Publications

2015

• Magnetorheological elastomers: Experimental and modeling aspects
  
  • Bodelot L.
  • Pössinger T.
  • Danas K.
  • Triantafyllidis N.
  • Bolzmacher C.
  , 2016, 7, pp.251-256. Magnetorheological elastomers (MREs) are active composite materials that deform under a magnetic field because they are made of a soft elastomer matrix filled with magnetizable micrometric particles. Along with short response times and low magnetic inputs, not only do MREs alter their viscoelastic properties and stiffness in response to external magnetic fields but they can also undergo very high deformation states. While the former effect can be exploited in controllable-stiffness devices, the latter is of interest for haptic devices such as tactile interfaces for the visually impaired. In the perspective of developing a persistent tactile MRE surface exhibiting reversible and large out-of-plane deformations, the first part of this work focuses on the fabrication of MREs that can sustain large deformations. In particular, we determine the critical strain threshold up to which the interfacial adhesion between particles and matrix is ensured. In the second part of this work, an experimental setup is developed in order to characterize MRE composites under coupled magneto-mechanical mechanical loading. The experiments conducted on this setup will eventually serve as an input for a continuum model describing magneto-mechanical coupling. (10.1007/978-3-319-21762-8_32)
  DOI : 10.1007/978-3-319-21762-8_32
• Study of damage mechanisms in A319 aluminium alloy by X-ray tomography and Digital Volume Correlation
  
  • Dahdah Nora
  • Limodin Nathalie
  • El Bartali Ahmed
  • Witz Jean-Francois
  • Seghir Rian
  • Charkaluk Eric
  • Buffiere Jean-Yves
  , 2015. In the cylinder heads produced by the Lost Foam Casting process, the microstructure consists of hard intermetallic phases and large gas and microshrinkage pores. In order to study the influence of this complex 3D microstructure on fatigue crack initiation and propagation, an experimental protocol using laboratory and synchrotron tomography, Finite Element simulation and 3D Digital Volume Correlation has been used. Tests performed at low temperatures (room temperature and 150°C) revealed the initiation of 3D cracks at large pores and a propagation along the hard inclusions towards the free surface. At temperatures characteristics of in-service conditions (above 200°C), an additional damage mechanism was observed: cracks were detected in silicon particles around the main pore that drove to failure but also in other areas of the specimen gauge length.
• Stochastic representations and statistical inverse identification for uncertainty quantification in computational mechanics
  
  • Soize Christian
  • Desceliers Christophe
  • Guilleminot Johann
  • Le Thinh-Tien
  • Nguyen Manh-Tu
  • Perrin Guillaume
  • Allain Jean-Marc
  • Gharbi H.
  • Duhamel Denis
  • Funfschilling Christine
  , 2015, pp.1-26. The paper deals with the statistical inverse problem for the identification of a non-Gaussian tensor-valued random field in high stochastic dimension. Such a random field can represent the parameter of a boundary value problem (BVP). The available experimental data, which correspond to observations, can be partial and limited. A general methodology and some algorithms are presented including some adapted stochastic representations for the non-Gaussian tensor-valued random fields and some ensembles of prior algebraic stochastic models for such random fields and the corresponding generators. Three illustrations are presented: (i) the stochastic modeling and the identification of track irregularities for dynamics of high-speed trains, (ii) a stochastic continuum modeling of random interphases from atomistic simulations for a polymer nanocomposite, and (iii) a multiscale experimental identification of the stochastic model of a heterogeneous random medium at mesoscale for mechanical characterization of a human cortical bone.
• Wireless nanosensors for embedded measurement in concrete structures
  
  • Michelis Fulvio
  • Bodelot Laurence
  • Laheurte Jean-Marc
  • Zaki Fadi
  • Bonnassieux Yvan
  • Lebental Bérengère
  , 2015, pp.6p. In this work we propose a wireless architecture for embedded monitoring in concrete. The modular structure of the system allows it to be adapted to different types of sensors. We present the application of such architecture for the detection of microcracks in concrete. A carbon nanotube strain sensor recently developed by the group is used to track mechanical deformations. Full temperature compensation is achieved by a specific conditioning circuit.
• Approche variationnelle de la rupture dynamique via les modèles d'endommagement à gradient
  
