Erwan Verron

In the present work, mappings of two invariants of the true strain tensor, that measures the magnitude of the distortion and that quantifies the mode of distortion, are used to investigate the multiaxial fatigue of AE2 and AE42 diabolo samples under tension/torsion conditions. These mappings are used to set up two types of experimental tests. The first is called unimodal because it ensures a constant value of ; therefore, the mode of distortion remains the same along the cycles; three modes have been chosen: uniaxial tension (), simple shear () and a mix mode (). The second is called multimodal because the value of changes along a cycle, oscillating between simple shear and uniaxial tension with a constant magnitude of the distortion . Experimental results show large difference between the fatigue lifetime of the two samples: For both unimodal and multimodal tests, failure of AE42 samples occurs earlier than failure of AE2 samples for the same conditions. Numerical analysis show that, under the same conditions, the principal stresses and stretch ratios are identical for the two samples questioning the relevance of these quantities for multiaxial fatigue lifetime predictions. Finally, it appears that the stress gradient differs from one geometry to another, and it could be an important mechanical quantity to take into account. This experimental work highlights one of the weaknesses of the fatigue criteria proposed in the past in the literature: The geometry of the test specimens must be taken into account. Here, we emphasize that this can be accounted for using the spatial stress gradient.

Fatigue tests conducted on elastomers inherently exhibit significant variability. Aging may induce stiffening and embrittlement, leading to premature failures outside the specimen gauge length and resulting in right‐censored data. Combined with the limited number of specimens, this leads to large uncertainties in fatigue lifetime estimation. This paper presents a survival analysis strategy to propose a probabilistic prediction of elastomers' fatigue lifetime during aging. The approach explicitly accounts for censored data and incorporates aging effects through material descriptors such as crosslink density. A Weibull parametric model and a semi‐parametric Cox regression model with a frailty term are considered. Application to an experimental dataset shows that both models provide consistent predictions within the range supported by the data, while the Cox model offers increased flexibility by handling multiple aging‐related covariates without prescribing a baseline distribution. The proposed framework complements Weibull‐based approaches and provides a practical tool to quantify fatigue failure probabilities under data‐limited aging conditions.

This paper investigates the pressure–volume response of elastomer matrix composites filled with hollow thermoplastic microspheres and subjected to low hydrostatic pressure. The hysteretic response of the material up to a pressure of 0.8 MPa is measured using an original experimental set‐up that combines hydrostatic pressure loading by nitrogen pressurisation and volume measurement thanks to digital image correlation. In terms of volume change vs. pressure, a detailed analysis of the pressurisation and depressurisation paths shows firstly that the macroscopic pressure which is emerging from the successive buckling of the microspheres does not depend on their concentration in the composite. Secondly, it is established that the unloading path, even if it does not change its slope steeply, admits a pressure inflection point that seems to depend on the volume fraction of the microspheres. In the future, these experimental observations will be useful for developing constitutive models for these composites and in particular for the strain energy density function dedicated to their spherical response.

