Prediction of fatigue life improvement in natural rubber using configurational stress

AbstractTo some extent, continua can no longer be considered as free of defects. Experimental observations on natural rubber revealed the existence of distributed microscopic defects which grow upon cyclic loading. However, these observations are not incorporated in the classical fatigue life predictors for rubber, i.e. the maximum principal stretch, the maximum principal stress and the strain energy. Recently, Verron et al. [Verron, E., Le Cam, J.B., Gornet, L., 2006. A multiaxial criterion for crack nucleation in rubber. Mech. Res. Commun. 33, 493–498] considered the configurational stress tensor to propose a fatigue life predictor for rubber which takes into account the presence of microscopic defects by considering that macroscopic crack nucleation can be seen as the result of the propagation of microscopic defects. For elastic materials, it predicts privileged regions of rubber parts in which macroscopic fatigue crack might appear. Here, we will address our interest to a broader context. Rubber is assumed to exhibit inelastic behavior, characterized by hysteresis, under fatigue loading conditions. The configurational mechanics-based predictor is modified to incorporate inelastic constitutive equations. Afterwards, it is used to predict fatigue life. The emphasis of the present work is laid on the prediction of the well-known fatigue life improvement in natural rubber under tension–tension cyclic loading

Coupled swelling and large strain model for hydrogels: application to the nucleus pulposus of the intervertebral disc

The main constituents of the nucleus puposus , the centrl gelatinous part of the intervertebral disc, are water and a solid extracellular matrix of macromolecules. Based on this observation, the nucleus pulposus can be seen as a gel-like material in wich swelling - due to the diffusion of the fluid molecules into the macromolecular network - and large strain elasticity, induced by the macromollecular chains, occur. In recent literature, many autors have been interested in describing such a coupled deformation-diffusion problem for gels. Most of the tim, these works where formulated with respect to the dry configuration of the material. Howevver, for the nucleus pulposus, the dru configuration does not exist. Thus, the formulation of the deformation-diffusion problem should be modified in order to consider a reference configuration, wich is undeformed and unconstrained (but already swollen). The theoretical aspects of the derivation of this coupled deformation-diffusion model is proposed. Then, this model is numerically implemented in the finite element commercial software ABAQUS. The state of equilibrium are investigated on simple homogeneous examples. Finally, the himan nucleus pulposus of the intervertebral disc is chosen as a representative complex crample of application for this approach. The associated annulus fibrosus is modelled using an anisotropic hyperelastic material law

Constitutive modeling of strain-induced softening in swollen elastomers

AbstractUnder cyclic loading, elastomeric material exhibits strong inelastic responses such as stress-softening due to Mullins effect, hysteresis and permanent set. The corresponding inelastic responses are observed in both dry and swollen rubbers. Moreover, it is observed that inelastic responses depend strongly on the swelling level. For engineering applications involving the interaction and contact between rubber components and solvent, the understanding and consideration of swelling are essential pre-requisites for durability analysis. In this paper, a simple phenomenological model describing Mullins effect in swollen rubbers under cyclic loading is proposed. More precisely, the proposed model adopts the concept of evolution of soft domain microstructure with deformation originally proposed by Mullins and Tobin. The swollen rubbers are obtained by immersing dry ones in solvent until desired degrees of swelling are achieved. Subsequently, their mechanical responses, in particular Mullins effect, under cyclic loading are investigated. These experimental data are used to assess the efficiency of the proposed model. Results show that the model agrees qualitatively well with experiments. Furthermore, the model captures well the fundamental features of strain-induced softening

Data assimilation experiments using diffusive back-and-forth nudging for the NEMO ocean model

International audienceThe diffusive back-and-forth nudging (DBFN) is an easy-to-implement iterative data assimilation method based on the well-known nudging method. It consists of a sequence of forward and backward model integrations, within a given time window, both of them using a feedback term to the observations. Therefore, in the DBFN, the nudging asymptotic behaviour is translated into an infinite number of iterations within a bounded time domain. In this method, the backward integration is carried out thanks to what is called backward model, which is basically the forward model with reversed time step sign. To maintain numeral stability, the diffusion terms also have their sign reversed, giving a dif-fusive character to the algorithm. In this article the DBFN performance to control a primitive equation ocean model is investigated. In this kind of model non-resolved scales are modelled by diffusion operators which dissipate energy that cascade from large to small scales. Thus, in this article, the DBFN approximations and their consequences for the data assimilation system setup are analysed. Our main result is that the DBFN may provide results which are comparable to those produced by a 4Dvar implementation with a much simpler implementation and a shorter CPU time for convergence. The conducted sensitivity tests show that the 4Dvar profits of long assimilation windows to propagate surface information downwards, and that for the DBFN, it is worth using short assimilation windows to reduce the impact of diffusion-induced errors. Moreover, the DBFN is less sensitive to the first guess than the 4Dvar

Pour en finir avec le Bronze final ? Les haches à douille de type armoricain en France

A discussion about socket armorican bronze axes datation. They are from Ha D period (VII th & VIt h century B.C.)Révision de la datation des haches à douille de type armoricain, au seul Hallstatt D (VIIe-VIe s; av. J.-C.

Identification of apple varieties using acoustic measurements

This article shows that acoustic measurement can be a useful tool to discriminate different apple batches with a low error rate. Starting from the spectrum of the signal recorded by a microphone after the impact of a small hammer on the fruit, 18 key features were identified and used for the classification of apples belonging to 10 different varieties. A capability study of the gage has been done and the results show that the measuring instrument is repeatable and reproducible for the resonance frequency and amplitude of the signal. The prospects of this study are interesting in the context of automatic sorting of fruits

The response of pre-osteoblasts and osteoclasts to gallium containing mesoporous bioactive glasses.

Mesoporous bioactive glasses (MBGs) in the system SiO2-CaO-P2O5-Ga2O3 have been synthesized by the evaporation induced self-assembly method and subsequent impregnation with Ga cations. Two different compositions have been prepared and the local environment of Ga(III) has been characterized using 29Si, 71Ga and 31P NMR analysis, demonstrating that Ga(III) is efficiently incorporated as both, network former (GaO4 units) and network modifier (GaO6 units). In vitro bioactivity tests evidenced that Ga-containing MBGs retain their capability for nucleation and growth of an apatite-like layer in contact with a simulated body fluid with ion concentrations nearly equal to those of human blood plasma. Finally, in vitro cell culture tests evidenced that Ga incorporation results in a selective effect on osteoblasts and osteoclasts. Indeed, the presence of this element enhances the early differentiation towards osteoblast phenotype while disturbing osteoclastogenesis. Considering these results, Ga-doped MBGs might be proposed as bone substitutes, especially in osteoporosis scenarios

A reduced-order strategy for 4D-Var data assimilation

This paper presents a reduced-order approach for four-dimensional variational data assimilation, based on a prior EO F analysis of a model trajectory. This method implies two main advantages: a natural model-based definition of a mul tivariate background error covariance matrix $\textbf{B}_r$, and an important decrease of the computational burden o f the method, due to the drastic reduction of the dimension of the control space. % An illustration of the feasibility and the effectiveness of this method is given in the academic framework of twin experiments for a model of the equatorial Pacific ocean. It is shown that the multivariate aspect of $\textbf{B}_r$ brings additional information which substantially improves the identification procedure. Moreover the computational cost can be decreased by one order of magnitude with regard to the full-space 4D-Var method