Inflation of elastomeric circular membranes using network constitutive equations

International audienceThe present paper deals with the use of network-based hyperelastic constitutive equations in the context of thin membranes inflation. The study focus on the inflation of plane circular membranes and the materials are assumed to obey Gaussian and non-Gaussian statistical chains network models. The governing equations of the inflation of axisymmetric thin rubber-like membranes are briefly recalled. The material models are implemented in a numerical tool that incorporates an efficient B-spline interpolation method and a coupled Newton-Raphson/arc-length solving algorithm. Two numerical examples are studied: the homogeneous inflation of spherical balloons and the inflation of initially plane circular membranes. In the second example, the inflation profiles and the distributions of extension ratios along the membrane are extensively analysed during the inflation process. Both examples highlight the need of an accurate modelling of the strain-hardening phenomenon in elastomers

Efficiency of hyperelastic models for rubber-like materials

International audienceThis paper focuses on the modeling of rubber-like material behaviour under several modes of deformation using hyperelastic constitutive equations. A procedure based on genetic algorithms coupled to classical optimisation methods is proposed to identify the parameters of the models upon experimental data given in the literature. This leads to the classification of nineteen models with respect to criteria related to their capability to predict material behaviour

A comparison of the Hart-Smith model with the Arruda-Boyce and Gent formulations for rubber elasticity

International audienceThe present paper demonstrates that the Hart-Smith constitutive model and the more recent Arruda and Boyce eight chains and Gent constitutive models are closely related. The ability of these three models to predict both small and large strain responses of rubbers is highlighted and equations that relate their material parameters are established

Dynamic inflation of non-linear elastic and viscoelastic rubberlike membranes

International audienceThe present paper deals with the dynamic inflation of rubber-like membranes. The material is assumed to obey the hyperelastic Mooney's model or the non-linear viscoelastic Christensen's model. The governing equations of free inflation are solved by a total Lagrangian finite element method for the spatial discretization and an explicit finite-difference algorithm for the time-integration scheme. The numerical implementation of constitutive equations is highlighted and the special case of integral viscoelastic models is examined in detail. The external force consists in a gas flow rate, which is more realistic than a pressure time history. Then, an original method is used to calculate the pressure evolution inside the bubble depending on the deformation state. Our numerical procedure is illustrated through different examples and compared with both analytical and experimental results. These comparisons yield good agreement and show the ability of our approach to simulate both stable and unstable large strain inflations of rubber-like membranes

Stress analysis around crack tips in finite strain problems using the eXtended finite element method

International audienceFracture of rubber-like materials is still an open problem. Indeed, it deals with modelling issues (crack growth law, bulk behaviour) and computational issues (robust crack growth in 2D and 3D, incompressibility). The present study focuses on the application of the eXtended Finite Element Method (X-FEM) to large strain fracture mechanics for plane stress problems. Two important issues are investigated: the choice of the formulation used to solve the problem and the determination of suitable enrichment functions. It is demonstrated that the results obtained with the method are in good agreement with previously published works

Energy release rate of small cracks under finite multiaxial straining

International audienceThe energy release rate of small cracks governs fatigue crack nucleation. A method is presented here to efficiently and accurately evaluate the energy release rate of such cracks, arbitrarily oriented, under general conditions of finite multiaxial loading. As a motivation, the dependence on crack length is then investigated. It is demonstrated that the energy release rate of small cracks is proportional to the crack length and that the proportionality factor is a function of the far-field parameters only. An attempt is then made to search for a general expression of this proportionality factor under simple loading conditions

Energy release rate of small cracks under finite multiaxial straining

International audienceThe energy release rate of small cracks governs fatigue crack nucleation. A method is presented here to efficiently and accurately evaluate the energy release rate of such cracks, arbitrarily oriented, under general conditions of finite multiaxial loading. As a motivation, the dependence on crack length is then investigated. It is demonstrated that the energy release rate of small cracks is proportional to the crack length and that the proportionality factor is a function of the far-field parameters only. An attempt is then made to search for a general expression of this proportionality factor under simple loading conditions

Hyperelasticity with volumetric damage

International audienceThe present paper presents a simple framework to model continuous volumetric damage in elastomers. The formulation predicts phenomenologically the growth of microscopic cavities, and can be applied to both static and fatigue loading conditions. This first version of the approach cannot handle cavitation and is limited to small values of porosities. The derivation is based on the use of a simple scalar damage parameter, the irreversible volume change, and takes naturally into account the change in stiffness through the explicit dependence of the material parameters on the damage variable. The thermo-dynamic force which drives the volume change contains the hydrostatic stress and also a contribution due to stiffness evolution. As a first application, a damage compressible neo-Hookean constitutive equation is derived and a simple example is studied

Hyperelasticity with volumetric damage

International audienceThe present paper presents a simple framework to model continuous volumetric damage in elastomers. The formulation predicts phenomenologically the growth of microscopic cavities, and can be applied to both static and fatigue loading conditions. This first version of the approach cannot handle cavitation and is limited to small values of porosities. The derivation is based on the use of a simple scalar damage parameter, the irreversible volume change, and takes naturally into account the change in stiffness through the explicit dependence of the material parameters on the damage variable. The thermo-dynamic force which drives the volume change contains the hydrostatic stress and also a contribution due to stiffness evolution. As a first application, a damage compressible neo-Hookean constitutive equation is derived and a simple example is studied

Simulation numérique d'un dispositif de retenue d'enfant

International audienceThe present paper deals with the use of numerical methods in the design project of a child restraint system (CRS). First, the experimental dynamic test of child restraint systems is presented as imposed by the European reglamentation R44/03. Then, a first numerical simulation of the CRS is performed using both an elastostatic mode! and an elastodynamic approach. In order to improve the mode!, we focus on the modelling of the material behaviour (polypropylene). The constitutive equation of glassy polymer developed by Boyce, Parks and Argon is chosen. This mode! superimposes an isotropie resistance that simulates defaults in the molecular chains during shear and an entropie resistance due to the chain alignment induced by deformation. A comparison between explicit and implicit integration methods is performed. This study, which aim is the limitation of CPU time during finite elements analysis, will pave the way for the implementation of the constitutive equation in a commercial code.Le présent article s'intéresse à l'utilisation de la simulation numérique dans la boucle de conception d'un dispositif de retenue d'enfant (DRE). L'essai dynamique expérimental d'homologation de DRE imposé par le règlement européen R44/03 est tout d'abord présenté. Une première simulation numérique de DRE est ensuite réalisée dans un cas élastostatique, puis avec un modèle élastodynamique. Afin d'améliorer le modèle, l'accent est mis sur une modélisation fiable du comportement du matériau utilisé (polypropylène). Le choix se porte sur le modèle de comportement de polymère vitreux développé par Boyce, Parks et Argon. Ce modèle superpose une résistance isotrope simulant l'inclusion de défauts dans les chaînes moléculaires lors du cisaillement et une résistance entropique due à l'alignement de ces chaînes sous l'effet de la déformation, et simulée par un modèle moléculaire. Une comparaison entre intégration explicite et intégration implicite de cette loi de comportement est réalisée, dans le but de limiter les temps de calcul en vue d'une implantation de la loi dans un code de calcul commercial