Three-dimensional Finite Element Analysis of Elastic Continua for Tactile Sensing

Abstract

This article presents a method for determining three- dimensional stress and strain tensors within elastic layers covering or embedding tactile sensors. When an object comes in contact with the elastic surface of a sensing array, the distribution of forces on the surface is mechani cally filtered before reaching the underlying sensing ele ments. In order to predict the response of embedded sen sors and to understand the nature of the transduced variables, the relationship between surface forces and interior stress and strain tensors must be known. To deter mine this, we need to know the shape of the surface con tact area and the distribution of forces over that area, both normal and tangential. The algorithm described here discretizes the known surface force distribution into a dense array of independent point loads, approximating the surface force profile. The stress field produced by a single normal and/or a single tangential point load can be expressed analytically, given the elasticity and compressi bility of the material. Fields for each point load are calcu lated and can be summed to determine the resultant stress tensor at any point within the medium. Strains can be computed from stresses using a simple set of translation formulas. A detailed example is illustrated, analyzing the inter action between a sphere and a planar elastic half space. From the example the relative effects of depth and dis tance from the center of contact on the response of underlying sensors is discussed. Using results from the example, methods are proposed to exploit sensors at dif ferent depths and at different orientations within the medium. An algorithm for determining the direction of surface tangential forces and a method for determining the ratio between normal and tangential forces are ana lyzed, using unidirectionally sensitive sensors at different depths in the elastic layer.