical Journal B 88(9) (Springer Science+Business Media) · 17 pages, 15 figures
arxiv created 2015/08/15 · openalex publication_date 2015/09/01 · arxiv updated 2015/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Shear-strain and shear-stress correlations in isotropic elastic bodies are investigated both theoretically and numerically at either imposed mean shear-stress τ (λ=0) or shear-strain γ (λ=1) and for more general values of a dimensionless parameter λ characterizing the generalized Gaussian ensemble. It allows to tune the strain fluctuations μγγ ≡ βV \la δγ2 \ra = (1-λ)/Geq with β being the inverse temperature, V the volume, γ the instantaneous strain and Geq the equilibrium shear modulus. Focusing on spring networks in two dimensions we show, e.g., for the stress fluctuations μττ ≡ βV \la δτ2 \ra (τ being the instantaneous stress) that μττ = μA - λGeq with μA = μττ|λ=0 being the affine shear-elasticity. For the stress autocorrelation function cττ(t) ≡ βV \la δτ(t) δτ(0) \ra this result is then seen (assuming a sufficiently slow shear-stress barostat) to generalize to cττ(t) = G(t) - λ\Geq with G(t) being the shear-stress relaxation modulus.