Identification modale numérique-expérimentale des propriétés élastiques et dissipatives de matériaux composites

Composite materials undoubtedly belong to one of the most studied classes of materials nowadays. In order to model the behaviour of mechanical structures made of this type of materials, it is necessary to know their constitutive properties. The varieties of composite materials as well as their manufacturing process – almost specific to each application – lead to the difficulty of knowing precisely their mechanical properties. The determination of these properties is usually carried out by static tests compared to analytical models. Recently, a new class of experiments does not compare the experimental results with a simple analytical model any more but uses a more complete discrete numerical model. As the latter is not invertible, it is then necessary to use an iterative optimization procedure to extract the constitutive properties of the material. This type of procedure requires a discrete numerical model which has to be precise while of fast execution, because the model will have a direct influence on the precision and convergence rate of the whole identification method. In this work, we propose to develop a mixed numerical-experimental method capable of estimating the elastic and dissipative properties of composite materials. The effects of intrinsic dissipation in materials are studied as their evaluation is necessary for the complete vibratory behaviour characterization of a structure. In this study, we take into account the fact that the dissipative properties present an anisotropic character as the elastic properties. To realize this work, we selected a constitutive law taking into account the dissipative effects and implemented it within an existing finite element code. After studying the available damping models, we retained a hysteretic (or structural) model in order to obtain a behaviour close to what was observed on various samples. We formulated shell elements with a polynomial through-the-thickness displacement approximation of variable order, allowing to model accurately thick structures. The association within a finite element software of a dissipative behaviour law – leading to a complex eigenvalue problem – and a variable-order shell element constitutes a new useful tool for the numerical modal analysis of dissipative structures. The numerical model developed represents one of the key elements necessary for the creation of a mixed numerical-experimental method devoted to the identification of the elastic and dissipative properties in composite materials. Other fundamental features of this method are the modal measurements of specimens, the extraction of the modal data from the frequency response functions measured, as well as the optimization routine itself. We developed a measurement technique which is based upon a laser interferometer as well as an excitation system – of acoustic type, by using a loudspeaker, or mechanical type, by using an electrodynamic shaker – to extract the frequency response functions of the structure under investigation. From these functions, we extracted the modal properties – eigenfrequencies, modal damping ratios and complex mode shapes – by means of a modal analysis software using multiple degrees of freedom. The identification routine developed under Matlab® modifies the input parameters of the numerical model until an output close to the experimental data is obtained, by using a Levenberg-Marquardt optimisation algorithm with specific error functions based on the modal parameters. The procedure has been numerically validated, then applied to several materials through test examples. We verified that for plate-type specimens, the six elastic properties E1, E2, ν12, G12, G23 and G31 are generally correctly identified, with an error from 1 to 10 % depending on the parameter investigated. Regarding the dissipative properties, we highlighted that their estimation is more difficult than the one of the corresponding elastic properties. This resulted mainly from the measure of the modal damping factors, affected by an error larger than the uncertainty on the estimation of the eigenfrequencies. However, we obtained accurate results for the identified loss tangents tan dδ(E1), tan dδ(E2) and tan dδ(G12). We could demonstrate that the residual error on the eigenfrequencies and the modal damping ratios between the experimental and identified models was of the order of 0.2 % and 10 % respectively.