Yearly Technical Report for DE-FG02-03ER46026

We propose a unique, all-electron, thermodynamic density functional theory (DFT) code that directly predicts full or partial long-range order in crystalline (defected) solids and their effect on electronic properties via a first-principles mean-field theory, scales linear with number of atoms N per unit-cell [i.e. O(N), due to use of a mathematical-based screening in k-space], and addresses up to 1 million atoms using parallel architectures. Novel O(N) algorithms will be developed to permit this for an all-electron KKR Green's functional density-functional theory code

Peridynamics review

Peridynamics (PD) is a novel continuum mechanics theory established by Stewart Silling in 2000 [1]. The roots of PD can be traced back to the early works of Gabrio Piola according to dell'Isola et al. [2]. PD has been attractive to researchers as it is a nonlocal formulation in an integral form; unlike the local differential form of classical continuum mechanics. Although the method is still in its infancy, the literature on PD is fairly rich and extensive. The prolific growth in PD applications has led to a tremendous number of contributions in various disciplines. This manuscript aims to provide a concise description of the peridynamic theory together with a review of its major applications and related studies in different fields to date. Moreover, we succinctly highlight some lines of research that are yet to be investigated