A review on the Mullins effect

The Mullins’ effect remains a major challenge in order to provide good mechanical modeling of the complex behavior of industrial rubber materials. It’s been forty years since Mullins [1] wrote his review on the phenomenon and still no general agreement has been found either on the physical source or on the mechanical modeling of this effect. Therefore, we reviewed the literature dedicated to this topic over the past six decades. We present the experimental evidences, which characterize the Mullins’ softening. The phenomenon is observed in filled and crystallizing rubbers. Then, the phenomenological models dedicated to fit the mechanical behavior of rubbers undergoing some Mullins’ softening are studied. To overcome the limit of a descriptive phenomenological modeling, several authors looked for a physical understanding of the phenomenon. Various theories have been exposed, but none of them has been supported unanimously. Nonetheless, these theories favor the emergence of physically based mechanical behavior laws. We tested some of these laws, which show little predictive abilities since the values of their parameters do not compare well with the physical quantities they are linked to.Projet ANR jeunes chercheurs MELAC JC05_43403

The Mullins effect in the wrinkling behavior of highly stretched thin films

Recent work demonstrates that finite-deformation nonlinear elasticity is essential in the accurate modeling of wrinkling in highly stretched thin films. Geometrically exact models predict an isola-center bifurcation, indicating that for a bounded interval of aspect ratios only, stable wrinkles appear and then disappear as the macroscopic strain is increased. This phenomenon has been verified in experiments. In addition, recent experiments revealed the following striking phenomenon: For certain aspect ratios for which no wrinkling occurred upon the first loading, wrinkles appeared during the first unloading and again during all subsequent cyclic loading. Our goal here is to present a simple pseudo-elastic model, capturing the stress softening and residual strain observed in the experiments, that accurately predicts wrinkling behavior on the first loading that differs from that under subsequent cyclic loading. In particular for specific aspect ratios, the model correctly predicts the scenario of no wrinkling during first loading with wrinkling occurring during unloading and for all subsequent cyclic loading.Comment: 15 pages, 9 figure

Experimental investigation of the Mullins effect in swollen elastomers

International audienceNatural rubber distinguishes itself by its particular mechanical properties. It has become an almost irreplaceable important component part in industrial applications such as vibration isolator, sealing system, flexible piping or structural bearing. During the service, these components are subjected to fluctuating mechanical loading. Under cyclic loading conditions, rubber exhibits strong inelastic responses such as stress-softening due to Mullins effect. It is believed that such inelastic response plays major role in determining the durability in service of rubber component. In engineering applications where the components are concurrently exposed to aggressive solvent, further material degradation in the form of swelling occurs. Thus, it is essential to investigate the effect of swelling on the stress-softening due to Mullins effect in rubber like materials for durability analysis. In this study, the Mullins effect in swollen carbon black-filled natural rubber under cyclic loading conditions is investigated. The swollen rubbers are obtained by immersing initially dry rubber in solvent at room temperature for various immersion durations. The stress-strain responses for both dry and swollen rubber are found qualitatively similar. However, the stress-softening in swollen rubbers are notably lower compared to that in the dry one. This work is later extended for future modelling purpose by adapting the concept of Continuum Damage Mechanics (CDM) [Chagnon, G., Verron,E., Gornet, L., Markmann, G., Charrier, P., 2004. On the relevance of Continuum Damage Mechanics as applied to the Mullins effect in elastomers. J. Mech. Phys. Sol. 52, 627-1650] and pseudo-elastic model [Ogden, R.W., Roxburgh, D.G., 1999. A pseudo-elastic model for the Mullins effect in filled rubber.Proc. R. Soc. A. 455, 2861-2877]

On the relevance of Continuum Damage Mechanics as applied to the Mullins effect in elastomers

