Free-Form Deformation Digital Image Correlation (FFD-DIC): A non-invasive spline regularization for arbitrary finite element measurements

Abstract

Regularizing Finite-Element Digital Image Correlation (FE-DIC) problems is essential when using fine meshes, for instance to get a direct bridge with simulation tools or in view of performing data assimilation. Shape optimization brings comparable concerns so it is proposed to draw inspiration from this field of research. In this respect, a new general spline-based non-invasive regularization scheme is proposed, based on the Free-Form Deformation (FFD) concept that offers the opportunity to decouple the design space from that of the actual geometry to be updated. The main idea is to embed the input FE mesh, with any element type or size, into a simple cuboid B-spline box and to relate the nodal FE dof of the measured field to another more regular field discretized by the box. The regularization length is thus directly driven by the box refinement. A specific care is taken to handle possible conditioning problems caused by non-influential control points. From a practical point of view, the method can be interpreted as a projection on a reduced basis; therefore, it results in a regularized but conventional FE measured field which can be simply computed from a standard FE-DIC code. The developed scheme is applied for FE displacement measurement using DIC and for mesh-based measurement in stereo-DIC. For the latter, a novel procedure based on additional projections over local directions complements the FFD method for full efficiency. The performance of the strategy is assessed on real images coming from various experimental tests and comparisons are made with other published techniques to prove its effectiveness.