Nanoscale linear response of strongly disordered stable solids

Abstract

Strongly disordered solids exhibit distinctive properties at the nanoscale, where conventional continuum theory breaks down. We show that their disorder-averaged linear response can be described by a modified continuum theory in which the response coefficients are local but depend nonlocally on the structural properties. The stability criterion requires the response operator to be positive semidefinite, which naturally leads to a correlated Wishart disorder. In the limit of strong disorder, the resulting theory reduces the long-wavelength response to a scalar disorder-induced contrast field. In elasticity, this field describes the formation of a stiffened interphase around rigid nanoparticles and boundaries, whose characteristic extent is set by the nonaffine length. The predictions are confirmed by molecular-dynamics simulations of a Lennard-Jones glass and a model polymer. Direct calculations of the nonlocal elastic kernels show that their spatial range is much shorter than the extent of the stiffened interphase, demonstrating that the latter does not require long-range constitutive nonlocality.