Abstract: The problem of N cracks interaction in an isotropic
elastic solid is decomposed into a subproblem of a homogeneous solid
without crack and N subproblems with each having a single crack
subjected to unknown tractions on the two crack faces. The unknown
tractions, namely pseudo tractions on each crack are expanded into
polynomials with unknown coefficients, which have to be determined
by the consistency condition, i.e. by the equivalence of the original
multiple cracks interaction problem and the superposition of the N+1
subproblems. In this paper, Kachanov-s approach of average tractions
is extended into the method of moments to approximately impose the
consistence condition. Hence Kachanov-s method can be viewed as
the zero-order method of moments. Numerical results of the stress
intensity factors are presented for interactions of two collinear cracks,
three collinear cracks, two parallel cracks, and three parallel cracks.
As the order of moment increases, the accuracy of the method of
moments improves.
Abstract: When the characteristic length of an elastic solid is
down to the nanometer level, its deformation behavior becomes size
dependent. Surface energy /surface stress have recently been applied
to explain such dependency. In this paper, the effect of
strain-independent surface stress on the deformation of an isotropic
elastic solid containing a nanosized elliptical hole is studied by the
finite element method. Two loading cases are considered, in the first
case, hoop stress along the rim of the elliptical hole induced by pure
surface stress is studied, in the second case, hoop stress around the
elliptical opening under combined remote tension and surface stress is
investigated. It has been shown that positive surface stress induces
compressive hoop stress along the hole, and negative surface stress has
opposite effect, maximum hoop stress occurs near the major semi-axes
of the ellipse. Under combined loading of remote tension and surface
stress, stress concentration around the hole can be either intensified or
weakened depending on the sign of the surface stress.
Abstract: Nanomaterials have attracted considerable attention
during the last two decades, due to their unusual electrical, mechanical
and other physical properties as compared with their bulky
counterparts. The mechanical properties of nanostructured materials
show strong size dependency, which has been explained within the
framework of continuum mechanics by including the effects of surface
stress. The size-dependent deformations of two-dimensional
nanosized structures with surface effects are investigated in the paper
by the finite element method. Truss element is used to evaluate the
contribution of surface stress to the total potential energy and the
Gurtin and Murdoch surface stress model is implemented with
ANSYS through its user programmable features. The proposed
approach is used to investigate size-dependent stress concentration
around a nanosized circular hole and the size-dependent effective
moduli of nanoporous materials. Numerical results are compared with
available analytical results to validate the proposed modeling
approach.