# Indentation Measurement in Thin Plates under Bending Using 3D Digital Image Correlation
###### Abstract  
In the current paper, a novel experimental methodology to characterize the contact behavior on thin plates under bending is presented. The method is based on the experimental measurement of the indentation observed during contact experiments. Tests were conducted using aluminum thin plates and a steel sphere to evaluate the effect of thickness and bending during contact. For this purpose, a non-contact optical technique, 3D Digital Image Correlation (3D-DIC), has been employed to measure the out-of-plane displacements experienced at the rear face of the specimens (opposite where the contact is occurring). An indirect measurement of the experimental contact law is obtained for different plate thicknesses (2 mm, 3 mm, 4 mm, 5 mm and 6 mm) as the contact load increases. An energy balance performed during contact experiments made it possible to evaluate and quantify the applied energy to generate bending and contact deformation. When the specimen thickness increases from 2 mm to 6 mm, contact deformation reaches higher values from the total applied energy. In addition, it is also possible to evaluate the portion of the elastically recovered energy for contact and bending deformation during the unloading. It has been observed that thicker specimens show a lower elastic energy recovery due to bending and a higher elastic energy recovery due to contact. Results clearly show how the ratio between absorbed and applied energy changes as the specimen thickness increases, highlighting the relevance of the proposed method for the characterization of contact behavior in thin plates. contact; indentation; absorbed energy; 3D Digital Image Correlation +
Footnote †: journal: Applied Sciences  
19 February 20211 March 20211 March 202117  
Recently, [PERSON] et al. [9] proposed an analytical model which included the influence of the specimen thickness to consider the effect of bending during contact. The reported experimental set up to measure indentation by [PERSON] et al. [10] and [PERSON] et al. [11] was crucial in the performed contact analysis providing high accuracy results. However, most of the reported methodologies so far are not able to differentiate accurately between the induced deformation due to bending and contact respectively. An example is the set-up proposed by [PERSON] et al. [4], who were able to quantify indentation but not the bending occurring during experiments, which could lead to inaccurate indentation results. Similar problems were found by other authors such as [PERSON] et al. [12], and [PERSON] et al. [13], who minimized the bending effect using fully supported plate geometry and measuring from both faces of the specimens, and hence introducing more variability and less precision in the results. An alternative solution was then adopted by [PERSON] et al. [14], who subtracted from experimental results the estimated deflection calculated from Finite Element Analysis to obtain the true relative approach as a function of applied load. Moreover, in the case of impact tests, indentation was measured after the impact and using manual methodologies [15; 16] showing discrepancies with the static contact law depending on the loading rate. Within this framework, large efforts have been performed towards the development of light-weight structures for high performance in dynamics applications using thin plates. Within this context, it is worth noting relevant works published in this field [17; 18]. The purpose of this paper is to present a novel experimental methodology to characterize the contact behavior of thin plates with different thicknesses using a full-field technique. Thicknesses between 2 mm and 6 mm have been used so as to be considered as thin plates with ratios _a/h_ between 10 and 100 [19], where \(h\) is a typical dimension of a plate in a plane and \(h\) is the plate thickness.