2 7 A pr 2 00 7 epl draft Particle displacements in the deformation of amorphous materials : local fluctuations versus non - affine field

We study the local disorder in the deformation of amorphous materials by decomposing the particle displacements into a continuous, inhomogeneous field and the corresponding fluctuations. We compare these fields to the commonly used affine and non-affine displacements, in an elastically deformed 2D Lennard-Jones glass. The continuous field captures the main features of the non-affine field; however, unlike the non-affine field, the fluctuations are very localized, and exhibit a much smaller (and system size independent) correlation length of about one particle diameter. We propose a local scalar " noise " field to characterize the fluctuations, as an additional field for extended continuum models, e.g., to describe the localized irreversible events observed during plastic deformation. Introduction. – The nature of fluctuations in glasses and other amorphous materials out of equilibrium is of much current interest. While elasticity and plasticity are often employed for describing both crystalline and amorphous materials, their microscopic basis is well-established only in crystalline (or polycrystalline) materials, and relies on the periodicity of the microscopic structure (possibly with localized defects) [1, 2]. As in crystal plasticity , localized rearrangements appear to play an important role in the plastic deformation of amorphous materials [3–5], but the lack of underlying order renders the identifications of localized " defects " difficult. In crystals (with a simple unit cell) under homogeneous deformation , the particle displacements conform to the imposed (affine) strain, but in amorphous materials they do not [6]. The non-affine displacements (obtained by subtracting the expected homogeneous deformation) have recently been studied in experiments and simulations of different amorphous systems (e.g., glasses, colloids, granular materials and foams [7–14]). They are typically of the same order of magnitude as the relative affine displacements of neighbor