Sharif Digital Repository

To account for certain essential features of material such as dispersive behaviour and optical branches in dispersion curves, a fundamental departure from classical elasticity to polar theories is required. Among the polar theories, micromorphic elasticity of appropriate grades and anisotropy is capable of capturing these physical phenomena completely. In the mathematical framework of micromorphic elasticity, in addition to the traditional elastic constants, some additional constants are introduced in the pertinent governing equations of motion. A precise evaluation of the numerical values of the aforementioned elastic constants in the realm of the experimentations poses serious... 

In this work, after formulating the weakly nonlocal micromorphic equations of motion for non-Bravais crystals with general anisotropy, specialization to diamond structures is made. A critical dilemma is the determination of the elastic moduli tensor appearing in the equations of motion. From the equivalency of these equations with the pertinent equations obtained in the context of lattice dynamics, the expressions of the components of the elastic moduli tensors in terms of the atomic force constants are derived analytically. Subsequently, the atomic force constants are calculated via ab initio density functional perturbation theory (DFPT) with high precision. As a benchmark for the accuracy... 

Eringen's nonlocal theory and an accurate determination of the nonlocal kernel functions for hexagonal close-packed (hcp) crystals are of interest. The kernel functions are closely related to the anisotropy as well as any crystalline symmetries. To this end, five new distinct nonlocal kernel functions which have the characteristics of discrete atomistic Green's functions in the stress space are obtained through consideration of the nonlocal dispersion relations associated with certain directions combined with ab initio Density Functional Perturbation Theory (DFPT) calculations of the pertinent phonon frequencies. This is the first work which provides the nonlocal hcp kernel functions... 

The dilemma with the deficiencies of the nonlocal kernel functions as the building blocks of the Eringen’s nonlocal theory has been of concern. The aim of the current work is to provide a remedy for the calculation of the components of the nonlocal moduli tensor pertinent to face center cubic (fcc) crystals accounting for their true symmetry group. To this end, three new distinct nonlocal kernel functions which are the discrete atomistic Green’s functions in the stress space are obtained through the nonlocal dispersion relations associated with the longitudinal and shear waves in fcc crystals combined with the corresponding ones calculated via ab initio based on density functional...