Related papers: Analytic elastic constants in molecular calculatio…
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…
The method of many body Green's functions is used to derive algebraic expressions for the different elastic and thermodynamical quantities such as the free energy, internal energy, entropy, heat capacity, elastic constants (adiabatic and…
We derive expressions for determination of the stress and the elastic constants in systems composed of particles interacting via non-central two-body potentials as thermal averages of products of first and second partial derivatives of the…
Change in the interatomic spacing of a two-atom system under tension and compression has been modelled by the elastic deformation of atoms. The critical elastic strain of atoms before separation or cracking from tension was estimated by the…
Recent progress in approaches to determine the elastic constants of solids starting from the microscopic particle interactions is reviewed. On the theoretical side, density functional theory approaches are discussed and compared to more…
Mechanical and elastic properties of materials are among the most fundamental quantities for many engineering and industrial applications. Here, we present a formulation that is efficient and accurate for calculating the elastic and bending…
The modeling of the elastic properties of disordered or nanoscale solids requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which…
Strain gradient elasticity and nonlocal elasticity are two enhanced elastic theories intensively used over the last fifty years to explain static and dynamic phenomena that classical elasticity fails to do. The nonlocal elastic theory has a…
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…
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…
Acousto-elasticity is concerned with the propagation of small-amplitude waves in deformed solids. Results previously established for the incremental elastodynamics of exact non-linear elasticity are useful for the determination of third-…
A statistical theory of cholesteric liquid crystals composed of short rigid biaxial molecules is presented. It is derived in the thermodynamic limit at a small density and a small twist. The uniaxial (biaxial) cholesteric phase is regarded…
Elastic constants of zero-temperature amorphous solids are given as the difference between the Born term, which results from a hypothetical affine deformation of an amorphous solid, and a correction term which originates from the fact that…
Using the density functional formalism we derive expression for the distortion free energy for systems with continuous broken symmetry and use it to derive expression for the elastic constants of smectic phases in which director is tilted…
Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…
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…
The mechanical properties of a solid, which relate its deformation to external applied forces, are key factors in enabling or disabling the use of an otherwise optimal material in any application, strongly influencing also its service…
In complex crystals close to melting or at finite temperatures, different types of defects are ubiquitous and their role becomes relevant in the mechanical response of these solids. Conventional elasticity theory fails to provide a…
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…
We obtain an exact strain consistency equation for full, elastic, and plastic strain characteristics that have a clear physical meaning and are naturally related to stresses. The dynamic equations are represented in a form that does not use…