  • Li Tianyi
  • Marigo Jean-Jacques
  • Guilbaud Daniel
  • Potapov Serguei
  , 2015. Nous présentons une extension en dynamique des modèles d’endommagement à gradient qui peuvent être vus comme une régularisation de l’approche variationnelle de la rupture capable de prédire dans un cadre unifié l’initiation et le trajet spatio-temporel (propagation, bifurcation, branchement, arrêt) de fissures complexes dans des matériaux quasi-fragiles sous chargement dynamique. La formulation variationnelle précise ainsi que son implémentation numérique par éléments finis sont détaillées et illustrées par des simulations représentatives en accord avec les résultats théoriques et expérimentaux.
• Modèles d'endommagement à gradient et simulation numérique des phénomènes de rupture fragile
  
  • Maurini Corrado
  • Bourdin Blaise
  • Li Tianyi
  • Marigo Jean-Jacques
  • Tanne Erwan
  , 2015. Le but de cette contribution est d'illustrer les résultats fondamentaux obtenus sur la modélisation et simulation numérique des phénomènes de rupture fragile dans le cadre de l'approche variationnelle à la mécanique de la rupture. On illustre à l'aide d'exemples numériques comment les modèles d'endommagement à gradient peuvent être utilisés pour rendre compte des phénomènes d'initiation et nucléation. Dans le cas de chargement thermique (choc thermique), on montre qu'on peut prédire la nucléation d'un réseaux complexe de fissures et sa propagation en bon accord avec les résultats théoriques et expérimentaux.
• Effet du Champ de Contrainte Non-Uniforme sur Évolution de Fissure Cohésive 2D
  
  • Pham Tuan-Hiep
  • Laverne Jérôme
  • Marigo Jean-Jacques
  , 2015. L'article a pour but d'étudier l'initiation et la propagation de la fissure cohésive au sein d'une structure élastique bidimensionnelle infinie en prenant en compte l'effet essentiel de la non-uniformité du champ de contrainte. L'évolution de la longueur et l'ouverture de la fissure seront mise en évidence. Cette évolution est montrée régulière en temps jusqu'à l'instant critique où la partie libre de contrainte apparaît au centre de fissure. Au delà de cet instant critique, les longueurs de la fissure devraient sauter brutalement à l'échelle supérieure. Les lois cohésives de type Dugdale et Barenblatt sont considérées successivement.
• Etude du comportement post-bifurqué des matériaux architecturés
  
  • Combescure Christelle
  • Elliott Ryan
  • Triantafyllidis Nicolas
  , 2015. Les matériaux à microstructure régulière tels que les matériaux architecturés présentent un grand nombre de symétries géométriques internes et leur comportement à la ruine peut ainsi devenir compliqué à étudier du fait d'instabilités multiples pouvant subvenir simultanément. Les techniques usuelles d'étude de la bifurcation comprennent alors un risque de passer à côté d'une instabilité critique. Nous proposons ici une technique d'étude systématique des matériaux à grand nombre de symétries basée sur la théorie des groupes et des représentations et permettant d'accéder à toutes les bifurcations possibles dans le matériau de manière exhaustive.
• Intégration réduite d'un élément de coque isogéométrique de type Reissner-Mindlin dans le cadre de l'analyse non-linéaire par T-splines
  
  • Adam Cédric
  • Bouabdallah Salim
  • Zarroug Malek
  • Maitournam Habibou
  , 2015. L'intégration réduite d'un élément de coque géométriquement non linéaire de ReissnerMindlin est proposée dans le cadre de l'analyse des structures par T-splines. La formulation de coque est basée sur les déplacements et une approximation du premier ordre est utilisée dans l'épaisseur pour prendre en compte le cisaillement transverse. La formulation Lagrangienne totale est utilisée pour prendre en non linéarités en déplacements finis. La mise à jour des grandes rotations est traitée par la théorie des quaternions.
• Variational Approach to Dynamic Brittle Fracture via Gradient Damage Models
  
