Publications

2010

• Multi-scale viscoplastic behaviour of Halite: In-situ SEM full field measurements, a micro-mechanical approach
  
  • Bourcier Mathieu
  • Dimanov Alexandre
  • Héripré Eva
  • Bornert Michel
  • Raphanel Jean
  , 2010. Halite geological formations are already extensively used for underground storage of hydrocarbons. For example, the entire USA federal reserve of petrol resides in deep (500 - 1000 m) artificial salt caverns, which are realized by controlled dissolution. In France, many such salt caverns are used for storage of natural gas by GDF. Salt caverns and carries are also intended to become nuclear waste repositories. At this point, salt caverns are also seriously envisaged for the daily storage of energy from renewable, but intermittent sources (photovoltaic, Aeolian), under the form of compressed air. Halite mechanical behaviour was extensively studied for the purpose of safe geothechnical applications. Halite is a ductile type rock. Its differed (time-dependent) mechanical response dominates by far, and therefore deep salt caverns experience convergence (closure), which may result in catastrophic subsidence of the overlaying geological layers. Hence, a particular attention was drawn to characterize salt single crystal creep properties (active slip systems and critical resolved shear stresses), and the rheology of poly-crystalline salt, at various temperatures, pressures, differential stresses and water contents (Ter Heege et al., 2007). But, most studies were concerned with macroscopically derived flow laws, corresponding to rather high differential stresses (as compared with those experienced on site), where crystal slip plasticity (CSP) dominates. But, many studies have also shown that halite is very sensitive to solution-precipitation creep (SPC) mechanisms, which may result in solution transfer accommodated grain boundary sliding (GBS). Conversely, some recent studies report that halite is able to flow at ambient conditions, and under very small loads, with strain rates much faster (four orders of magnitude) than those extrapolated from high stress experiments (Bérest et al., 2005). Though, the specific creep micro-mechanisms were not identified, Bérest et al. (2005) invoked possible SPC. Additionally, the effects on long term behaviour of cyclic loading (fatigue) are still poorly known. It is therefore still questionable weather it is really possible to safely extrapolate the laboratory data to the long term envisaged geotechnical applications. To answer we need i) additional experimental work in order to up date the deformation mechanism maps on the basis of better identified micro-physical mechanisms and quantification of their respective activity; and ii) numerical modelling at the scales of the material, and of the underground storage structures, in respect with the appropriated thermo-hygro-mechaniclal loadings. In the present work, we present our preliminary investigation of viscoplastic global and local responses of synthetic fine grained (50 - 500 m) halite by the means of full field measurements (FFM) of local strain by digital image correlation (DIC) during simple compression in-situ SEM (Doumalain et al., 2003). Figure 1 shows a typical loading curve obtained incrementally at the constant strain rate of c.a. 5x10-5 s-1. CSP evidenced by the development of slip lines on the free grain surfaces, and characterized by quasi-linear strain hardening, dominates the overall response up to several % of strain (microfracturing did not appear before 8 % strain). Yet, at the scale of the microstructure, the development of viscoplastic strain is heterogeneous, as shown by the strain maps obtained by DIC and corresponding to four incremental stages of the loading sequence. The heterogeneity of the strain field relates to the loading boundary conditions and to the local microstructure, such crystal size and orientation (which is characterized by electron back scattering diffraction, EBSD). Such micromechanical approach aims to provide the basis for the development of FE (finite element) computational CSP of polycrystalline halite.
• Cyclic behavior of short glass fiber reinforced polyamide for fatigue life prediction of automotive components
  
