Sharif Digital Repository

In addition to enhancement of the results near the point of application of a concentrated load in the vicinity of nano-size defects, capturing surface effects in small structures, in the framework of second strain gradient elasticity is of particular interest. In this framework sixteen additional material constants are revealed, incorporating the role of atomic structures of the elastic solid. In this work, the analytical formulations of these constants corresponding to fcc metals are given in terms of the parameters of Sutten-Chen interatomic potential function. The constants for ten fcc metals are computed and tabulized. Moreover, the exact closed-form solution of the bending of a... 

The  usual  continuum  theories  are  inadequate  in  predicting  the  mechanical  behavior of solids in presence of small defects and stress concentrators; it is well known that such continuum methods are unable to detect the change of the size of  the  inhomogeneities  and  defects.   For  these  reasons  various  augmented  continuum theories and strain gradient theories have been proposed in the literature. The major difficulty in implication of these theories lies in the lack of information  about  the  additional  material  constants.  For  fcc  metals,  for  calculation of the associated characteristic lengths which arise in first strain gradient  theory,  an ... 

In this thesis one of the mesh-free methods called RKPM is employed to solve the differential equations of strain-gradient elasticity. To this end the corresponding weak form is laid down. Subsequently the relevant stiffness-matrix is obtained by discretization of the weak form. To be sure about the accuracy of the relations, the problem of a plate weakened by a hole under uniform far-field tension, for which the exact solution is available in the literature, is solved. The obtained numerical result is in good agreement with the solution of Eshel and Rosenfeld. Afterwards, a plate containing a crack of finite length subjected to uniform far-field tension (mode I) is considered. This problem... 

There are experimental observations that show material response in micro-scale is dependent on some other parameters rather than Lame parameters. Strain gradient elasticity has been recently developed to take into account this characteristic of materials response. In strain gradient elasticity, characteristic length parameters enter the constitutive equations through the elastic strain energy density function. The elastic strain energy density function is assumed to be a function of the gradient of strain tensor in addition to the strain tensor. In this way, new material constant (characteristic length parameters) are introduced and entered into the constitutive equations. In recent years,... 

In many structures, crack creation is one of the most significant fracture mechanisms. To predict these fracture mechanisms accurate numerical modeling is necssary. Finite Element Method (FEM) is one of the substantial methods in analysis of numerical fracture problems in recent past decades. But, this method has difficulties in remeshing of elements in each step of calculation in fracture mechanics or large deformation analysis. Therefore, the theory was defined that, without using elements, just with setting of characteristics nodes in geometry of problem, the differential equations can be solved. These methods are called Meshfree or Meshless methods. RKPM is a new meshfree method for...