International audienceThe present paper reports and rationalizes the use of Continuum Damage Mechanics (CDM) to describe the Mullins effect in elastomers. Thermodynamics of rubber-like hyperelastic materials with isotropic damage is considered. Since it is demonstrated that stress-softening is not strictly speaking a damage phenomenon, the limitations of the CDM approach are highlighted. Moreover, connections with two-network-based constitutive models proposed by other authors are exhibited through the choice of both the damage criterion and the measure of deformation. Experimental data are used to establish the evolution equation of the stress-softening variable, and the choice of the maximum deformation endured previously by the material as the damage criterion is revealed as questionable. Nevertheless, the present model agrees qualitatively well with experiments except to reproduce the strain-hardening phenomenon that takes place as reloading paths rejoin the primary loading path. Finally, the numerical implementation highlights the influence of loading paths on material response and thereby demonstrates the importance of considering the Mullins effect in industrial design

Surface Instability of Icicles

Quantitatively-unexplained stationary waves or ridges often encircle icicles. Such waves form when roughly 0.1 mm-thick layers of water flow down the icicle. These waves typically have a wavelength of 1cm approximately independent of external temperature, icicle thickness, and the volumetric rate of water flow. In this paper we show that these waves can not be obtained by naive Mullins-Sekerka instability, but are caused by a quite new surface instability related to the thermal diffusion and hydrodynamic effect of thin water flow.Comment: 11 pages, 5 figures, Late

Unified model for Mullins effect and high cycle fatigue life prediction of rubber materials

Proceedings of the 8th European Conference on constitutive models for rubbers (ECCMR VIII), San Sebastian, Spain, 25-28 June 2013International audienceThe study describes the basic principles of a general damage model (GDMF) for Mullins effect and high cycle fatigue loadings of rubber materials and demonstrates its prediction possibilities for simulating the complete fatigue failure phenomenon. The present paper focuses on stiffness modelling of rubber materials for uniaxial and multiaxial static and fatigue loadings with a minimal number of material parameters in order to ensure robustness of the identification. The proposed hyperplastic model is expressed in terms of classical independent strain invariants. Mullins effect and high cycle fatigue loadings are both modelled according to a continuum damage mechanics approach

Constitutive modeling of the anisotropic behavior of Mullins softened filled rubbers

Original constitutive modeling is proposed for filled rubber materials in order to capture the anisotropic softened behavior induced by general non-proportional pre-loading histo-ries. The hyperelastic framework is grounded on a thorough analysis of cyclic experimental data. The strain energy density is based on a directional approach. The model leans on the strain amplification factor concept applied over material directions according to the Mul-lins softening evolution. In order to provide a model versatile that applies for a wide range of materials, the proposed framework does not require to postulate the mathematical forms of the elementary directional strain energy density and of the Mullins softening evo-lution rule. A computational procedure is defined to build both functions incrementally from experimental data obtained during cyclic uniaxial tensile tests. Successful compari-sons between the model and the experiments demonstrate the model abilities. Moreover, the model is shown to accurately predict the non-proportional uniaxial stress-stretch responses for uniaxially and biaxially pre-stretched samples. Finally, the model is effi-ciently tested on several materials and proves to provide a quantitative estimate of the anisotropy induced by the Mullins softening for a wide range of filled rubbers

Grain growth beyond the Mullins model, capturing the complex physics behind universal grain size distributions

Grain growth experiments on thin metallic films have shown the geometric and topological characteristics of the grain structure to be universal and independent of many experimental conditions. The universal size distribution, however, is found to differ both qualitatively and quantitatively from the standard Mullins curvature driven model of grain growth; with the experiments exhibiting an excess of small grains (termed an "ear") and an excess of very large grains (termed a "tail") compared with the model. While a plethora of extensions of the Mullins model have been proposed to explain these characteristics, none have been successful. In this work, large scale simulations of a model that resolves the atomic scale on diffusive time scales, the phase field crystal model, is used to examine the complex phenomena of grain growth. The results are in remarkable agreement with the experimental results, recovering the characteristic "ear" and "tail" features of the experimental grain size distribution. The simulations also indicate that while the geometric and topological characteristics are universal, the dynamic growth exponent is not.Comment: 4 pages, 5 figure