a JKR theory of adhesion for anisotropic solids

Jim Barber and I just got accepted this paper in JMPS, and it is also already available on Arxiv.  We found a remarkably simple closed form solution for adhesion on orthotropic materials in the planes of symmetry.  This shows adhesion can increase significantly due to anisotropy, namely the JKR solution continues to hold in the sense of mean elastic modulus, but the prefactor can grow without limit. We expect applications in crystals indentation, but also in locomotion in biological world.

http://arxiv.org/abs/1312.2779

Title: JKR solution for an anisotropic half space
Authors: J. R. Barber, M.Ciavarella
Categories: cond-mat.mtrl-sci
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  In this paper, the classical JKR theory of the adhesive contact of isotropic
elastic spheres is extended to consider the effect of anisotropic elasticity.
The contact area will then generally be non-circular, but in many cases it can
reasonably be approximated by an ellipse whose dimensions are determined by
imposing the energy release rate criterion at the ends of the major and minor
axes. Analytical expressions are obtained for the relations between the contact
force, the normal displacement and the ellipse semi-axes. It is found that the
eccentricity of the contact area decreases during tensile loading and for cases
when the point load solution can be accurately described by only one Fourier
term, it is almost circular at pull-off, permitting an exact closed form
solution for this case. As in the isotropic JKR solution, the pull-off force is
independent of the mean elastic modulus, but we find that anisotropy increases
the pull-off force and this effect can be quite significant.

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