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Size-dependent torsional and longitudinal free vibrations of restrained saturated porous nanorods are studied by a higher-order elasticity theory. The strain gradient elasticity model is used in this study able to overcome inconsistencies of classical elasticity model. The presented higher-order model leads to well-posed boundary value problem for arbitrary value of the small size parameter. Two elastic springs in torsional and axial directions are attached to saturated porous nanorods at two boundary points. Angular rotation and axial deflection functions based on the strain gradient elasticity model are represented by two Fourier sine series. The difference of this proposed solution is that it does not impose a limitation on the support conditions and allows the frequencies to be obtained with a single solution. Two coefficient matrices including torsional or axial effects are obtained by using Stokes' transformation and non-classical boundary conditions. Free vibration frequencies of saturated nanorods are calculated by an effective eigen-value solution strategy. It is shown clearly that elastic spring coefficients, small-scale parameter and saturation a notable impact on the dynamic response of nanorods. [ABSTRACT FROM AUTHOR]

The present paper develops a size-dependent Kirchhoff microplate model with surface effects by using simplified strain gradient elasticity theory and surface elasticity theory. This new model is able to capture size-dependent behaviors and surface effects. The most noticeable difference of the proposed model from the existing plate models about microplates is that not only strain gradient and surface stress are taken into account, but also the surface-induced internal residual stresses are considered. Based on whether the plates having surface-induced internal residual stress or not, their governing equations have distinct differences. An extended Kantorovich method is employed to provide approximate closed-form solution for the rectangular microplate with simply supported boundary conditions. For the microplate with biaxial initial residual surface stress, the numerical results reflect that when the simply supported microplates do not have surface-induced internal residual stresses, internal length scale and biaxial surface residual stress have significant influence on the static bending of the microplates. However, when the simply supported microplates have nonzero surface-induced internal residual stresses, the effects of internal length scale and biaxial surface residual stress become very weak. It indicates that the effect of surface-induced internal residual stresses can counteract most of the effects of internal length scale and surface residual stress. This work provides a more general model for the analysis of microplate problems. [ABSTRACT FROM AUTHOR]

In the paper, by taking advantage of a strain gradient crystal plasticity theory with consideration of dislocation absorption by surfaces, plastic behaviors of thin films with two active slip systems under constrained shear is analytically studied. It is found that the critical loads for the onset of dislocations absorption by surfaces for the two slip systems are size dependent and are greatly affected by the latent hardening in the grain interior, and dislocations absorption by surfaces can significantly change the distributions of the plastic deformation and dislocation density and hence the strain-hardening behaviors. [ABSTRACT FROM AUTHOR]

The strain and velocity gradient framework is formulated for the third-order shear deformable beam theory. A variational approach is applied to determine the governing equations together with initial and boundary conditions. Within the gradient framework, the strain energy is generalized to include strain as well as strain gradient. Furthermore, the kinetic energy is also generalized to include velocity and the velocity gradient. Such approach results in the introduction of the static and kinetic internal length scales. For dynamic analysis of beams, most of the gradient theories do not take the velocity gradient into account. The model developed in this paper depicts the influence of the velocity gradient on the governing equations and initial and boundary conditions of the third-order shear deformable theory. Through the assumption of the velocity gradients, kinematic quantities are distinguished on the microscale and on the macroscale. Finally, Timoshenko and Euler-Bernoulli beam theories are also presented by simplifying the third-order theory. [ABSTRACT FROM AUTHOR]

Since stress fibers have micro-size dimensions, their biomechanical behavior should demand mechanical models conforming with gradient strain deformation theories. In particular, the torsion and the stretching of stress fibers are discussed into the context of strain gradient elasticity theory and their size effects. It is proven for the torsion problem that the torsion moment varies with the axial length of the bar for constant twist angle, whereas for the simple tension problem, the strain is non-uniform along the stress fiber. The proposed theory is supported by experimental evidence. [ABSTRACT FROM AUTHOR]