Digital Image Correlation Analyses Using Moving Least Squares Approximation

Introduction Moving least squares approximation is one kind of meshless methods in which the approximation is built from nodes only. Comparing to mesh-based methods, meshless methods have advantages on (1) refining is simpler to incorporate, (2) moving discontinuities can be treated easily, (3) large deformation can be handled robustly, (4) higher-order continuous shape functions, (5) non-local interpolation character and (6) no mesh alignment sensitivity[1]. Moving least squares approximation has been used for constructing smooth approximations to fit a specific cloud of points in many surface generation applications. One of the most famous applications is probably the meshless or element-free Galerkin methods in solving boundary-value partial differential equations [2]. In this talk, a recent developed method of one-dimensional digital image correlation (DIC) analyses using moving least squares (MLS) approximation will be discussed. Specifically, MLS approximation has been applied to (1) subpixel interpolation of image grayscales; (2) deformation of a subset in a digital image correlation analysis. The new analyses algorithms are implemented in a MATLAB program. The results of MLS approximation are compared against other conventional DIC methods, such as linearized DIC and finite element DIC, in image subpixel interpolation and subset deformation mapping.