Laboratoire Mécanique des Solides

The objective of this work was to observe and quantify the onset and evolution of localised deformation processes in sand with grain-scale resolution. The key element of the proposed approach is combining state-of-the-art X-ray micro tomography imaging with three-dimensional volumetric digital image correlation techniques. This allows not only the grain-scale details of a deforming sand specimen to be viewed, but also, and more importantly, the evolving three-dimensional displacement and strain fields throughout loading to be assessed. X-ray imaging and digital image correlation have been in the past applied individually to study sand deformation, but the combination of these two methods to study the kinematics of shear band formation at the grain scale is the first novel aspect of this work. Moreover, the authors have developed a completely original grain-scale volumetric digital image correlation method that permits the characterisation of the full kinematics (i.e. three-dimensional displacements and rotations) of all the individual sand grains in a specimen. The results obtained using the discrete volumetric digital image correlation confirm the importance of grain rotations associated with strain localisation.

Admettant l'hypothèse de dissipativité normale, nous établissons pour une classe de matériaux élastoviscoplastiques et élastoplastiques à déformation plastique instantanée, les lois d'évolution de la transformation plastique et des paramètres internes caractérisant ! 'écrouissage. Ces lois nous permettent d'étudier ensuite en transformation infiniment petite isotherme quelques problèmes relatifs à l'évolution des champs de contrainte, de paramètres internes et de déplacement pour un trajet de charge quelconque. Nous établissons en particulier un théorème d'unicité des contraintes et des paramètres internes.

The linear response to stochastic and optimal harmonic forcing of small coherent perturbations to the turbulent channel mean flow is computed for Reynolds numbers ranging from Re τ = 500 to 20000. Even though the turbulent mean flow is linearly stable, it is nevertheless able to sustain large amplifications by the forcing. The most amplified structures consist of streamwise-elongated streaks that are optimally forced by streamwise-elongated vortices. For streamwise-elongated structures, the mean energy amplification of the stochastic forcing is found to be, to a first approximation, inversely proportional to the forced spanwise wavenumber while it is inversely proportional to its square for optimal harmonic forcing in an intermediate spanwise wavenumber range. This scaling can be explicitly derived from the linearized equations under the assumptions of geometric similarity of the coherent perturbations and of logarithmic base flow. Deviations from this approximate power-law regime are apparent in the pre-multiplied energy amplification curves that reveal a strong influence of two different peaks. The dominant peak scales in outer units with the most amplified spanwise wavelength of λ z ≈ 3.5 h , while the secondary peak scales in wall units with the most amplified λ z + ≈ 80. The associated optimal perturbations are almost independent of the Reynolds number when, respectively, scaled in outer and inner units. In the intermediate wavenumber range, the optimal perturbations are approximatively geometrically similar. Furthermore, the shape of the optimal perturbations issued from the initial value, the harmonic forcing and the stochastic forcing analyses are almost indistinguishable. The optimal streaks corresponding to the large-scale peak strongly penetrate into the inner layer, where their amplitude is proportional to the mean-flow profile. At the wavenumbers corresponding to the large-scale peak, the optimal amplifications of harmonic forcing are at least two orders of magnitude larger than the amplifications of the variance of stochastic forcing and both increase with the Reynolds number. This confirms the potential of the artificial forcing of optimal large-scale streaks for the flow control of wall-bounded turbulent flows.

This chapter presents an overview of diffusion data for pyroxenes, amphiboles and micas. These minerals are grouped together since amphiboles and micas are closely related in structure to pyroxenes, with amphiboles essentially constructed of alternating layers with structures of mica and pyroxene. We begin with discussion of diffusion in pyroxenes, for which an extensive literature exists, with diffusion studies of major, minor and trace elements. We consider diffusion mechanisms in light of present understanding of defect chemistry, and discuss various crystal-chemical factors that may affect cation diffusion. The last section of the chapter presents a review of diffusion data for amphiboles and micas. Selected Arrhenius relations for these all these mineral phases are summarized in the Appendix Tables A1, A2, A3 and A4. This chapter focuses primarily on cation diffusion, since oxygen, hydrogen and noble gas diffusion are discussed in other chapters; readers interested in more detailed discussion of diffusion of these species in pyroxene, amphibole and mica are directed to Chapters 10 (Farver 2010, this volume) and 11 (Baxter 2010, this volume).

