by Frédéric Sur (Université de Lorraine, Inria), Benoît Blaysat and Michel Grédiac (Université Clermont-Auvergne)
Experimental mechanics is currently experiencing a revolution: the rapid development and spread of camera-based measurement systems, which enable experimentalists to visualise the displacement and strain distributions occurring in structures or specimens subjected to a load. In order to obtain information that is as valuable as that provided by numerical models, we need to move on from lowly to highly-resolved maps, and from qualitative to quantitative measuring tools. To this end, new mathematical results and algorithms are needed.
The research field of experimental solid mechanics focusses mainly on characterising the response of engineering materials and structures when they are subjected to thermo-mechanical loads. Tests may be performed to observe the response of the constitutive materials, to help propose relevant models to describe this response, to identify their associated governing parameters which are then employed in numerical models, or to validate design procedures relying on predictive numerical calculations.
This work encompasses research areas ranging from civil engineering, aeronautics, ground transportation industry and microelectronics. Recently a new research domain named photomechanics has emerged, which is aimed at developing full-field measurement systems and using them to best characterise materials and structures. This domain is at the crossroads of traditional experimental mechanics and image analysis, since full-field measurements, namely displacement and strain fields, are obtained from a series of images of a (generally slightly) deformed specimen. Despite their appeal, these measuring tools are far from having reached maturity for several reasons.
First, the lack of procedures and standards enabling the metrological performance of full-field measurement systems still limits their use to qualitative measurements in many cases, or leads to the provision of quantitative information with a poor measurement resolution compared to conventional localised measurement means such as strain gauges. For instance, it is of utmost importance to quantify the measurement resolution, the spatial resolution, or the measurement systematic error. These quantities are intrinsically linked to each other and to the estimation process. Measurement resolution is impaired by signal-dependent noise coming from the imaging sensor. The spatial resolution not only depends on the sensor’s pixel density but also on the computational method used to estimate the displacement or strain fields. It is also related to th e systematic error, which links the measurement to the ‘true’, and unknown, value of interest. Thus, mathematically analysing the whole estimation process is of prime importance. Restoration methods such as denoising or super-resolution are to be investigated here in order to improve these quantities. For instance, Figure 1 a) shows a strain field on the surface of a shape memory alloy under tension. Since a relation was established between the measured strain field and the unknown real field, it is possible to restore the strain field and to improve the metrological performances in turn.
Preliminary results on this topic are discussed in  and are illustrated in Figure 1 b). This is a challenging problem for a number of reasons: the restored quantities are not images but measurement fields extracted from these images, information on displacement and strain hardly emerges from the noise floor in the case of small strains, and it is crucial to quantify the improvement of the restoration techniques on the metrological performances. In addition to carefully modelling sensor noise. It is essential to take into account subtle effects that cannot be ignored such as vibrations affecting the experimental setup, or optical distortions. These aspects contrast with many traditional applications of computational imaging which usually give qualitative results.
Figure 1:Shape memory alloy under tension: a strain map obtained with the grid method, before (left) and after restoration (right) as discussed in . Two martensite needles (in red) are now visible and well separated.
Second, the availability of strain maps while testing materials has progressively raised the following question: what is the best way of processing measurement fields to retrieve the parameters governing constitutive equations which describe the response of the material being tested? To answer this question it is necessary to address inverse problems. This requires dedicated numerical procedures that have only been developed recently in response to the advent of full-field measurement techniques. Some of these procedures are still in their infancy, and their respective performances have only been compared in embryonic form, so there is still much work to be done. Again, this confronts the experimental mechanics community with largely open problems.
To address these issues, the acquisition chain must be thoroughly modelled, from the imaging sensor to the measurement field, and eventually to the parameters which are retrieved from the images. For example,  is a recent survey and analysis of the grid method; one of the available full-field systems. The advantage of this method based on spectral analysis is that predictive formulas are available to assess the metrological performance. For these reasons, the establishment of a new scientific domain which could be called computational photomechanics is undoubtedly warranted. It would give access to metrologically certified measurement fields by a thorough mathematical analysis, and to more information than traditional methods thanks to appropriate image processing tools.
 M. Grédiac, F. Sur, C. Badulescu, J.-D. Mathias : “Using deconvolution to improve the metrological performance of the grid method” Optics and Lasers in Engineering, vol. 51, no. 6, pages 716-734, Elsevier, 2013.
 M. Grédiac, F. Sur, B. Blaysat: “The grid method for in-plane displacement and strain measurement: a review and analysis”, Strain, vol. 52, no. 3, pages 205-243, Wiley, 2016.
Frédéric Sur, Université de Lorraine, Loria and Inria