  • Launay Antoine
  • Marco Yann
  • Maitournam Habibou
  • Raoult Ida
  • Szmytka Fabien
  Procedia Engineering, Elsevier, 2010, 2 (1), pp.901-910. Fatigue life prediction of polymer matrix composites requires the investigation of the cyclic behavior. This paper deals with the experimental study conducted on a polyamide 66 reinforced with 35 wt% of short glass fibers (PA66 GF35), at room temperature. The material was tested dry-as-molded or at the equilibrium with an air containing 50% of relative humidity. The dynamic mechanical analysis leads us to focus on the material conditioned at RH=50%, which appears to exhibit the most complex mechanical effects, and is yet representative of the actual service life. An exhaustive experimental campaign in tensile mode has been carried out, including various strain or stress rates, complex mechanical histories and local thermo-mechanical recording. The material has thus been tested in static tension at stress rates ranging over four decades (from 2.5 to 2500 MPa/s), and also in cyclic tension with loading histories combining creep, stress relaxation or strain recovery steps at different strain/stress levels. Such an extended database allowed us to highlight several mechanical phenomena: at least two characteristic viscous times co-exist, and are independent of any irreversible mechanism. Residual strain appears above a stress threshold, and a kinematic hardening law is suggested to explain tension-relaxation-recovery tests. Eventually, hints of a non-linear viscous flow law and of a cyclic damage law are pointed out. (10.1016/j.proeng.2010.03.097)
  DOI : 10.1016/j.proeng.2010.03.097
• Approche variationnelle de l'endommagement : I. Les concepts fondamentaux
  
  • Marigo Jean-Jacques
  • Pham Kim
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2010, 338 (4), pp.191-198. This Note is devoted to the construction of local brittle damage laws. We first justify by the Drucker–Ilyushin postulate to set their formulation within the framework of Generalized Standard Materials. Accordingly, the strain work becomes a state function whose convexity properties are directly related to the hardening or softening properties of the material. Moreover, the evolution problem can be read as a variational problem which is reinforced so that it finally contains the concepts of stability and of energy conservation. (10.1016/j.crme.2010.03.009)
  DOI : 10.1016/j.crme.2010.03.009
• Approche variationnelle de l'endommagement : II. Les modèles à gradient
  
  • Pham Kim
  • Marigo Jean-Jacques
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2010, 338 (4), pp.199-206. This second part of the variational approach to damage is devoted to the construction of non-local gradient-enhanced models. That consists in extending to these regularized models the concepts introduced in the first part for local damage models. Specifically, once the gradient of damage has been inserted into the energy expression, the damage evolution problem is still based on the three physical principles of irreversibility, stability and energy balance. This new formulation is compared with that usually postulated and its merits are emphasized. (10.1016/j.crme.2010.03.012)
  DOI : 10.1016/j.crme.2010.03.012
• Elastic and nonlinear behaviour of argillaceous rocks under combined moisture and mechanical loads investigated by means of multiscale full full-field strain measurement techniques
  
  • Yang D.S.
  • Bornert Michel
  • Nguyen Minh D.
  • Chanchole S.
  • Gharbi H.
  • Valli P.
  , 2010.
• Déchets nucléaires : le stockage doit-il être réversible ?
  
  • Berest Pierre
  • Bérest P.
  , 2010, pp.82-83.
• Identification of Young's Modulus from Indentation Testing and Inverse Analysis
  
  • Prou Joris
  • Kishimoto Kikuo
  • Constantinescu Andrei
  Journal of Solid Mechanics and Materials Engineering, 2010, 4 (6), pp.781--795. In this study, a numerical method for the identification of the Young's modulus of linear elastic coated materials from continuous indentation test is first presented. The identification is based on an inverse analysis where the minimization of a cost functional is performed by a gradient descent algorithm. The main result is the computation of cost function gradient by using a direct differentiation technique, resulting in a time saving method compared to the widely used finite difference method. The validity and illustration of this approach is shown through several numerical examples. The second part of this article is dedicated to the identification of elasto-plastic thin films Young's modulus. A new method is proposed, where the inverse analysis relies only on finite element computations for elastic materials.
• Revisiting energy release rates in brittle fracture
  
