Permanent set and stress softening constitutive equation applied to rubber like materials and soft tissues

International audienceMany rubber like materials present a phenomenon known as Mullins effect. It is characterized by a difference of behavior between the first and second loadings and by a permanent set after a first loading. Moreover, this phenomenon induces anisotropy in an intially isotropic material. A new constitutive equation is proposed in this paper. It relies on the decomposition of the macromolecular network into two parts: chains related together and chains related to fillers. The first part is modeled by a simple hyperelastic constitutive equation whereas the second one is described by an evolution function introduced in the hyperelastic strain energy. It contributes to describe both the anisotropic stress softening and the permanent set. The model is finally extended to soft tissues mechanical behavior that present also stress softening but with an initially anisotropic behavior. The two models are successfully fitted and compared to experimental data

Etude du comportement thermomécanique d'un fil fin de NiTi par spectromètre dynamique mécanique et thermique

National audienceLes alliages à mémoire de forme de type NiTi présentent des phénomènes de déformation complexes liés aux transformations entre les différentes phases Austénitique (A), Martensitique (M) et phase R (R). Ces phénomènes sont observés à l'aide de nombreux dispositifs expérimentaux ayant pour objectif de déterminer les caractéristiques nécessaires pour la modélisation et la simulation. Ce travail présente les résultats expérimentaux issus d'une analyse par un dispositif non conventionnel, qui couple un spectromètre mécanique et thermique, plus connu sous le nom DMTA (Dynamical Mechanical and Thermal Analysis) à une machine de traction classique. Des mesures du module de conservation (E') ont été effectuées pendant deux types d'essais sur des fils de NiTi à grains nanométriques. Les essais du premier type sont des tractions isothermes pour des températures allant de -100°C à +150°C, en charge/décharge et en charge jusqu'à rupture. Les essais de second type sont effectués sous contrainte constante s'échelonnant de 50 MPa à 1000MPa, au chauffage et refroidissement entre 200°C et -140°C. A partir de l'évolution de E' sur l'ensemble des essais, il est possible de détecter les changements de phase par une analyse des variations de E'. Il est ainsi possible de déterminer les domaines d'existence des différentes phases, séparés par les lieux de transformations directes et inverses. De plus, il a été effectué une analyse de l'évolution de E' en fonction de la température et de la contrainte de traction dans les domaines où l'alliage est monophasique, totalement austénitique ou martensitique. Les évolutions de E' sont importantes. Pour l'austénite, E' augmente avec la température, contrairement aux alliages métalliques usuels

Development of constitutive equation of filled silicone architectured membrane

International audienceArchitectured membranes can be developed in order to mimic living tissues. The main point is to generate anisotropic membranes that can endure large deformations. In this way, crenellated membranes are elaborated with a filled silicone rubber. The aim of this work is to develop a constitutive equation which describes the mechanical behavior of such architectured materials. Membranes with different crenel orientations are elaborated and tested. The architectured membranes endure the same phenomena as the bulk silicone, they are made with, i.e. principally the Mullins effect for this filled silicone. This phenomenon must be taken account in the modeling. An equivalent constitutive equation is built for the architectured membrane by taking into account the mechanical behavior of the silicone and the geometrical parameters of the crenelated membrane. First, a constitutive equation is chosen to describe the core of the membrane. Second, this equation is adapted to the behavior of the crenels and third a coupling term describing the interactions between the crenels and the membrane is developed. Finally, the model is validated on experimental data

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

Theory and identification of a constitutive model of induced anisotropy by the Mullins effect

International audienceRubber-like materials present a stress softening phenomenon after a first loading known as the Mullins effect. Some recent experimental data on filled silicone rubber is presented in literature, using uniaxial and biaxial tests to precondition samples thus induce some primary stress softening. A generic modeling based on the polymer network decomposition into an isotropic hyperelastic one, and a stress-softening evolution one, is proposed taking into account the contribution of many spatial directions. A new stress softening criterion tensor is built by means of a tensor that measures the repartition of energy in space. A general form of the stress softening function associated to a spatial direction is written by the way of two variables: one, the maximal eigenvalue of the energy tensor; the other, the energy in the considered direction. Finally, a particular form of constitutive equation is proposed. The model is fitted and compared to experimental data. The capacities of such modeling are finally discussed

Anisotropic modeling of the Mullins effect and the residual strain of filled silicone rubber

International audienceMany rubber like materials present a stress-softening phenomenon known as Mullins effect. It is characterized by a difference of behavior between the first and second loading and by a residual strain after a first loading. Moreover according to the literature this stress softening is anisotropic. A new constitutive equation is proposed. It relies on the decomposition of the macromolecular network into two parts: chains related together and chains related to fillers. The first part is modeled by a simple hyperelastic constitutive equation whereas the second one is described by a constitutive equation describing both the anisotropic stress softening and the residual strain. A 42 directions discretization is chosen to describe the anisotropic part of the model. An evolution function is introduced in the constitutive equation in each direction to record the history of the material. The equations are written by means of strain invariants in order to build a model easy to implement in a finite element code. The constitutive equation is finally validated on experimental data

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

A conical mandrel tube drawing test designed to assess failure criteria

International audienceCold tube drawing is a metal forming process which enables to produce tubes with high dimensional precision. It consists in reducing tube dimensions by pulling it through a die. Tube outer diameter is calibrated by a die and the tube inner diameter and thickness are calibrated by a mandrel. One of the major concern of metal forming industry is the constant improvement of productivity and product quality. In the aim of pushing the process to the limit the question is how far the material can be processed without occurrence of failure. In the present study, a long conical mandrel with a small cone angle was designed in order to carry out drawing tests up to fracture with experimental conditions very close to the industrial process. The FEM of the process was built in order to access the local stress and strain data. A specific emphasis was put on the friction characterisation. For that purpose force measurement during the conical mandrel experiments enabled to characterise a pressure dependent friction coefficient constitutive law by means of an inverse analysis. Finally, eleven failure criteria were selected to study the drawability of cobalt-chromium alloy tubes. The assessment of failure criteria based on damage variables or damage accumulation variables involved their calibration on uniaxial tensile tests. The experimental studies were completed by SEM fractography which enabled to understand the fracture locus and the propagation direction of the fracture

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

Création de membranes anisotropes à partir d'un matériau silicone chargé

International audienceLes matériaux architecturés sont l'un des sujets émergents de ces dernières années, notamment grâce à leurs spécificités mécaniques qui leur permettent de s'ouvrir à de nouvelles applications. Il existe deux types d'architecturations possibles : une architecturation à une échelle microstructurale et une architecture à une échelle macroscopique souvent obtenue par géométrie. Cette étude présente la réalisation de membranes anisotropes à l'aide d'un même matériau constitutif initialement isotrope: un silicone chargé RTV3428. L'architecturation géométrique est obtenue parfabrication de membranes où des bandes de créneaux orientés sont placées sur les surfaces externes, ces membranes sont réalisées par un procédé d'injection.. L'orientation relative des créneaux entre les surfaces des créneaux peut être choisie et donc l'anisotropie induite contrôlée.L'architecturation par microstructure est obtenue par un procédé de sur-réticulation sur une membrane soumise à un niveau de déformations de 60% après une réticulation initiale. Ainsi une orientation préférentielle des chaines polymères est imposée. Une loi de comportement pour prendre en compte l'anisotropie initiale,l'effet Mullins et la viscoélasticité du matériau par une approche microsphère a été proposée