Sharif Digital Repository

The stress-energy tensor of a matter shell whose history coincides with a null hypersurface in the Einstein-Cartan gravity is revisited. It is demonstrated that with a proper choice for the torsion discontinuity taken to be orthogonal to the null hypersurface and consistent with the antisymmetric property of torsion tensor, the modified expression for the asymmetric stress-energy tensor is automatically tangent to the hypersurface. The main differences with respect to a previous work are addressed. © 2019 IOP Publishing Ltd  

A thermodynamically consistent phase field approach for fracture including surface stresses is presented. The surface stresses which are distributed inside a finite width layer at the crack surface are introduced as a result of employing some geometrical nonlinearities, i.e., by defining energy terms per unit volume at the current time and evaluating gradient of the order parameter in the current configuration. A double-well barrier term is included in the structure of the Helmholtz free energy which allows one to use the energy terms per unit volume at the current time when introducing the surface stresses in the current approach. Thus, the surface stresses are introduced in a similar way... 

A thermodynamically consistent phase field approach for fracture including surface stresses is presented. The surface stresses which are distributed inside a finite width layer at the crack surface are introduced as a result of employing some geometrical nonlinearities, i.e., by defining energy terms per unit volume at the current time and evaluating gradient of the order parameter in the current configuration. A double-well barrier term is included in the structure of the Helmholtz free energy which allows one to use the energy terms per unit volume at the current time when introducing the surface stresses in the current approach. Thus, the surface stresses are introduced in a similar way... 

A thermodynamically consistent phase field approach for fracture including surface stresses is presented. The surface stresses which are distributed inside a finite width layer at the crack surface are introduced as a result of employing some geometrical nonlinearities, i.e., by defining energy terms per unit volume at the current time and evaluating gradient of the order parameter in the current configuration. A double-well barrier term is included in the structure of the Helmholtz free energy which allows one to use the energy terms per unit volume at the current time when introducing the surface stresses in the current approach. Thus, the surface stresses are introduced in a similar way... 

This study investigates the performance of geogrid-reinforced unbound pavement layer. In this study, geogrid was used in various layouts and numbers using three different gradation of granular materials. Light weight deflectometer (LWD) device is known as a useful tool to evaluate the stiffness of unbound pavement layers. In this study, the LWD was utilized to experimentally investigate factors affecting the performance of geogrid reinforcement, including the number of geogrids, geogrid layout, and the gradation of unbound layer. There are several parameters which affect the LWD test results including the hammer weight, the falling height, and the surface stress. The effect of these... 

The elastic behavior of a screw dislocation which is positioned inside the shell domain of an eccentric core-shell nanowire is addressed with taking into account the surface/interface stress effect. The complex potential function method in combination with the conformal mapping function is applied to solve the governing non-classical equations. The dislocation stress field and the image force acting on the dislocation are studied in detail and compared with those obtained within the classical theory of elasticity. It is shown that near the free outer surface and the inner core-shell interface, the non-classical solution for the stress field considerably differs from the classical one, while... 

This paper investigates the subsurface stress field induced by a rigid cylinder rolling over a functionally graded coating-substrate system. The Fourier transform is employed to extract the stress components within the graded coating and the homogeneous substrate. The distributions of the stresses are given through the depth and along the coating-substrate interface. The contour plots of normalized Von Mises stresses are provided as well. The results indicate that continuous variation of the shear modulus substantially reduces the difference between the in-plane stresses along the interface. Also, the softening coating leads to the minimum value of the stress concentration near the contact... 

The problem of edge dislocation inside the wall of a multi-walled nanotube accounting for the surface effects is addressed. Within the framework of surface elasticity the stress field is obtained, using complex potentials. Furthermore, the stress field and image forces acting on the dislocation, with and without an account of the surface stress, are compared together and discussed  

In this paper the surface effects in 3D complex parts are investigated via classical FEM and the modified boundary Cauchy-Born method, which are continuum based theories, and the results are compared with molecular dynamics simulations. The boundary Cauchy-Born covers the weakness of the surface Cauchy-Born in modeling edge and corner elements, so the results are in better agreement with molecular dynamics simulations. Using super convergent patch recovery method, MBCB shows more precise results in comparison with BCB as it can model acute and obtuse angles which cannot be modeled via BCB. The flexibility of MBCB in modeling 3D complex and non-right angle geometries are utilized to model... 