Identifying the mechanical response of a material without presupposing any constitutive equation is possible thanks to the Data-Driven Identification algorithm developed by the authors. It allows to measure stresses from displacement fields and forces applied to a given structure; the peculiarity of the technique is the absence of underlying constitutive equation. In the case of real experiments, the algorithm has been successfully applied on a perforated elastomer sheet deformed under large strain. Displacements are gathered with Digital Image Correlation and net forces with a load cell. However, those real data are incomplete for two reasons: some displacement values, close to the edges or in a noise-affected area, are missing and the force information is incomplete with respect to the original DDI algorithm requirements. The present study proves that with appropriate data handling, stress fields can be identified in a robust manner. The solution relies on recovering those missing data in a way that no assumption, except the balance of linear momentum, has to be made. The influence of input parameters of the method is also discussed. The overall study is conducted on synthetic data: perfect and incomplete data are used to prove robustness of the proposed solutions. Therefore, the paper can be considered as a practical guide for implementing the DDI method. L'identification de la réponse mécanique d'un matériau sans présupposer d'équation constitutive est possible grâce à l'algorithme Data-Driven Identification développé par les auteurs. Il permet de mesurer les contraintes à partir des champs de déplacement et des forces appliquées à une structure donnée ; la particularité de la technique est l'absence d'équation constitutive sous-jacente. Dans le cas d'expériences réelles, l'algorithme a été appliqué avec succès sur une feuille d'élastomère perforée déformée sous une grande contrainte. Les déplacements sont recueillis par corrélation d'images numériques et les forces nettes à l'aide d'une cellule de charge. Cependant, ces données réelles sont incomplètes pour deux raisons : certaines valeurs de déplacement, près des bords ou dans une zone affectée par le bruit, sont manquantes et les informations sur les forces sont incomplètes par rapport aux exigences de l'algorithme DDI d'origine. La présente étude prouve qu'avec un traitement approprié des données, les champs de contrainte peuvent être identifiés de manière robuste. La solution repose sur la récupération des données manquantes de manière à ce qu'aucune hypothèse, à l'exception de l'équilibre de la quantité de mouvement linéaire, ne doive être faite. L'influence des paramètres d'entrée de la méthode est également discutée. L'étude globale est menée sur des données synthétiques : des données parfaites et incomplètes sont utilisées pour prouver la robustesse des solutions proposées. Par conséquent, le document peut être considéré comme un guide pratique pour la mise en œuvre de la méthode DDI.

A novel method for accurately identifying the large strain elastic response of elastomeric materials is presented. The method combines the data-driven identification (DDI) algorithm with a unique heterogeneous experiment, deviating from the conventional approach of conducting multiple simple experiments. The primary objective of the method is to decouple the experimental process from the fitting technique, relying instead on a single comprehensive experiment to generate an extensive collection of stress and strain energy fields. This collection is then used in conjunction with a standard fitting technique to determine the parameters of hyperelastic models. Notably, the approach places significant emphasis on the strain energy density field as a critical factor in model identification, as it encompasses the full material response within a single scalar quantity. To demonstrate the effectiveness of the proposed approach, a proof of concept is provided using synthetic data. The results highlight the efficiency of the method and emphasize the importance of incorporating the strain energy density field for precise model identification, surpassing the reliance on stress data alone. In addition, several graphical tools are introduced to evaluate and analyze the quality of both the generated mechanical fields and the identification results. The proposed approach offers a more comprehensive representation of the material behavior and enhances the reliability and prediction capabilities of hyperelastic material models. It holds significant potential for advancing the field of solid mechanics, particularly in accurately characterizing the mechanical responses of elastomeric materials.

Dynamic crack propagation in elastomer membranes is investigated; the focus is laid on cracks reaching the speed of shear waves in the material. The specific experimental setup developed to measure crack speed is presented in details. The protocol consists in (1) stretching an elastomer membrane under planar tension loading conditions, then (2) initiating a small crack on one side of the membrane. The crack speed is measured all along the crack path in both reference and actual configurations, including both acceleration and deceleration phases, i.e. non steady-state crack propagation phases. The influence of the prescribed stretch ratio on crack speed is analysed in the light of both these new experiments and the few previously published studies. Conclusions previously drawn for steady-state crack growth are extended to non steady-state conditions: stretch perpendicular to the crack path governs crack speed in intersonic crack propagation regime, and the role of the stretch in crack direction is minor.

Identifying the mechanical response of a material without presupposing any constitutive equation is possible thanks to the Data-Driven Identification algorithm developed by the authors. It allows to measure stresses from displacement fields and forces applied to a given structure; the peculiarity of the technique is the absence of underlying constitutive equation. In the case of real experiments, the algorithm has been successfully applied on a perforated elastomer sheet deformed under large strain. Displacements are gathered with Digital Image Correlation and net forces with a load cell. However, those real data are incomplete for two reasons: some displacement values, close to the edges or in a noise-affected area, are missing and the force information is incomplete with respect to the original DDI algorithm requirements. The present study proves that with appropriate data handling, stress fields can be identified in a robust manner. The solution relies on recovering those missing data in a way that no assumption, except the balance of linear momentum, has to be made. The influence of input parameters of the method is also discussed. The overall study is conducted on synthetic data: perfect and incomplete data are used to prove robustness of the proposed solutions. Therefore, the paper can be considered as a practical guide for implementing the DDI method.