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Nonlinear Size-Dependent Finite Element Analysis of Functionally Graded Elastic Tiny-Bodies

M. Shaat's picture

This paper is now in Press and available on line at the Intenational Journal of Mechanical Sciences.

In this paper, a nonlinear size-dependent finite element model
incorporating surface energy effects is developed to study the mechanical
behavior of tiny elastic functionally graded (FG) bodies. Here the classical
elasticity theory is modified to incorporate the surface energy effects.
Most of previous studies assumed that the
surface energy depends only on the 2D symmetric infinitesimal surface strains
and neglects the second-order products of surface strains/displacement
gradients. These descriptions assume a small strain deformation of the surface
and neglect the pre-strain that is, already, developed on the surface – before
loading – due the pre-tension stress

. Here in this paper, the pre-strain is considered which forces the
surface to a state of large strain after loading instead of small strain. In
this sense, in the presence of initial surface tension, the theory of surface
elasticity is a hybrid formulation characterized by linearized bulk elastic
material and second order finite deformation of the surface. In the proposed
finite element model, the surface energy effect is
taken into account in the derivation of the element stiffness matrix for the
material elements located very close to the boundary surface.
proposed model is then used to study the effects of surface energy, including
the 2nd order displacement gradient, on the mechanical behavior of plane-strain functionally
graded elastic body.

The paper is available at:

M. Shaat

Best regards,
Mohammed Ibrahim Shaat (M.Shaat) 
Research Assistant
Mechanical Engineering Department, Zagazig University, Zagazig 44511, Egypt 
Tel: +20 0122 2232469

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