We present an atomic scale theory of lattice distortions using strain-related variables and their constraint equations. Our approach connects constrained atomic length scale variations to continuum elasticity and can describe elasticity at all length scales. We apply the general approach to a two-dimensional square lattice with a monatomic basis, and find the atomic scale elastic textures aroun...

In this paper, we propose a novel and efficient differential quadrature element based on Lagrange interpolation to solve a sixth order partial differential equations encountered in non-classical beam theories. These non-classical theories render displacement, slope and curvature as degrees of freedom for an Euler-Bernoulli beam. A generalize scheme is presented herein to implementation the mult...

Fabrication, characterization and application of micro-/nano-rods/wires are among the hottest topics in materials science and applied physics. Micro-/nano-rod-based structures and devices are developed for a wide-ranging use in various fields of micro-/nanoscience (e.g. biology, electronics, medicine, optics, optoelectronics, photonics and sensors). It is well known that the structure and prope...

PURPOSE We aimed to assess the feasibility and reproducibility of real-time elastography (RTE) for displaying the effects of morphological changes in the ovary in polycystic ovary syndrome (PCOS). METHODS Forty-eight patients diagnosed with PCOS and 48 healthy women were enrolled in the study. Ultrasonography and RTE were performed on the 3rd day of the menstrual cycle. Evaluations were perfo...

The accuracy of the Theory Critical Distances, Gradient Elasticity and Averaged Strain Energy Density criterion in estimating fatigue lifetime notched additively manufactured Ti6Al4V is assessed against numerous experimental results generated under load ratios equal to ?1 0.1. 3D-printed Ti-alloy investigation was tested by keeping notches as-manufactured condition. common feature considered de...

We provide the proof of an existence and uniqueness theorem for weak solutions equilibrium problem in linear dilatational strain gradient elasticity bodies occupying, reference configuration, Lipschitz domains with edges. The considered elastic model belongs to class so-called incomplete continua whose potential energy density depends quadratically on strains dilatation only. Such a has many ap...