  • Li Tianyi
  • Marigo Jean-Jacques
  • Guilbaud Daniel
  • Potapov Serguei
  , 2015. In this paper we present a family of gradient-enhanced continuum damage models which can be viewed as a regularization of the variational approach to fracture capable of predicting in a unified framework the onset and space-time dynamic propagation (growth, kinking, branching, arrest) of complex cracks in quasi-brittle materials under severe dynamic loading. The dynamic evolution problem for a general class of such damage models is formulated as a variational inequality involving the action integral of a generalized Lagrangian and its physical interpretation is given. Finite-element based implementation is then detailed and mathematical optimization methods are directly used at the structural scale exploiting fully the variational nature of the formulation. Finally, the link with the classical dynamic Griffith theory and with the original quasi-static model as well as various dynamic fracture phenomena are illustrated by representative numerical examples in quantitative accordance with theoretical or experimental results.
• Microscale insight into the influence of humidity on the mechanical behavior of mudstones
  
  • Wang Linlin
  • Bornert Michel
  • Héripré Eva
  • Chanchole Serge
  • Pouya Ahmad
  • Halphen Bernard
  Journal of Geophysical Research, American Geophysical Union, 2015, 120 (5), pp.3173-3186. (10.1002/2015JB011953)
  DOI : 10.1002/2015JB011953
• A micromechanical model of the viscoplastic behaviour of titanium accounting for its anisotropic and strain-rate-dependent viscosity
  
  • Doquet Véronique
  • Barkia Bassem
  Mechanics of Time-Dependent Materials, Society for Experimental Mechanics, 2015, 19 (2), pp.153-166. The viscoplastic behaviour of two batches of commercially pure titanium with different oxygen contents was characterized at room temperature through tension, creep, relaxation, and strain rate jumps tests along the rolling and transverse directions. Depending on the applied stress, creep saturated, or the primary creep stage was followed by secondary and even tertiary creep leading to fracture within a few hours. 33 to 40% of the flow stress was relaxed within 20 hours. The strain rate sensitivity was found to increase with the oxygen content and when the strain-rate-decreased. It was up to 25% higher along the transverse direction than along the rolling direction. The experimental data were used to identify a simple mean field crystal viscoplasticity model. Assuming different viscosities on prismatic and non prismatic slip systems, the anisotropy and strain rate dependence of the strain rate sensitivity were captured. As a consequence of these different viscosities, the relative contributions of each type of slip system to the overall deformation are predicted to vary with the strain rate, in accordance with some data from the literature. (10.1007/s11043-015-9257-9)
  DOI : 10.1007/s11043-015-9257-9
• On the second-order homogenization of wave motion in periodic media and the sound of a chessboard
  
  • Wautier Antoine
  • Guzina Bojan B
  Journal of the Mechanics and Physics of Solids, Elsevier, 2015, 78, pp.382-414. The goal of this study is to better understand the mathematical structure and ramifications of the second-order homogenization of low-frequency wave motion in periodic solids. To this end, multiple-scales asymptotic approach is applied to the scalar wave equation (describing anti-plane shear motion) in one and two spatial dimensions. In contrast to previous studies where the second-order homogenization has lead to the introduction of a single fourth-order derivative in the governing equation, present investigation demonstrates that such (asymptotic) approach results in a family of field equations uniting spatial, temporal, and mixed fourth-order derivatives-that jointly control incipient wave dispersion. Given the consequent freedom in selecting the affiliated lengthscale parameters, the notion of an optimal asymptotic model is next considered in a one-dimensional setting via its ability to capture the salient features of wave propagation within the first Brillouin zone, including the onset and magnitude of the phononic band gap. In the context of two-dimensional wave propagation, on the other hand, the asymptotic analysis is first established in a general setting, exposing the constant shear modulus as sufficient condition under which the second-order approximation of a bi-periodic elastic solid is both isotropic and limited to even-order derivatives. On adopting a chessboard-like periodic structure (with contrasts in both modulus and mass density) as a testbed for in-depth analytical treatment, it is next shown that the second-order approximation of germane wave motion is governed by a family fourth-order differential equations that: (i) entail exclusively even-order derivatives and homogenization coefficients that depend explicitly on the contrast in mass density; (ii) describe anisotropic wave dispersion characterized by the "sin cos 4 4 θ θ + " term, and (iii) include the asymptotic model for a square lattice of circular inclusions as degenerate case. For completeness, the analysis is illustrated by a set of numerical results highlighting the effects of periodic structure on the long-wavelength material response in terms of wave dispersion, pho-nonic band gap, and second-order anisotropy. (10.1016/j.jmps.2015.03.001)
  DOI : 10.1016/j.jmps.2015.03.001
• Prestrained biaxial DMA investigation of viscoelastic nonlinearities in highly filled elastomers
  
