In this article, the Second Strain Gradient (SSG) theory proposed by Mindlin is used within a Wave Finite Element Method (WFEM) framework for dynamic analysis of one-dimensional Euler–Bernoulli bending beam and torsional bar. Firstly, strong forms continuum models including governing equations boundary conditions torsion cases, respectively, are derived using Hamilton’s principle. New “non-loca...

In this paper, the dynamic response of resonating nano-beams is investigated using a strain gradient elasticity theory. A nonlinear model is obtained based on the Galerkin decomposition method to find the dynamic response of the investigated beam around its statically deflected position. The mid-plane stretching, axial residual stress and nonlinear interaction due to the electrostatic force on ...

This study deals with the vibration and stability analysis of double-graphene nanoribbon-system (DGNRS) based on different nonlocal elasticity theories such as Eringen's nonlocal, strain gradient, and modified couple stress within the framework of Rayleigh beam theory. In this system, two graphene nanoribbons (GNRs) are bonded by Pasternak medium which characterized by Winkler modulus and shear...

The damping vibration characteristics of magneto-electro-viscoelastic (MEV) nanobeam resting on viscoelastic foundation based on nonlocal strain gradient elasticity theory (NSGT) is studied in this article. For this purpose, by considering the effects of Winkler-Pasternak, the viscoelastic medium consists of linear and viscous layers. with respect to the displacement field in accordance with th...

Phase-field modelling has been shown to be a powerful tool for simulating fracture processes and predicting the crack path under complex loading conditions. Note that total energy of in classical phase-field formulations includes strain density from linear elasticity theory resulting singular stresses at tip. Recently, we have demonstrated integrating gradient into conventional may improve fina...

Microstructure related deviation from elastic response is known as “size-effect.” Metamaterials – for example modeled by strain gradient elasticity capture this effect adequately means of additional parameters to be determined. We employ a methodology based on asymptotic homogenization in order obtain metamaterials and then present the influence these using simulations. By finite element method...

We discuss and solve an inverse problem in nonlinear elasticity imaging in which we recover spatial distributions of hyperelastic material properties from measured displacement fields. This problem has applications to elasticity imaging of soft tissue because the strain dependence of the apparent stiffness may potentially be used to differentiate between malignant and normal tissues. We account...