  • Chambolle Antonin
  • Francfort Gilles A.
  • Marigo Jean-Jacques
  Journal of Nonlinear Science, Springer Verlag, 2010, 20 (4), pp.395-424. We revisit in a 2d setting the notion of energy release rate, which plays a pivotal role in brittle fracture. Through a blow-up method, we extend that notion to crack patterns which are merely closed sets connected to the crack tip. As an application, we demonstrate that, modulo a simple meta-stability principle, a moving crack cannot generically kink while growing continuously in time. This last result potentially renders obsolete in our opinion a longstanding debate in fracture mechanics on the correct criterion for kinking. (10.1007/s00332-010-9061-2)
  DOI : 10.1007/s00332-010-9061-2
• Evaluation of Stress-strain Curve Estimates in Dynamic Experiments
  
  • Mohr Dirk
  • Gary Gérard
  • Lundberg Bengt
  International Journal of Impact Engineering, Elsevier, 2010, 37, pp.161-169. Accurate measurements of the forces and velocities at the boundaries of a dynamically loaded specimen may be obtained using split Hopkinson pressure bars (SHPB) or other experimental devices. However, the determination of a representative stress-strain curve based on these measurements can be challenging. Due to transient effects, the stress and strain fields are not uniform within the specimen. Several formulas have been proposed in the past to estimate the stress-strain curve from dynamic experiments. Here, we make use of the theoretical solution for the waves in an elastic specimen to evaluate the accuracy of these estimates. It is found that it is important to avoid an artificial time shift in the processing of the experimental data. Moreover, it is concluded that the combination of the output force based stress estimate and the average strain provides the best of the commonly used stress-strain curve estimates in standard SHPB experiments. (10.1016/j.ijimpeng.2009.09.007)
  DOI : 10.1016/j.ijimpeng.2009.09.007
• Displacement correction for punching at a dynamically loaded bar end
  
  • Safa Kamal
  • Gary Gérard
  International Journal of Impact Engineering, Elsevier, 2010, 37, pp.371-384. The object of this work is to provide a 3-D displacement correction for local punching due to axial load at the end of a bar. For this purpose, an analytical calculation of the indentation at the end of an elastic isotropic bar subjected to a dynamic loading is carried out. It provides a first-order correction of the displacement obtained through the 1-D wave analysis commonly used in SHPB processing. This correction improves the results obtained for the dynamic behavior of the specimen, in particular at early instants of loading where its response is often purely elastic. Tabulated values are provided for easy use in SHPB testing. (10.1016/j.ijimpeng.2009.09.006)
  DOI : 10.1016/j.ijimpeng.2009.09.006
• Localisation de la déformation dans un milieu granulaire vue jusqu'à l'échelle du grain à l'aide de la tomographie à rayons X
  
  • Bésuelle Pierre
  • Hall S.
  • Viggiani Gioacchino Cinno
  • Lenoir Nicolas
  • Desrues J.
  • Pannier Y.
  • Bornert Michel
  , 2010.
• On micro-macro transition in non linear mechanics
  
  • Stolz Claude
  Materials, MDPI, 2010, 3 (1), pp.296-317. This paper is devoted to the description of the general relationships between microscopic and macroscopic mechanical quantities in non-linear mechanics. From a thermodynamical viewpoint, it is only necessary to know the two macroscopic potentials (macroscopic free energy and macroscopic potential of dissipation) to describe the state of the body and its quasistatic evolution. These global potentials are the averages of the local ones. We point out some particular cases of non-linearities, especially the case of damaged materials. (10.3390/ma3010296)
  DOI : 10.3390/ma3010296
• Investigation of the Microstructural Deformation Behavior of Extruded Magnesium Through the Coupling of EBSD and DIC-based Micro-strain Measurements
  
  • Héripré Eva
  • Laraiedh Aymen
  • Caldemaison Daniel
  • Mohr Dirk
  , 2010.
• Muscle contraction: a mechanical perspective
  
