A study of optimal equivalent characteristics of insole materials

In this preliminary study, a methodology was illustrated in the determination of the characteristics of an insole material by modeling it as an equivalent mass-spring-damper system. The experimental deceleration-time data obtained from specimens of twenty commercial formulations of shoe insole materials were utilized to verify a suitable mathematical model that could be used as an adequate representation of a shoe insole material. The suitable equivalent model was used to search for parameter values that would yield the best cushioning effect. For this study, two linear and two nonlinear mass-spring-damper systems were investigated. The two models with linear spring and damping elements were found to be unsuitable representations of the tested materials. The nonlinear six-parameter model was found to perform only marginally better than the nonlinear four-parameter model. Therefore, the simpler four-parameter model was selected for optimization study. In the optimization study, multiple local minima were found with the nonlinear four-parameter model using an unbounded variable optimization routine. However, when lower and upper bounds were specified for the four parameters, two of the parameters consistently approached the lower bound values, one parameter approached the upper bound value, and the remaining parameter settled at a value close to the lower bound. Global minimum was unattainable in the present study