No abstract

International audienceThe ply elastic constants needed for classical lamination theory analysis of multi-directional laminates may differ from those obtained from unidirectional laminates because of three dimensional effects. In addition, the unidirectional laminates may not be available for testing. In such cases, full-field displacement measurements offer the potential of identifying several material properties simultaneously. For that, it is desirable to create complex displacement fields that are strongly influenced by all the elastic constants. In this work, we explore the potential of using a laminated plate with an open-hole under traction loading to achieve that and identify all four ply elastic constants (E 1 , E 2 , ν 12 , G 12 ) at once. However, the accuracy of the identified properties may not be as good as properties measured from individual tests due to the complexity of the experiment, the relative insensitivity of the measured quantities to some of the properties and the various possible sources of uncertainty. It is thus important to quantify the uncertainty (or confidence) with which these properties are identified. Here, Bayesian identification is used for this purpose, because it can readily model all the uncertainties in the analysis and measurements, and because it provides the full coupled probability distribution of the identified material properties. In addition, it offers the potential to combine properties identified based on substantially different experiments. The full-field measurement is obtained by moiré interferometry. For computational efficiency the Bayesian approach was applied to a proper orthogonal decomposition (POD) of the displacement fields. The analysis showed that the four orthotropic elastic constants are determined with quite different confidence levels as well as with significant correlation. Comparison with manufacturing specifications showed substantial difference in one constant, and this conclusion agreed with earlier measurement of that constant by a traditional four-point bending test. It is possible that the POD approach did not take full advantage of the copious data provided by the full field measurements, and for that reason that data is provided for others to use (as on line material attached to the article)

The basic formulation of the least-squares method, based on the L 2 norm of the residuals, is still widely used today for identifying elastic constants of aerospace materials from experimental data. While this method often works well, methods that can benefit from statistical information, such as the Bayesian method, may sometimes be more accurate. We seek situations with significant difference between the material properties identified by the two methods. For a simple three-bar truss example we illustrate three situations in which the Bayesian approach systematically leads to more accurate results: different sensitivity of the measured response to the parameters to be identified, different uncertainty in the measurements, and correlation among response components. When all three effects add up, the Bayesian approach can be much more accurate. Furthermore, the Bayesian approach has the additional advantage of providing the uncertainty in the identified parameters. We also compare the two methods for a more realistic problem of identification of elastic constants from natural frequencies of a composite plate.