Atomic-scale origin of dynamic viscoelastic response and creep in disordered solids

Abstract

Viscoelasticity has been described since the time of Maxwell as an interpolation of purely viscous and purely elastic response, but its microscopic atomic-level mechanism in solids has remained elusive. We studied three model disordered solids: a random lattice, the bond-depleted fcc lattice, and the fcc lattice with vacancies. Within the harmonic approximation for central-force lattices, we applied sum-rules for viscoelastic response derived on the basis of non-affine atomic motions. The latter motions are a direct result of local structural disorder, and in particular, of the lack of inversion-symmetry in disordered lattices. By defining a suitable quantitative and general atomic-level measure of nonaffinity and inversion-symmetry, we show that the viscoelastic responses of all three systems collapse onto a master curve upon normalizing by the overall strength of inversion-symmetry breaking in each system. Close to the isostatic point for central-force lattices, power-law creep $G(t)\sim t^{-1/2}$ emerges as a consequence of the interplay between soft vibrational modes and non-affine dynamics, and various analytical scalings, supported by numerical calculations, are predicted by the theory.

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• Theory of sound attenuation in amorphous solids from nonaffine motions
• Non-affine deformation of semiflexible polymer and fiber networks
• Molecular interpretation of the non-Newtonian viscoelastic behavior of liquid water at high frequencies
• Equilibrium and non-equilibrium molecular dynamics approaches for the linear viscoelasticity of polymer melts
• Possible origin of $\beta$-relaxation in amorphous metal alloys from atomic-mass differences of the constituents
• Scaling up the lattice dynamics of amorphous materials by orders of magnitude
• Predicting plasticity of amorphous solids from instantaneous normal modes
• Complete mathematical theory of the jamming transition: A perspective
• Strain-controlled critical slowing down in the rheology of disordered networks
• Timescale bridging in atomistic simulations of epoxy polymer mechanics using non-affine deformation theory
• Ioffe-Regel criterion and viscoelastic properties of amorphous solids
• Theory of heavy-quarks contribution to the quark-gluon plasma viscosity
• Viscosity of polymer melts using non-affine theory based on vibrational modes
• Effective medium theory for viscoelasticity of soft jammed solids
• Unified study of viscoelasticity and sound damping in hard and soft amorphous solids
• Viscoelastic scaling regimes for marginally-rigid fractal spring networks
• A Linear Time-Variant Rheological Model for Frictional Aging, Stress Relaxation, and Creep