Abstract This paper focuses on the introduction of a lumped mass matrix for enriched elements, which enables one to use a pure explicit formulation in X‐FEM applications. A proof of stability for the 1D and 2D cases is given. We show that if one uses this technique, the critical time step does not tend to zero as the support of the discontinuity reaches the boundaries of the elements. We also show that the X‐FEM element's critical time step is of the same order as that of the corresponding element without extended degrees of freedom. Copyright © 2006 John Wiley & Sons, Ltd.

The Sumatra, December 26th, 2004, tsunami produced internal gravity waves in the neutral atmosphere and large disturbances in the overlying ionospheric plasma. To corroborate the tsunamigenic hypothesis of these perturbations, we reproduce, with a 3D numerical modeling of the ocean‐atmosphere‐ionosphere coupling, the tsunami signature in the Total Electron Content (TEC) data measured by the Jason‐1 and Topex/Poseidon satellite altimeters. The agreement between the observed and synthetic TEC shows that ionospheric remote sensing can provide new tools for offshore tsunami detection and monitoring.

Abstract: Digital image correlation techniques (DIC) are applied to sequences of optical images of argillaceous rock samples submitted to uniaxial compression at various saturation states at both the global centimetric scale of the samples and the local scale of their composite microstructure, made of a water-sensitive clay matrix and other mineral inclusions with a typical size of 50 μm. Various scales of heterogeneities are revealed by the optical technique. Not only is it confirmed that the clay matrix deforms much more than the other mineral inclusions, but it also appears that the deformation is very inhomogeneous in the matrix, with some areas almost not deformed, while others exhibit deformation twice the average overall strain (for a gauge length of 45 μm), depending on the local distribution of the inclusions. In almost-saturated rocks, overall heterogeneities are also linked to the presence of a network of cracks, induced by the preliminary hydric load. On such wet samples, DIC analysis shows that the overall strain results both from the bulk deformation of the sound rock, with deformation levels similar to those in dry samples, and the closing or opening of these mesoscopic cracks.

We investigated the high‐temperature creep strength of fine‐grained anorthite‐diopside rocks at temperatures ranging from 1323 K to 1523 K and at 300 MPa confining pressure in a Paterson‐type gas‐medium deformation apparatus. Flow stress varied between 20 and 450 MPa resulting in strain rates between 6.1 × 10 −7 s −1 and 7.5 × 10 −4 s −1 . Pure diopside and anorthite samples were hot pressed from crushed natural single crystals and glass powders, respectively. Two‐phase samples were produced by hot isostatic pressing of mechanically mixed powders of anorthite glass with 25, 50 and 75 vol % diopside particles. Arithmetic mean grain size of the anorthite matrix is d An ≈ 3.5 μm. Three different ranges of diopside particle size were used: d Di < 25 μm, <35 μm, and <45 μm. Water content of as is samples was about 0.05 ± 0.02 wt % H 2 O, and predried samples contain about 0.004 ± 0.001 wt % H 2 O. At experimental conditions, as is samples are assumed to be water saturated. Water content of predried samples is about 3 times less than that of starting diopside single crystals. The specimens contain about 1 vol % glass located at fluid inclusions and some multiple grain junctions. Two‐grain boundaries examined by high‐resolution transmission electron microscopy did not show amorphous layers to a resolution of 1 nm. At experimental conditions, pure diopside aggregates are about 2–3 orders of magnitude stronger than pure anorthite samples for as is and predried specimens, respectively. In general, strength of the two‐phase aggregates increases with increasing diopside content but remains between isostress and isostrain rate bounds. Aggregate strengths predicted from continuum mechanics models are in good agreement with the experimental data for dilute diopside particle mixtures and high‐volume fractions, when diopside particles form a load‐bearing framework. At low stresses (<100–200 MPa) the stress exponent is n ≈ 1, suggesting diffusion‐controlled creep. At higher stresses, mechanical data and microstructures suggest that samples deformed in the transition region between diffusion‐controlled creep and dislocation creep. For pure anorthite and diopside aggregates deforming in dislocation creep we estimated stress exponents of n ≈ 3 and n ≈ 5.5, respectively. For the two‐phase aggregates, n is between n ≈ 3 and n ≈ 5, depending on diopside content. At low stresses, deformation microstructures indicate load transfer from a weak anorthite matrix to stronger diopside particles. Creep activation energies for pure diopside and anorthite mixtures range from 286 kJ mol −1 for wet anorthite deformed at low stresses to 691 kJ mol −1 for dry diopside deformed at high stresses. Activation energies of two‐phase mixtures are between or close to those of the end‐members. As is samples have significantly lower activation energies than predried samples.

