Related papers: On elastic constants of zero-temperature amorphous…
We derive expressions for the lowest nonlinear elastic constants of amorphous solids in athermal conditions (up to third order), in terms of the interaction potential between the constituent particles. The effect of these constants cannot…
It is known by now that amorphous solids at zero temperature do not possess a nonlinear elasticity theory: besides the shear modulus which exists, all the higher order coefficients do not exist in the thermodynamic limit. Here we show that…
What characterises a solid is its way to respond to external stresses. Ordered solids, such crystals, display an elastic regime followed by a plastic one, both well understood microscopically in terms of lattice distortion and dislocations.…
We study the elastic theory of amorphous solids made of particles with finite range interactions in the thermodynamic limit. For the elastic theory to exist one requires all the elastic coefficients, linear and nonlinear, to attain a finite…
Sound attenuation in low temperature amorphous solids originates from their disordered structure. However, its detailed mechanism is still being debated. Here we analyze sound attenuation starting directly from the microscopic equations of…
Elastic constants are central material properties, frequently reported in experimental and theoretical studies. While their computation is straightforward in the absence of thermal fluctuations, finite--temperature methods often suffer from…
A new microscopic derivation of the elastic constants of amorphous solids is presented within the framework of nonaffine lattice dynamics, which makes use of a perturbative form of the low-frequency eigenvectors of the dynamical matrix…
We derive expressions for classical isothermal and adiabatic elastic constants for periodic systems with the boundary contributions included explicitly. The potential-dependent part of these expressions is written in terms of potential…
An effective temperature $T_{\rm eff}$ which differs from the bath temperature is believed to play an essential role in the theory of elasto-plasticity of amorphous solids. The definition of a measurable $T_{\rm eff}$ in the literature on…
Elastic constants are among the most fundamental and important properties of solid materials, which is why they are routinely characterized in both experiments and simulations. While conceptually simple, the treatment of elastic constants…
We study amorphous solids with strong elastic disorder and find an un-jamming instability that exists, inter alia, in an harmonic model built using Euclidean random matrices (ERM). Employing the Zwanzig-Mori projection operator formalism…
The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the…
Nonlinear elastic theory studies the elastic constants of a material (such as Young's modulus or bulk modulus) as a power series in the applied load. The inverse bulk modulus K, for example depends on the compression P: $ {1/ K(P)} = c_0 +…
The low-frequency vibrational and low-temperature thermal properties of amorphous solids are markedly different from those of crystalline solids. This situation is counter-intuitive because any solid material is expected to behave as a…
In crystals, molecules thermally vibrate around the periodic lattice sites. Vibrational motions are well understood in terms of phonons, which carry heat and control heat transport. The situation is notably different in disordered solids,…
The universal anomalous vibrational and thermal properties of amorphous solids are believed to be related to the local variations of the elasticity. Recently it has been shown that the vibrational properties are sensitive to the glass's…
Elastic phase transitions of crystals and phase transitions whose order parameter couples linearly to elastic degrees of freedom are reviewed with particular focus on instabilities at zero temperature. A characteristic feature of these…
A general procedure to investigate the elastic response and calculate the elastic constants of stressed and unstressed materials through continuum field modeling, particularly the phase field crystal (PFC) models, is presented. It is found…
Amorphous solids tend to present an abundance of soft elastic modes, which diminish their transport properties, generate heterogeneities in their elastic response, and affect non-linear processes like thermal activation of plasticity. This…
Stress-stress correlations in crystalline solids with long-range order can be straightforwardly derived using elasticity theory. In contrast, the `emergent elasticity' of amorphous solids, rigid materials characterized by an underlying…