  • Jalocha Dimitri
  • Constantinescu Andrei
  • Nevière Robert
  Polymer Testing, Elsevier, 2015, 42, pp.37-44. Highly filled elastomers present strong nonlinear mechanical behavior. This study proposes a biaxial dynamic mechanical analysis (DMA) experiment to study the prestrain induced nonlinearity. This phenomenon has already been observed for uniaxial tests, revealing an increase of the amplitude of the dynamic modulus with prestrain. The novelty proposed here is to investigate the problem under biaxial conditions. For this purpose, a specific apparatus and an appropriate specimen have been designed. Strains and stresses have been measured using localization formulae and compared with measurements from digital image correlation and finite element computations. Biaxial DMA tests were performed on a propellant specimen, for different values of biaxial prestrain. The material is a highly filled elastomer with an important influence of the prestrain on the global viscoelastic behavior. The results exhibit increasing amplitude of the complex modulus with increasing prestrain, as in uniaxial experiments. Moreover, the dependence can be characterized using the second invariant of the prestrain, and the viscoelastic behavior is modeled using a closed-form spectrum of relaxation times. (10.1016/j.polymertesting.2015.01.005)
  DOI : 10.1016/j.polymertesting.2015.01.005
• Dynamic stability of a bar under high loading rate: Response to local perturbations
  
  • Ravi-Chandar K.
  • Triantafyllidis N.
  International Journal of Solids and Structures, Elsevier, 2015, 58, pp.301-308. Of interest here is the influence of loading rate on the stability of structures where inertia is taken into account. The approach currently used in the literature to analyze these stability problems, is the method of modal analysis that determines the structure’s fastest growing wavelength, which is meaningful only for cases where the velocity of the perfect structure is significantly lower than the associated characteristic wave propagation speeds. The novel idea here is to analyze the time-dependent response to perturbations of the transient (high strain rates) states of these structures, in order to understand the initiation of the corresponding failure mechanisms. We are motivated by the recent experimental studies of Zhang and Ravi-Chandar (2006) on the high strain rate extension of thin rings that show no evidence of a dominant wavelength in their failure mode and no influence of strain-rate sensitivity on the necking strains. In the interest of analytical tractability, we study the extension of an incompressible, nonlinearly elastic bar at different strain rates. The dynamic stability of these bars is studied by following the evolution of localized small perturbations introduced at different times. It is shown that these structures are stable until the static necking strain is reached at some point. Moreover their failure pattern is dictated by the distribution of defects, the minimum distance between necks diminishes with increasing strain rate and there is no dominant wavelength mode, exactly as observed experimentally in Zhang and Ravi-Chandar (2006). (10.1016/j.ijsolstr.2014.09.015)
  DOI : 10.1016/j.ijsolstr.2014.09.015
• Competition between microstructure and defect in multiaxial high cycle fatigue
  
