Vol. 5, No. 5, 2010

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Axial compression of hollow elastic spheres

Robert Shorter, John D. Smith, Vincent A. Coveney and James J. C. Busfield

Vol. 5 (2010), No. 5, 693–705
Abstract

When thin-walled hollow elastic spheres are compressed between two parallel rigid surfaces, there is an initial flattening of the sphere in the contact regions, followed by a snap-through buckling of the flattened surface. As the compression increases the sphere undergoes further buckling modes as a number of ridges and folds are formed. This elastic buckling deformation is investigated using a finite element analysis (FEA) technique. It is shown that the ratio of displacement at buckling to wall thickness depends weakly not only on Poisson’s ratio, $\nu$, but also on the ratio of the geometric wall thickness, $h$, to sphere radius, $R$. This approach is validated by comparison with experimental compression results on microspheres of approximately 40 $\mu$m in diameter to table tennis balls with a diameter of 40 mm.

The analysis shows that a simple axial compression of a thin-walled hollow sphere can be used to measure both the average wall thickness of the sphere, from the deformation at the buckling snap-through, and the modulus from the force at this point. This provides a good technique to fully characterise the geometry and the elastic behaviour of thin-walled spheres of any size.

Keywords
compression, buckling, instability, hollow spheres, finite element analysis