Surfaces and interfaces behave differently from their bulk counterparts especially when the dimensions approach small scales. The recent studies have shown that the surface/interface free energy (surface stress) plays an important role in the effective mechanical properties of solids with nanosized inhomogeneities. In this work, within a micromechanical framework, the effect of surface stress is taken into account to obtain a macroscopic yield function for nanoporous materials containing cylindrical nanovoids. Gurtin-Murdoch model of surface elasticity is incorporated in the generalized self-consistent method to obtain a closed-form expression for the transverse shear modulus of transversely... 

Presented herein is a comprehensive analysis on the size-dependent dynamic behaviors of electrostatically actuated nano-resonator including surface stresses effect. To this end, partial differential equation of nano-resonator based on Gurtin–Murdoch and Euler–Bernoulli theories is converted to ordinary differential equation utilizing assumed mode method. Effect of applied DC voltage on stability and bi-stability of nano-resonator is investigated and it revealed that surface elasticity and stress affect the bi-stability region of nano-resonator. By plotting frequency response of the resonator, hardening and softening behavior of nano-resonator are analyzed and it is shown that surface effect... 

Surface/interface stresses, when notable, are closely associated with a surface/interface layer in which the interatomic bond lengths and charge density distribution differ remarkably from those of the bulk. The presence of such topographical defects as edges and corners amplifies the noted phenomena by large amounts. If the principal features of interest are such studies as the physics and mechanics of evolving microscopic-/nanoscopic-interfaces and the behavior of nano-sized structures which have a very large surface-to-volume ratio, traditional continuum theories cease to hold. It is for the treatment of such problems that augmented continuum approaches like second strain gradient and... 

Phase field theory for fracture is developed at large strains with an emphasis on a correct introduction of surface stresses at nanoscale. This is achieved by multiplying the cohesion and gradient energies by the local ratio of the crack surface areas in the deformed and undeformed configurations and with the gradient energy in terms of the gradient of the order parameter in the reference configuration. This results in an expression for the surface stresses which is consistent with the sharp surface approach. Namely, the structural part of the Cauchy surface stress represents an isotropic biaxial tension, with the magnitude of a force per unit length equal to the surface energy. The surface... 

This study investigates the performance of geogrid-reinforced unbound pavement layer. In this study, geogrid was used in various layouts and numbers using three different gradation of granular materials. Light weight deflectometer (LWD) device is known as a useful tool to evaluate the stiffness of unbound pavement layers. In this study, the LWD was utilized to experimentally investigate factors affecting the performance of geogrid reinforcement, including the number of geogrids, geogrid layout, and the gradation of unbound layer. There are several parameters which affect the LWD test results including the hammer weight, the falling height, and the surface stress. The effect of these... 

Mechanical properties of a material near the surfaces and interfaces are different from those of the same material far from the surfaces/interfaces. The effect of this difference on the effective mechanical properties of heterogeneous materials becomes significant when the size of inhomogeneities is at the scale of nanometers. In this article, within a micromechanical framework, the effects of surface residual stress and surface elasticity are taken into account to obtain a macroscopic size-dependent yield function for nanoporous materials containing aligned cylindrical nanovoids. Based on the modified Hill's condition, the strains are decomposed into two parts, a part due to the external... 

Behavior of nanostructures, which are characterized by a large surface-to-volume ratio, is greatly influenced by their surface parameters, such as surface elastic moduli tensor. Accurate determination of the surface elastic constants by first principles is of particular interest. To this end, through consideration of the fundamental thermodynamic arguments for free solid surfaces, an analytical formulation for the change in specific Helmholtz surface free energy is developed. Relating this formulation to the corresponding energy calculated via first principles leads to the determination of the surface elastic moduli tensor. The surface mechanical properties, namely surface energy, surface... 

The effect of surface and interface elasticity in the analysis of the Saint-Venant torsion problem of an eccentrically two-phase fcc circular nanorod is considered; description of the behavior of such a small structure via usual classical theories cease to hold. In this work, the problem is formulated in the context of the surface/interface elasticity. For a rigorous solution of the proposed problem, conformal mapping with a Laurent series expansion are employed together. The numerical results well illustrate that the torsional rigidity and stress distribution corresponding to such nanosized structural elements are significantly affected by the size. In order to employ surface and interface...