Comparison of the Helmholtz, Gibbs, and Collective-modes methods to obtain nonaffine elastic constants
arXiv:1908.08758 · doi:10.1016/j.jmps.2020.103954
Abstract
We review and compare the Born-Huang and the Lemaitre-Maloney's theories that lead to analytical expressions for elastic constants, accounting for affine and nonaffine deformations in a lattice. The Born-Huang method is based on Helmholtz energy while the Lemaitre-Maloney's formalism focus on Gibbs force. Although starting from different perspectives, in the linear elastic limit, and in equilibrium, elastic material constants must be the same in all these methods. This is explicitly verified on examples of linear chains, and numerical simulation of a non-centrosymmetric crystal.
References in corpus (11)
- Approximate analytical description of the nonaffine response of amorphous solids
- Continuum limit of amorphous elastic bodies: A finite-size study of low frequency harmonic vibrations
- Turbulent-like fluctuations in quasistatic flow of granular media
- A Model for the Elasticity of Compressed Emulsions
- Local inversion-symmetry breaking controls the boson peak in glasses and crystals
- Disorder-assisted melting and the glass transition in amorphous solids
- New fitting scheme to obtain effective potential from Car-Parrinello molecular dynamics simulations: Application to silica
- Vibrations of amorphous, nanometric structures: When does continuum theory apply?
- Fluctuation-dissipation relation between shear stress relaxation modulus and shear stress autocorrelation function revisited
- Theory of elastic constants of athermal amorphous solids with internal stresses
- Compressibility and pressure correlations in isotropic solids and fluids