  • Morel Franck
  • Guerchais Raphaël
  • Saintier Nicolas
  , 2015, 33, pp.404-414. This study aims at providing a better understanding of the effects of both microstructure and defect on the high cycle fatigue behavior of metallic alloys using finite element simulations of polycrystalline aggregates. It is well known that the microstructure strongly affects the average fatigue strength and when the cyclic stress level is close to the fatigue limit, it is often seen as the main source of the huge scatter generally observed in this fatigue regime. The presence of geometrical defects in a material can also strongly alter the fatigue behavior. Nonetheless, when the defect size is small enough, i.e. under a critical value, the fatigue strength is no more affected by the defect. The so-called Kitagawa effect can be interpreted as a competition between the crack initiation mechanisms governed either by the microstructure or by the defect. Surprisingly, only few studies have been done to date to explain the Kitagawa effect from the point of view of this competition, even though this effect has been extensively investigated in the literature. The primary focus of this paper is hence on the use of both FE simulations and explicit descriptions of the microstructure to get insight into how the competition between defect and microstructure operates in HCF. In order to account for the variability of the microstructure in the predictions of the macroscopic fatigue limits, several configurations of crystalline orientations, crystal aggregates and defects are studied. The results of each individual FE simulation are used to assess the response at the macroscopic scale thanks to a probabilistic fatigue criterion proposed by the authors in previous works. The ability of this criterion to predict the influence of defects on the average and the scatter of macroscopic fatigue limits is evaluated. In this paper, particular emphasis is also placed on the effect of different loading modes (pure tension, pure torsion and combined tension and torsion) on the experimental and predicted fatigue strength of a 316 stainless steel containing artificial defect. (10.3221/IGF-ESIS.33.45)
  DOI : 10.3221/IGF-ESIS.33.45
• Micro-macro tracking of the deformation field. Application to halite rock
  
  • Bornert Michel
  • Gaye Ababacar
  • Dimanov A.
  • Bourcier Mathieu
  • Raphanel Jean
  • Heripre Eva
  • Ludwig Wolfgang
  • King A.
  , 2015.
• Influence of the casting microstructure on LCF damage mechanisms in an Al-Si alloy using X-ray tomography
  
  • El Bartali Ahmed
  • Wang Long
  • Dahdah Nora
  • Limodin Nathalie
  • Witz Jean-Francois
  • Seghir Rian
  • Buffiere Jean-Yves
  • Charkaluk Eric
  , 2015.
• Micromécanismes actifs dans le sel gemme : quantifications expérimentales pour une modélisation pertinente
  
  • Bornert Michel
  • Dimanov Alexandre
  • Raphanel Jean
  • Gaye Ababacar
  • Bourcier Mathieu
  • Heripre Eva
  • D. Picard
  • Ludwig Wolfgang
  , 2015. La formulation pertinente d'une loi de comportement représentative du comportement des matériaux reste un enjeu majeur pour garantir la capacité predictive des calculs numériques de structures, notamment lorsque l'on considère des réponses à long terme, ou sous des modes de sollicitation difficilement accessibles à l'expérimentation en laboratoire. Dans ce contexte, les approches multiéchelles reposant sur la connaissance des mécanismes physiques élémentaires actifs à l'échelle d'un grain constitutif et l'utilisation de lois de changement d'échelle adéquates peuvent être une réponse. Le comportement de la halite a fait et fait encore l'objet de nombreuses études dans ce sens, notamment en vue d'applications de stockage en cavités souterraines. Les modèles proposés reposent pour la plupart sur la connaissance des mécanismes de glissement plastique intracristallins, étudiés par exemple sur des monocristaux sous diverses conditions thermodynamiques. Il s'avère toutefois qu'une prévision raisonnable des réponses macroscopiques reposant sur ces seuls mécanismes de glissement cristallin conduit à des contradiction sur la nature des systèmes activés et/ou les valeurs de leurs paramètres constitutifs. On montrera dans cet exposé comment une analyse expérimentale quantitative à l'échelle d'un ensemble de grains constitutifs, combinant expérimentation in situ sous MEB ou tomographe, à température ambiante et haute température, et traitement d'image par corrélation, permet de revisiter ces hypothèses de modélisation. On établit en particulier, d'une part, l'importance d'un mécanismes de déformation par glissement aux joints de grains, qui, certes secondaire en termes de contribution globale à la déformation, s'avère indispensable à l'écoulement ductile macroscopique. D'autre part, l'analyse permet aussi une quantification des contributions relatives de mécanismes de glissement plastique et de leurs conditions d'activation au sein du polycristal. Cette vision rénovée du comportement de cette roche est plus généralement susceptible d'expliquer certaines observations paradoxales et illustre le danger potentiel d'une extrapolation hâtive.
• Data Assimilation for hyperbolic conservation laws. A Luenberger observer approach based on a kinetic description
  
