Surface effects in the pure bending problem in the theory of elastic materials with voids

Abstract eng:
g We consider the pure bending problem in the theory of linear elastic materials with voids using modified type of boundary conditions. First, it is shown that Inicro—dilatation theory is a special case of the general theory of media with conserved dislocations. Variational statement of the last one provides a specific and more common type of boundary conditions due to presence of surface stresses. It is known that pure bending solution in the Inicro—dilatation theory contains the nonzero values of transverse normal stresses in the beam, which do not appear in the classical linear elasticity. We prove that it could be found the solutions without transversal stresses, due to special values of surface parameters in the considered model. Additionally it is shown the possibility of the effective elastic properties introduction in the problem of pure bending, which depends on the thickness of a beam and surface parameter.

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