A two-scale model is developed for fluid flow in a deforming, unsaturated and progressively fracturing porous medium. At the microscale, the flow in the cohesive crack is modelled using Darcy’s relation for fluid flow in a porous medium, taking into account changes in the permeability due to the progressive damage evolution inside the cohesive zone. From the micromechanics of the flow in the cavity, identities are derived that couple the local momentum and the mass balances to the governing equations for an unsaturated porous medium, which are assumed to hold on the macroscopic scale. The finite element equations are derived for this two-scale approach and integrated over time. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures are independent from the underlying discretization. The resulting discrete equations are nonlinear due to the cohesive crack model and the nonlinearity of the coupling terms. A consistent linearization is given for use within a Newton–Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach. The calculations indicate that the evolving cohesive cracks can have a significant influence on the fluid flow and vice versa.

Abstract We introduce a new numerical method to model the fluid–structure interaction between a microcapsule and an external flow. An explicit finite element method is used to model the large deformation of the capsule wall, which is treated as a bidimensional hyperelastic membrane. It is coupled with a boundary integral method to solve for the internal and external Stokes flows. Our results are compared with previous studies in two classical test cases: a capsule in a simple shear flow and in a planar hyperbolic flow. The method is found to be numerically stable, even when the membrane undergoes in‐plane compression, which had been shown to be a destabilizing factor for other methods. The results are in very good agreement with the literature. When the viscous forces are increased with respect to the membrane elastic forces, three regimes are found for both flow cases. Our method allows a precise characterization of the critical parameters governing the transitions. Copyright © 2010 John Wiley & Sons, Ltd.

Drop impacts are difficult to characterize due to their transient, non-stationary nature. We discuss the force generated during such impacts, a key quantity for animals, plants, roofs or soil erosion. Although a millimetric drop has a modest weight, it can generate collision forces on the order of thousand times this weight. We measure and discuss this amplification, considering natural parameters such as drop radius and density, impact speed and response time of the substrate. We finally imagine two kinds of devices allowing us to deduce the size of the raindrop from impact forces.

Low‐angle extensional shear zones, which often characterize the brittle–ductile transition of the continental crust, are seen here to result from strain localization. The potentially destabilizing deformation mechanism is assumed to be the progressive transformation of fractured coarse feldspar grains into white mica as observed in the East Tenda Shear Zone, Alpine Corsica. The coupling between microfracturing and feldspar‐to‐mica reaction is coeval with strain localization that occurred in that field case at a depth close to 15 km. This reaction is proposed as the main destabilizing factor responsible for the onset of localization, with feldspar having a stationary dislocation creep flow stress larger than mica. To test this hypothesis, a rheological model is constructed based on the field observations for a mixture of three phases—mica, quartz and feldspar—deforming at a common strain rate. The phase concentrations change with time according to the feldspar‐to‐mica reaction, which takes place only if feldspar grains are fractured, a condition detected with the Mohr–Coulomb criterion. The tendency for the strain to localize is assessed by numerical means for the structure composed of an upper crust gliding rigidly over the lower crust, which sustains an overall simple shear. The onset of strain localization is defined by an increase of at least two orders of magnitude in strain rate over part of the lower crust. The upper crust gliding velocity has to be increased by at least a factor of 5 for localization to occur. The time lapse for this velocity change determines the depth of the shear zone (15–17 km). The kinetics of the metamorphic reaction and the final amount of white mica control its width (1–4 km). The time of the shear zone formation is less than half a million years.

Recent studies to assess very long-term seismic hazard in the United States and in Europe have brought the issue of upper limits on earthquake ground motions into the arena of problems requiring attention from the engineering seismological community. Few engineering projects are considered sufficiently critical to warrant the use of annual frequencies of exceedance so low that ground-motion estimates may become unphysical if limiting factors are not considered, but for nuclear waste repositories, for example, the issue is of great importance. The definition of upper bounds on earthquake ground motions also presents an exciting challenge for researchers in the area of seismic hazard assessment. This paper looks briefly at historical work on maximum values of ground-motion amplitudes before illustrating why this is an important issue for hazard assessments at very long return periods. The paper then discusses the factors that control the extreme values of motion, both in terms of generating higher amplitude bedrock motions and of limiting the values of motion at the ground surface. Possible channels of research that could be explored in the quest to define maximum possible ground motions are also discussed.

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.