  • Boulanger Anne-Céline
  • Moireau Philippe
  • Perthame Benoît
  • Sainte-Marie Jacques
  Communications in Mathematical Sciences, International Press, 2015, 13 (3), pp.587 – 622. Developing robust data assimilation methods for hyperbolic conservation laws is a challenging subject. Those PDEs indeed show no dissipation effects and the input of additional information in the model equations may introduce errors that propagate and create shocks. We propose a new approach based on the kinetic description of the conservation law. A kinetic equation is a first order partial differential equation in which the advection velocity is a free variable. In certain cases, it is possible to prove that the nonlinear conservation law is equivalent to a linear kinetic equation. Hence, data assimilation is carried out at the kinetic level, using a Luenberger observer also known as the nudging strategy in data assimilation. Assimilation then resumes to the handling of a BGK type equation. The advantage of this framework is that we deal with a single "linear" equation instead of a nonlinear system and it is easy to recover the macroscopic variables. The study is divided into several steps and essentially based on functional analysis techniques. First we prove the convergence of the model towards the data in case of complete observations in space and time. Second, we analyze the case of partial and noisy observations. To conclude, we validate our method with numerical results on Burgers equation and emphasize the advantages of this method with the more complex Saint-Venant system. (10.4310/CMS.2015.v13.n3.a1)
  DOI : 10.4310/CMS.2015.v13.n3.a1
• From Mild to Wild Fluctuations in Crystal Plasticity
  
  • Weiss J.
  • Ben Rhouma Wafa
  • Richeton T.
  • Deschanel Stéphanie
  • Louchet F.
  • Truskinovsky L.
  Physical Review Letters, American Physical Society, 2015, 114 (10). Macroscopic crystal plasticity is classically viewed as an outcome of uncorrelated dislocation motions producing Gaussian fluctuations. An apparently conflicting picture emerged in recent years emphasizing highly correlated dislocation dynamics characterized by power-law distributed fluctuations. We use acoustic emission measurements in crystals with different symmetries to show that intermittent and continuous visions of plastic flow are not incompatible. We demonstrate the existence of crossover regimes where strongly intermittent events coexist with a Gaussian quasiequilibrium background and propose a simple theoretical framework compatible with these observations. (10.1103/PhysRevLett.114.105504)
  DOI : 10.1103/PhysRevLett.114.105504
• Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography
  
  • Corrado Cesare
  • Gerbeau Jean-Frédéric
  • Moireau Philippe
  Journal of Computational Physics, Elsevier, 2015, 283, pp.271–298. This work addresses the inverse problem of electrocardiography from a new perspective, by combining electrical and mechanical measurements. Our strategy relies on the defini-tion of a model of the electromechanical contraction which is registered on ECG data but also on measured mechanical displacements of the heart tissue typically extracted from medical images. In this respect, we establish in this work the convergence of a sequential estimator which combines for such coupled problems various state of the art sequential data assimilation methods in a unified consistent and efficient framework. Indeed we ag-gregate a Luenberger observer for the mechanical state and a Reduced Order Unscented Kalman Filter applied on the parameters to be identified and a POD projection of the electrical state. Then using synthetic data we show the benefits of our approach for the estimation of the electrical state of the ventricles along the heart beat compared with more classical strategies which only consider an electrophysiological model with ECG measurements. Our numerical results actually show that the mechanical measurements improve the identifiability of the electrical problem allowing to reconstruct the electrical state of the coupled system more precisely. Therefore, this work is intended to be a first proof of concept, with theoretical justifications and numerical investigations, of the ad-vantage of using available multi-modal observations for the estimation and identification of an electromechanical model of the heart. (10.1016/j.jcp.2014.11.041)
  DOI : 10.1016/j.jcp.2014.11.041
• Selective and reduced numerical integrations for NURBS-based isogeometric analysis
  
