The present paper aims at providing a comprehensive investigation of the abilities and limitations strain gradient crystal plasticity (SGCP) theories in capturing different kinds localization modes single crystals. To this end, small deformation Gurtin-type SGCP model recently proposed by authors, based on non-quadratic defect energy uncoupled dissipation assumption, is extended to finite defor...

In this paper, vibration of the protein microtubule, one of the most important intracellular elements serving as one of the common components among nanotechnology, biotechnology and mechanics, is investigated using stress and strain gradient elasticity theory and orthotropic elastic shells model. Microtubules in the cell are influenced by internal and external stimulation and play a part in con...

We extend the application of the method of initial values (also known as the transfer matrix method) to find frequencies of free vibrations of a strain-gradient-dependent Euler–Bernoulli beam (EBB) under different boundary conditions at the two end faces of the beam. For the classical EBB, we find the exact matricant or the carry-over matrix but it is numerically evaluated for the strain-gradie...

This article is concerned with the multiagent optimization problem. A distributed randomized gradient-free mirror descent (DRGFMD) method developed by introducing a oracle in scheme where non-Euclidean Bregman divergence used. The classical gradient generalized without using subgradient information of objective functions. proposed algorithms are first zeroth-order methods, which achieve an appr...