Measuring spatial distribution of the local elastic modulus in glasses

Abstract

Glasses exhibit spatially inhomogeneous elastic properties, which can be investigated by measuring their elastic moduli at a local scale. Various methods to evaluate the local elastic modulus have been proposed in the literature. A first possibility is to measure the local stress-local strain curve and to obtain the local elastic modulus from the slope of the curve, or equivalently to use a local fluctuation formula. Another possible route is to assume an affine strain and to use the applied global strain instead of the local strain for the calculation of the local modulus. Most recently a third technique has been introduced, which is easy to be implemented and has the advantage of low computational cost. In this contribution, we compare these three approaches by using the same model glass and reveal the differences among them caused by the non-affine deformations.

Time-dependent elastic response to a local shear transformation in amorphous solids

“…The shear and bulk modulus, G 2 = 17 and K 2 = 98, have been measured with the method described in Ref. 23; the associated Poisson ratio is ν 2 = 0.70 (the subscript is used to indicate two-dimensional quantities).…”

On the nontrivial wave-vector dependence of the elastic modulus of glasses

“…In particular, a correlation length of tens of interatomic distances has been revealed in the nonaffine displacement field of various simulated glasses * giacomo.baldi@cnr.it under an external perturbation [4,5]. Numerical simulations of polymeric glasses [6,7] and of Lennard-Jones and softsphere systems [8,9] indicate that the local elastic modulus is heterogeneous and the width of its distribution increases as the length scale over which it is computed is reduced, implying that on the macroscopic scale these fluctuations are averaged out. However, at present, the numerical works do not indicate a length scale for the heterogeneities, although there have been indications for a fractal-like distribution of the local elastic modulus [7].…”

“…Recent numerical simulation studies have revealed that the elasticity of glasses is heterogeneous on the nanometer length scale [4][5][6][7][8][9], suggesting a possible relation with the dynamical heterogeneities above T g . In particular, a correlation length of tens of interatomic distances has been revealed in the nonaffine displacement field of various simulated glasses * giacomo.baldi@cnr.it under an external perturbation [4,5].…”

Fast evaluation of local elastic constants and its application to nanosized structures

“…Additionally, a better atomic volume model for the free surface layer will lead to improved 21 results. Overall, this new approach will be a powerful tool for the modeling and simulation of other inhomogeneous materials, such as the interphase of polymer-based nano-composites [45], interface formed between different crystallographic directions [46], etc.…”

“…For the deformation-based technique [20], Mizuno et al compared with three different approaches by using the same glassy materials [7,21]. In order to suppress the fluctuation of stresses and strains, the simulation temperature is extremely low.…”