Comportement multiaxial de pièces élastomères pré-contraintes: Application aux suspensions moteur

The purpose of this thesis is to develop a method for characterizing and modelling the behavior of elastomeric engine mounts. Loading conditions undergone by these parts are decomposed in two steps, which are a large preload caused by the weight of the engine, considered as quasi-static, and some superimposed displacements caused by road conditions. During both steps, loading conditions are likely to be multiaxial. For this goal, following steps have been developed:1. Determination of the range of strain undergone by an engine mount through experiments on vehicles. Using original strain invariants allows to quantify the strain amplitude as well as its multiaxiality;2. Development of an experimental method of tension-torsion on elastomers. An almost cylindrical specimen is specially designed for this type of test. Thanks to stereo-digital image correlation tests, displacements and angles imposed on the specimen are linked to the strain field in its cylindrical zone;3. Hyperelastic modelling based on tension-torsion large strain quasi-static tests. A specific attention is paid on the method of post-treating this kind of test, studying the relevance of calculating some mechanical quantities;4. Viscoelastic modelling based on tests of small oscillations in tension or torsion superimposed on a large tension-torsion static preload. The influence of the preload on the dynamic properties is considered, and the ability of two linearized viscoelastic models to take into account this influence is studied and discussed;5. Simulation of the behaviour of an engine mount through finite elements, using both hyperelastic and viscoelastic models previously identified. Results of this simulation are compared with experiments on the engine mount.L'objectif de cette thèse est de développer une méthode de caractérisation et de modélisation du comportement de pièces de suspension moteur en élastomères. En service, les chargements que subissent ces pièces peuvent être décomposés en deux parties à savoir une grande précharge due au poids du moteur, considérée comme quasi-statique et des débattements dus aux conditions de route qui se superposent à la précharge précédente. Lors de ces deux étapes, la multiaxialité des sollicitations peut être importante. Dans ce but, les travaux suivants ont été mis en œuvre :1. Détermination de l'enveloppe de déformations subies par une pièce de suspension par des essais sur véhicule. L'utilisation d'invariants originaux de la déformation permet de quantifier d'une part l'amplitude de la déformation et d'autre part sa multiaxialité ;2. Mise en place d'une méthodologie expérimentale de traction-torsion sur élastomères. Une éprouvette quasi-cylindrique est spécialement conçue pour ce type d'essais. Des essais de stéréo-corrélation d'images permettent de relier les déplacements et angles imposés à l'éprouvette au champ de déformation ;3. Modélisation hyperélastique identifiée sur des essais quasi-statiques en traction-torsion en grandes déformations. Une attention particulière est portée sur la méthodologie de post-traitement de ce type d'essais en étudiant la pertinence du calcul de certaines grandeurs mécaniques ;4. Modélisation viscoélastique identifiée sur des essais de petites oscillations en traction ou torsion, superposée à une grande précharge statique en traction-torsion. L'influence de la précharge sur les propriétés dynamiques du matériau est considérée. La prise en compte ou non de cette influence par deux modèles viscoélastiques linéarisés est étudiée et discutée ;5. Simulation du comportement d’une suspension moteur par éléments finis. Les résultats de cette simulation sont comparés avec des essais sur pièce

Caractérisation d'élastomères soumis à de petites oscillations superposées à une grande précharge statique en traction-torsion

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How to identify a hyperelastic constitutive equation for rubber-like materials with multiaxial tension–torsion experiments

International audienceThis paper discusses the different approaches that can be used to determine the strain energy density of a given rubber-like material based on tension–torsion experimental results. More precisely, the aim is to answer the question: how to handle the measured macroscopic quantities, i.e. load and torque, to determine the constitutive equation with the less possible assumptions? The method initially proposed by Penn and Kearsley [Trans. Soc. Rheol. 20 (1976) 227–238] is adopted: the strain energy derivatives with respect to kinematical quantities have to be calculated in terms of the measured load and torque. Here, we propose to consider different sets of kinematical quantities to overcome the incoherence encountered with the classical Cauchy–Green strain invariants I1 and I2. Two new sets are considered: the principal stretch ratios and two specific invariants of the logarithmic (true) Hencky strain tensor. The corresponding derivations coupled with new experimental results permit (i) to calculate the Cauchy stress tensor on the outer surface of the cylindrical samples, and (ii) to demonstrate that a well- conditioned set of kinematical quantities must be adopted to determine the strain energy density. It is proved here that the principal stretch ratios are good candidates to express and determine the strain energy density with tension–torsion experiments

Characterization of elastomers under simultaneous tension and torsion for application to engine mounts

International audienceABSTRACT: A general procedure is proposed to develop relevant multiaxial tension-torsion experiments that mimic the complex loading conditions undergone by engine mounts in service. First, displacements and forces exerted on the engine mount are measured on an instrumented vehicle. For several loading conditions, the displacements are introduced in a finite element model of the engine mount to determine the corresponding strain fields. To characterize and compare these strain fields, we consider the invariants of the Hencky strain tensor. For a given set of invariants, we determine displacements and angles that must be applied on the samples to reproduce the deformation of the engine mount. The present work focuses on the subsequent experimental campaign. Firstly, a new rubber specimen is designed for simultaneous tension-torsion tests. Its principal re- quirement is that the finite element strain field must be as close as possible to the analytical solution of the simultaneous extension and torsion of a cylinder. The geometry of the new sample is validated with the help of stereo digital images correlation (SDIC) on the lateral surface of the specimen. From SDIC results, rela- tionships between global axial displacement and local extension λ on the one hand, and between global angle and local angle per unit of height τ on the other hand are established. This validated method will be consid- ered in a next future to perform multiaxial quasi-static and dynamic experiments, leading to identification of a visco-hyperelastic model

Characterization and modeling of elastomers under tension/torsion small dynamic oscillations superimposed on large static preload

International audienceIntroduction Elastomers are widely used in industry for their anti-vibration properties. One of these applications concerns engine mounts, which are subjected to complex multiaxial loading conditions. In order to take into account this aspect, it has been chosen to focus on tension/torsion experiments. Indeed, performing tension/torsion tests allows to assess several multiaxial states with a unique specimen and a unique testing machine. Besides, typical loading conditions for engine mounts consist in vibrations, caused by either perturbation from the road or excitation of the engine, superimposed on a static preload due to the weight of the engine. Objectives The behavior of elastomers under small dynamic oscillations around a large static preload has received particular attention in the 1960s (for example [1]), and new studies have been recently developed ([2], [3]). The present work is based on Huber & Tsakmakis work ([4]), who studied two finite viscolelastic models (A and B). The main objective is to present multiaxial dynamic experimental results, and to confront them to the linearization of Models A and B. Methodology The used specimen is a dumbbell with a large perfectly cylindrical part. It has been specially designed for large tension/torsion tests. First, a quasi-static step with large strains is performed, applying tension, compression, torsion or combined tension/torsion. Then, small sinusoidal oscillations under tension or torsion are performed. Frequency is fixed and varies between 0.1 Hz and 30 Hz. This second step is applied either after maintaining the preload during one hour, or right after the end of the first step. Results and analysis The efficiency of presented models in predicting the dynamic response of an elastomer around an equilibrium position is discussed. The strain decomposition of Model A is easier to apply in this case, but it is also more restrictive than Model B. Indeed, Model A does not take into account any effects of static preload on viscous response of the oscillations, while Model B does