Inverse analysis to determine contact stresses using photoelasticity

Abstract

This chapter reviews a technique that is developed for determining contact stresses from photoelastic image data of one of the contacting bodies. The contact stress is determined by solving two problems: a problem to determine the distribution of the difference of the principal stresses inside the specimen from isochromatic fringe image data and an inverse problem to estimate the unknown boundary values from the difference of the principal stresses inside the specimen. The inverse problem is formulated and solved by using boundary element method (BEM) and a nonlinear optimization method. The effectiveness of the present technique is verified by determining the contact stress between a rectangular steel stamp and an epoxy plate. The contact stress is sometimes measured directly by some sensor inserted between contacting bodies. However, contact state is more or less altered by the sensor itself. Therefore, indirect methods that do not affect the contact state are needed for accurate measurement of contact stresses. One of the most favorable techniques is the technique based on the concept of inverse analysis in which the contact stress is estimated from experimental data obtained at some points away from the interface of the contacting bodies.