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In the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local minimizer...
Rate-independent problems are considered, where the stored energy
density is a function of the gradient. The stored energy density may
not be quasiconvex and is assumed to grow linearly. Moreover,
arbitrary behaviour at infinity is allowed. In particular, the
stored energy density is not required to coincide at infinity with a
positively 1-homogeneous function. The existence of a
rate-independent process is shown in the so-called energetic
formulation.
A justification of the two-dimensional nonlinear “membrane”
equations for a plate made of a Saint Venant-Kirchhoff material has
been given by Fox et al. [9] by means of the method of formal
asymptotic expansions applied to the three-dimensional equations of
nonlinear elasticity. This model, which retains the material-frame
indifference of the original
three dimensional problem in the sense that its energy density is
invariant under the rotations of , is equivalent to finding the
critical points...
In this paper we give an existence theorem for the equilibrium problem for nonlinear micropolar elastic body. We consider the problem in its minimization formulation and apply the direct methods of the calculus of variations. As the main step towards the existence theorem, under some conditions, we prove the equivalence of the sequential weak lower semicontinuity of the total energy and the quasiconvexity, in some variables, of the stored energy function.
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