L'utilisation de limiteurs de localisation est nécessaire pour prendre en compte l'apparition de macro-fissures lors de la simulation de l'évolution des dégradations dans les matériaux composites stratifiés en accord avec des expérimentations. Ceux-ci introduisent un paramètre qui peut être relié à une longueur, ou un temps caractéristique, qui peut alors être identifié. L'approche introduite au LMT-Cachan consiste, dans le cadre dynamique, à utiliser un modèle d'endommagement retardé. Elle est basée sur le fait qu'une fissure ne peut pas apparaître instantanément. Ce modèle donne d'excellents résultats en restant dans le cadre de la dynamique et a l'avantage d'être local en espace. Cependant il requiert une discrétisation temporelle de la taille du temps caractéristique introduit (de l'ordre de la microseconde pour les composites), qui le rend inexploitable pour des simulations de chargement en quasi-statique. Les simulations dans ces cas de chargement nécessitent donc l'utilisation d'un temps caractéristique différent de celui identifié qui ne permet plus de maintenir un résultat en accord avec l'expérience. On cherche alors à adapter les paramètres de la loi d'évolution de l'endommagement afin d'obtenir une propagation de la macro-fissure dans la zone localisée qui soit compatible énergétiquement avec la mécanique de la rupture en contrôlant le taux de restitution d'énergie. Ce travail est dédié à maintenir l'objectivité de la solution et à adapter l'énergie dissipé à la mécanique de la rupture afin de pouvoir utiliser un temps caractéristique exploitable lors de simulations d'éprouvettes en composites sous un chargement quasi-statique. / The use of localization limiters is needed to take into account the apparition of macro-cracks during the simulation of the evolution of degradations in laminated composite materials with respect to experiments. Those introduce a parameter which can be related to a characteristic length, or a characteristic time, and therefore be identified. The approach introduced at LMT-Cachan is, in dynamics, to use a delayed damage model. It's based on the fact that a crack can't appear instantaneously. This model gives excellent results in dynamics and has the advantage to be local in space. Unfortunately, it requires a time discretization related to the characteristic time introduced (of the order of a microsecond for composites), which is far too computationally expensive for quasi-static simulations. Simulations in these loading cases need the use of a different characteristic time from the one identified which can't maintain anymore a result in accordance to experiments. We then adapt the parameters of the damage evolution law to obtain a propagation of a macro-crack in the localized zone that is energetically compatible with fracture mechanics by controlling the strain energy release rate. This work is dedicated to maintain the objectivity of the solution and to adapt the dissipated energy to fracture mechanics to be able to use a characteristic time exploitable for the simulation of composite samples under quasi-static loading.

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The three-dimensional linear theory of piezo-elasticity is used to analyse steady state vibrations of a simply supported rectangular laminated composite plate with piezoelectric (PZT) actuator and sensor patches either embedded in it or bonded to the its surfaces. It is assumed that different layers are perfectly bonded to each other. The method of Fourier series is used to find an analytical solution of the problem. The analytical solution is then applied to study the shape control of a steadily vibrating composite plate by exciting different regions of a PZT actuator. Numerical results for a thin and a thick plate containing one embedded actuator layer and one embedded sensor layer are presented. For the former case, the optimum location of the centroid of the excited rectangular region that will require minimum voltage to control the out-of-plane displacements is determined. Keeping the location of the centroid and the shape of the excited region fixed, we ascertain the voltage required as a function of the length of its diagonal to nullify the deflections of the plate. The maximum shear stress at the interface between the sensor and the lamina is found to be lower than that between the actuator and the lamina. The point of maximum output voltage from the sensor coincides with that of its peak out-of-plane displacement. The variations of displacement and stress components through the thickness for the thin and thick plates are similar. The transient finite deformations of a neo-Hookean beam or plate with PZT patches bonded to its upper and lower surfaces are simulated by the finite element method. The constitutive relation for the piezoelectric material is taken to be linear in the Green-Lagrange strain tensor but quadratic in the driving voltage. A code using 8-noded brick elements has been developed and validated by comparing computed results with either analytical solutions or experimental observations. The code is then used to study flexural waves generated by PZT actuators and propagating through a cantilever beam both with and without a defect in it. The computed results are compared with test observations and with the published results for the linear elastic beam. The effects of both geometrical and material nonlinearities are discussed. A simple feedback control algorithm is shown to annul the motion of a neo-Hookean plate subjected to an impulsive load. / Ph. D.

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