Contracting cube equation

This is often referred to as the contracting volume (cube or sphere) equation and is the simplest example of a more general family of expressions [28—31,432,453,458,459], which includes consideration of different rates of interface advance in different crystallographic directions and of variations in crystallite dimensions and shapes. The approach is readily extended, by use of solid geometry, to allow for angles between planar surfaces. Some examples of characteristic behaviour are conveniently discussed with reference to the expression... 

Although Newton had measured the black spot at the contact of glass spheres, and also seen the black spot expand and contract reversibly as the spheres were pressed together, he did not pursue the relationship between the spot size and load. Almost 200 years were to elapse before Hertz defined the connection published in 1882. Hertz was a 23-year-old assistant to Helmholtz in Berlin when he was stimulated by Newton s rings and derived the elastic theory of sphere contact in his Christmas vacation in 1880." He found that the spot diameter increased with the cube root of load F, showed that the elastic modulus E, Poisson s ratio v and sphere diameter D were also important, and verified his equation... 

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