  • Adam Cédric
  • Hughes T.R.J.
  • Bouabdallah Salim
  • Zarroug Malek
  • Maitournam Habibou
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2015, 284, pp.732–761. We propose a new approach to construct selective and reduced integration rules for isogeometric analysis based on NURBS elements. The notion of an approximation space that approximates the target space is introduced. We explore the use of various approximation spaces associated with optimal patch-wise numerical quadratures that exactly integrate the polynomials in approximation spaces with the minimum number of quadrature points. Patch rules exploit the higher continuity of spline basis functions. The tendency of smooth spline functions to exhibit numerical locking in nearly-incompressible problems when using a full Gauss–Legendre quadrature is alleviated with selective or reduced integration. Stability and accuracy of the schemes are examined analyzing the discrete spectrum in a generalized eigenvalue problem. We propose a local algorithm, which is robust and computationally efficient, to compute element-by-element the quadrature points and weights in patch rules. The performance of the methods is assessed on several numerical examples in two-dimensional elasticity and Reissner–Mindlin shell structures. (10.1016/j.cma.2014.11.001)
  DOI : 10.1016/j.cma.2014.11.001
• Near-tip strain evolution under cyclic loading: In situ experimental observation and numerical modelling
  
  • Tong J
  • Lin B
  • Lu Y.-W
  • Madi Kamel
  • Doquet Véronique
  International Journal of Fatigue, Elsevier, 2015, 71, pp.45-52. The concept of ratchetting strain as a crack driving force in controlling crack growth has previously been explored at Portsmouth using numerical approaches for nickel-based superalloys. In this paper, we report the first quantitative experimental evidence of near-tip strain ratchetting with cycles, as captured in situ by digital image correlation (DIC) technique on a compact tension specimen of stainless steel 316L, using both Stereo and SEM systems. The evolution of the near-tip strains with loading cycles was monitored whilst the crack tip was kept stationary. The strains normal to the crack plane were examined over selected distances from 6 to 57 lm to the crack tip for a number of cycles. The results show that strain ratchetting occurs with loading cycles, and is particularly evident close to the crack tip and under higher loads. 3D finite element models have also been developed to simulate the experiments and the results from the simulation are compared with those from the DIC measurements. This is the first time that near-tip strain ratchetting has been captured in situ at the peak loads during cyclic loading. (10.1016/j.ijfatigue.2014.02.013)
  DOI : 10.1016/j.ijfatigue.2014.02.013
• Nonlinear Donati compatibility conditions and the intrinsic approach for nonlinearly elastic plates
  
  • Ciarlet Philippe G.
  • Geymonat Giuseppe
  • Krasucki Francoise
  Journal de Mathématiques Pures et Appliquées, Elsevier, 2015, 103 (1), pp.255-268. Linear Donati compatibility conditions guarantee that the components of symmetric tensor fields are those of linearized change of metric or linearized change of curvature tensor fields associated with the displacement vector field arising in a linearly elastic structure when it is subjected to applied forces. These compatibility conditions take the form of variational equations with divergence-free tensor fields as test-functions, by contrast with Saint-Venant compatibility conditions, which take the form of systems of partial differential equations. In this paper, we identify and justify nonlinear Donati compatibility conditions that apply to a nonlinearly elastic plate modeled by the Kirchhoff-von K'arm'an-Love theory. These conditions, which to the authors' best knowledge constitute a first example of nonlinear Donati compatibility conditions, in turn allow to recast the classical approach to this nonlinear plate theory, where the unknown is the position of the deformed middle surface of the plate, into the intrinsic approach, where the change of metric and change of curvature tensor fields of the deformed middle surface of the plate are the only unknowns. The intrinsic approach thus provides a direct way to compute the stress resultants and the stress couples inside the deformed plate, often the unknowns of major interest in computational mechanics. (10.1016/j.matpur.2014.04.003)
  DOI : 10.1016/j.matpur.2014.04.003