ABSTRACT This paper presents a global approach to the design of structures that experience thermomechanical fatigue loading, which has been applied successfully in the case of cast‐iron exhaust manifolds. After a presentation of the design context in the automotive industry, the important hypotheses and choices of this approach, based on a thermal 3D computation, an elastoviscoplastic constitutive law and the dissipated energy per cycle as a damage indicator associated with a failure criterion, are first pointed out. Two particular aspects are described in more detail: the viscoplastic constitutive models, which permit a finite element analysis of complex structures and the fatigue criterion based on the dissipated energy per cycle. The FEM results associated with this damage indicator permit the construction of a design curve independent of temperature; an agreement is observed between the predicted durability and the results of isothermal as well as non isothermal tests on specimens and thermomechanical fatigue tests on real components on an engine bench. These results show that thermomechanical fatigue design of complex structures can be performed in an industrial context.

Abstract An interative approach is proposed for the numerical analysis of elastic–plastic continua. This approach gives after convergence an implicit scheme of integration of the evolution problem, and is concerned with elastic‐perfectly plastic materials and with hardening standard materials. Under a generalized assumption of positive hardening, the proof of convergence of the iterative solutions is given. Some numerical examples by the finite element method are also discussed.

The strain hardening properties of FCC single crystals are examined with the help of a three-dimensional simulation of dislocation dynamics and interactions at mesoscale. The basic properties discussed are the line tension of the dislocations, the conditions at which sessile junctions are formed at the intersection of two slip systems and the stability of these locks. The relation between the flow stress and the square root of the intersecting dislocation density is examined in areal glide and in multislip conditions. A validation of the model is performed by comparison with experimental results on copper single crystals. At the small strains reached by the simulation and in multislip conditions, strain hardening is found to originate from the continuous increase of forest density rather than from the formation of immobile loops around clusters of forest obstacles. It is suggested that at larger strains a stabilizing mechanism, possibly cross-slip, should enhance the dislocation storage processes and initiate the formation of dislocation cells.

Martensitic phase transitions are often modeled by mixed-type hyperbolic-elliptic systems. Such systems lead to ill-posed initial-value problems unless they are supplemented by an additional kinetic relation. In this paper we explicitly compute an appropriate closing relation by replacing the continuum model with its natural discrete prototype. The procedure can be viewed as either regularization by discretization or a physically motivated account of underlying discrete microstructure. We model phase boundaries by traveling wave solutions of a fully inertial discrete model for a bi-stable lattice with harmonic long-range interactions. Although the microscopic model is Hamiltonian, it generates macroscopic dissipation which can be specified in the form of a relation between the velocity of the discontinuity and the conjugate configurational force. This kinetic relation respects entropy inequality but is not a consequence of the usual Rankine–Hugoniot jump conditions. According to the constructed solution, the dissipation at the macrolevel is due to the induced radiation of lattice waves carrying energy away from the propagating front. We show that sufficiently strong nonlocality of the lattice model may be responsible for the multivaluedness of the kinetic relation and can quantitatively affect kinetics in the near-sonic region. Direct numerical simulations of the transient dynamics suggest stability of at least some of the computed traveling waves.

We investigate the out-of-plane shape morphing capability of single-material elastic sheets with architected cut patterns that result in arrays of tiles connected by flexible hinges. We demonstrate that a non-periodic cut pattern can cause a sheet to buckle into three-dimensional shapes, such as domes or patterns of wrinkles, when pulled at specific boundary points. These global buckling modes are observed in experiments and rationalized by an in-plane kinematic analysis that highlights the role of the geometric frustration arising from non-periodicity. The study focuses on elastic sheets, and is later extended to elastic-plastic materials to achieve shape retention. Our work illustrates a scalable route towards the fabrication of three-dimensional objects with nonzero Gaussian curvature from initially-flat sheets.

The seismic bearing capacity of a strip-surface foundation resting on a Mohr-Coulomb material is evaluated. The upper-bound theorem of the yield design theory is used to obtain an estimate of the ultimate load. The loading parameters consist of a normal and tangential force applied to the foundation and of inertia forces developed within the soil volume. The classical Prandtl-like mechanism is used to show that the reduction in the bearing capacity is mainly caused by the load inclination; the consideration of inertia forces within the soil is only responsible for a decrease in the bearing capacity that is at least an order of magnitude smaller than the one caused by the load inclination. It is therefore concluded that, from a practical engineering standpoint, the soil-inertia forces can be neglected.