Chapter 5
Meshless Methods for Full Field Displacement and Strain Measurement


Over the last decade, full field measurement methods have become a very useful tool for experimental mechanics and other technical disciplines. The rapid evolution of digital imaging, that has materialized toward higher quality, more inexpensive digital cameras, and the increase in the available computational power, have made these methods accessible to a broader range of scientific laboratories. Our interest in the continuing development of meshless methods for full field measurements originates from the need to improve, generalize and integrate them into the data-driven composite material characterization methodology via multi-axial mechatronic systems that were developed by the Naval Research Laboratory (NRL). This methodology requires the measurement of both in-plane and out-of-plane strain fields, and therefore such methods are particularly attractive for this purpose. In addition, there is a large variety of applications in the area of experimental mechanics and other technical disciplines where the whole field displacement and strain measurement is very important, and consequently provide a unique opportunity for the usage of the meshless approximation schemes. In engineering applications traditional approximation schemes involve the use of discrete elements corresponding to typical meshes for representing field variable distributions. More specifically, the underlying geometry is subdivided into a number of sub-regions of simple geometry, usually in the shape of a triangle or quadrilateral. The values of the field quantities of interest within these subregions or elements can be calculated based on assumed shape functions of the respective elements. In meshless approaches such sub-regions are not defined and the values of the field variable are calculated based on shape functions operating on nodal values only. All the traditional full field measurement techniques are based on shape functions associated with element approaches. This chapter is motivated by the need to report on the advances related to the use of meshless approximations in full field displacement and strain measurements. These approximations were first introduced in [1] and were shown to be a very efficient way to increase the accuracy of these methods by taking advantage of the filtering characteristics of the representation. The method was more recently updated with a direct strain approximation scheme that increases the accuracy even further [2]. The goal of this chapter is to present the older meshless random grid method (MRG) and the newer direct strain imaging (DSI) methods, while comparing their performance and reporting on implementation details, like their 3-D extension.

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