This article investigates the theoretical and numerical analysis as well applications of three-dimensional theory first strain gradient elasticity. The corresponding continuous discrete variational formulations are established with error estimates stemming from continuity coercivity within a Sobolev space framework. An implementation isogeometric Ritz–Galerkin method is provided open-source sof...

Nanotechnology is one of the pillars of human life in the future. This technology is growing fast and many scientists work in this field. The behavior of materials in nano size varies with that in macro dimension. Therefore scientists have presented various theories for examining the behavior of materials in nano-scale. Accordingly, mechanical behavior of nano-plates, nanotubes nano-beams and n...

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 describes elasticity at several length scales. We apply the approach to a two-dimensional square lattice with a monatomic basis and find the elastic deformations and hierarchical atomi...

B Pingbing Ming [email protected] Hongliang Li [email protected] Zhong-ci Shi [email protected] 1 Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621900, China 2 The State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, No. 55, Zhong-Guan-Cun East Road, Beijing 100190, China...

The accelerating fields (e. g. centrifugal acceleration and constant acceleration) can change the physical performance of nano-sensors significantly. Herein, a new size-dependent model is developed to investigate the scale-dependent dynamic behavior of nanowire-fabricated sensor operated in an accelerating field. The scale-dependent equation of motion is developed by employing a consolidation o...