Computing Strain Distributions from Measured Displacements on a Three-dimensional Surface

Abstract

A simple method for calculating strain distributions on a three-dimensional surface from measured displacements is proposed in the present study. Displacement components within a small region on the three-dimensional surface are transformed into the displacements on a local Cartesian coordinate system. The displacements on the local coordinate system are approximated by polynomial functions using least-squares. Strains within the small region are then obtained from the coefficients of the approximated functions. Repeating this procedure for the whole field, the distributions of the principal strains are obtained. The effectiveness of the proposed method is validated by applying the method to the displacements obtained by finite element method. Then, the application of the method to the surface strain measurement of human face is demonstrated. It is shown that the proposed method is a powerful and efficient tool for data reduction because the strains on a three-dimensional surface are obtained simply and easily by the proposed method.