On Compression of Rubber Elastic Sphere Over a Large Range of Displacements—Part 2: Comparison of Theory and Experiment

Abstract

This paper presents experimental results of simple compression of a soft rubber sphere in a very large range of forces attaining at 5000 N, presenting calculational results by a set of five equations presented in Part 1. The calculational values of approach, the radius of contact surface, and lateral expansion agree well with the experimental data in the large range of deformations. It is thus verified experimentally that the set of the equations (12), (13), (31), (40), and (43) in Part 1 is approximately valid in large deformations for rubber sphere. Program using a personal computer in calculating five quantities from the five nonlinear equations associated with the five quantities is noted.

Development of techniques to compare mechanical properties of reversible hydrogels with spherical, square columnar and ocular lens geometry

“…This is a critical link in developing a robust finite element model to determine the cause of presbyopia and identify possible methods of treatment. We have extended the seminal work of Hertz [20] and Tatara [21,22,25] on the mechanical properties of rubber spheres at low and high deformations, respectively, to that of the lens.…”

“…Thus, the elastic force is proportional to 3/2 power of approach, and the gradient of F(y) in a log-log plot is proportional to E. For large deformation, as in the current studies, incorporation of the non-linear rubber elasticity model becomes necessary [23,24]. Recently, Tatara [21,22,25] developed a general theory for the compressive deformation for a homogenous non-adhesive rubber sphere under large deformation (O15% strain) with non-linear elastic behavior. Here, the model derived by Tatara [21,22,25] was adopted.…”

“…Recently, Tatara [21,22,25] developed a general theory for the compressive deformation for a homogenous non-adhesive rubber sphere under large deformation (O15% strain) with non-linear elastic behavior. Here, the model derived by Tatara [21,22,25] was adopted. Fig.…”

“…This makes it possible to measure M n (number average molecular weight) and the subsequent determination of M c (molecular weight between cross-links) through an assay of the amount of free thiol group per chain. We used and extended theories of polymer network elasticity and theories of Hertz [20] and Tatara [21,22] that were initially developed for mechanical modeling of rubber spheres between parallel plates, to biconvex spherical gels in compression.…”

A compact, robust, and transportable ultra-stable laser with a fractional frequency instability of 1 × 10−15

“…For a perfectly linear elastic material, the squeezing force needs to balance the maximum reaction force. In our case this would require, for each of the four points in each direction, a squeezing force of 15 N. However, the large-range behavior of viton balls is strongly nonlinear, with the force increasing to the power 3/2 with approach [22,23]. This reduces the required squeezing force by 30% to 10 N. Implementing a higher nonlinearity, e.g.…”