Shearing effects on the breathing mechanism of a cracked beam section in bi-axial flexure

 The main purpose of this paper is to complete the works presented by
Andrieux and Varé (2002) and El Arem et al. (2003) by taking into
account the effects of shearing in the constitutive equations of a beam
cracked section in bi-axial flexure. The paper describes the derivation
of a lumped cracked beam model from the three-dimensional formulation of
the general problem of elasticity with unilateral contact conditions on
the crack lips. Properties of the potential energy and convex analysis
are used to reduce the three-dimensional computations needed for the
model identification, and to derive the final form of the elastic energy
that determines the nonlinear constitutive equations of the cracked
transverse section. We aim to establish a relation of behavior between
the applied forces and the resulting displacements field vectors, which
is compatible with the beams theory in order to allow the model
exploitation for shafts dynamics analysis. The approach has been applied
to the case of a cracked beam with a single crack covering the half of
its circular cross section.

http://www.sciencedirect.com/science/article/B6VKW-4WCTWN7-1/2/fbb7915ce...