The large deformation of a single micro-elastomeric sphere

Abstract

This paper reports on an experimental and theoretical study of the mechanical response of microscopic (about ) elastomer spheres compressed between two smooth parallel platens over a wide range of imposed deformations. An experimental arrangement for obtaining these data is described. Experimental results presented for these elastomeric micro-spheres confirm the theoretical predictions of various models for the dependence of the reaction force on the compressive deformation of a sphere. At values of the dimensionless approach [(compressive displacement)(initial particle diameter)] up to 10%, the classical Hertz theory was found to be in good agreement with experimental results and confirms that the load is a function of the approach to the power . At larger deformations (dimensionless approaches in the cases 10-37%), a numerical implementation of Tatara's large deformation model for the compression of an elastomeric sphere gives good agreement with experimental results. The Tatara analysis provides a numerical solution in which the load depends on the approach cubed for large deformations and follows the fifth power of the approach for even larger deformations. The good agreement between the experimental results and theoretical predictions described facilitates the determination of a number of mechanical properties of these microscopic particles from the experimental load versus displacement curves. The Tatara-based analysis, combined with experimental data for a 37% dimensionless approach, allows the explicit estimation of the Poisson ratio for these elastomeric particles. An application of the Hertz or Tatara analyses, depending upon the dimensionless approach regime investigated experimentally, also allows the plane strain modulus of a single particle to be determined.