  • Marcucci Lorenzo
  • Truskinovsky Lev
  European Physical Journal E: Soft matter and biological physics, EDP Sciences: EPJ / Springer Nature, 2010, 32 (4), pp.411-418. In this paper we present a purely mechanical analog of the conventional chemo-mechanical modeling of muscle contraction. We abandon the description of kinetics of the power stroke in terms of jump processes and instead resolve the continuous stochastic evolution on an appropriate energy landscape. In general physical terms, we replace hard spin chemical variables by soft spin variables representing mechanical snap-springs. This allows us to treat the case of small and even disappearing barriers and, more importantly, to incorporate the mechanical representation of the power stroke into the theory of Brownian ratchets. The model provides the simplest non-chemical description for the main stages of the biochemical Lymn-Taylor cycle and may be used as a basis for the artificial micro-mechanical reproduction of the muscle contraction mechanism. (10.1140/epje/i2010-10641-0)
  DOI : 10.1140/epje/i2010-10641-0
• 12-year pressure monitoring in an idle salt cavern — The 1997-1998 Etrez abandonment test revisited.
  
  • Berest Pierre
  • Bérest P.
  , 2010, pp.233-244.
• Mechanics of the power stroke in Myosin II
  
  • Marcucci Lorenzo
  • Truskinovsky Lev
  Physical Review E : Statistical, Nonlinear, and Soft Matter Physics [2001-2015], American Physical Society, 2010, 81, pp.051915. Power stroke in skeletal muscles is a result of a conformational change in the globular portion of the molecular motor myosin II. In this paper we show that the fast tension recovery data reflecting the inner working of the power stroke mechanism can be quantitatively reproduced by a Langevin dynamics of a simple mechanical system with only two structural states. The proposed model is a generalization of the two state model of Huxley and Simmons. The main idea is to replace the rigid bistable device of Huxley and Simmons with an elastic bistable snap spring. In this setting the attached configuration of a cross bridge is represented not only by the discrete energy minima but also by a continuum of intermediate states where the fluctuation induced dynamics of the system takes place. We show that such soft-spin approach explains the load dependence of the power stroke amplitude and removes the well-known contradiction inside the conventional two state model regarding the time scale of the power stroke. (10.1103/PhysRevE.81.051915)
  DOI : 10.1103/PhysRevE.81.051915
• A fast approximate global search methodology for defect identification based on small-inclusion asymptotics of misfit functionals
  
  • Bonnet Marc
  , 2010.
• Multiscale Full-Field Strain Measurements for Micromechanical Investigations of the Hydromechanical Behaviour of Clayey Rocks
  
  • Bornert Michel
  • Valès Frédéric
  • Gharbi Houria
  • Nguyen Minh D.
  Strain, Wiley-Blackwell, 2010, 46 (1), pp.33–46. 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. (10.1111/j.1475-1305.2008.00590.x)
  DOI : 10.1111/j.1475-1305.2008.00590.x
• Very slow creep tests on salt samples
  
  • Bérest Pierre
  • Béraud Jean-François
  • Brouard Benoit
  • Blum Pierre-Antoine
  • Charpentier Jean-Pierre
  • Greef Vincent De
  • Gharbi Hakim
  • Valès Frédéric
  EPJ Web of Conferences, EDP Sciences, 2010, 6. Long-term creep tests have been performed on rock-salt and argillite samples under very small uniaxial loadings (σ = 0.02 to 0.1 MPa) . To minimize the effects of temperature variations, testing devices were set in a mine where temperature fluctuations are of the order of one-hundredth of a degree Celsius. The mechanical loading was provided by dead weights. The deformations were measured through special displacement sensors with a resolution of ∆ε = 10-8. Strain rates as small as έ = 7 × 10-13s-1 were measured. These tests allow rock-sample creep to be investigated at very small strain rates. The tests also prove that extrapolation of constitutive laws at very small rates is often incorrect. (10.1051/epjconf/20100622002)
  DOI : 10.1051/epjconf/20100622002
• Comparison of Fully Coupled Modeling and Experiments for Electromagnetic Forming Processes in Finitely Strained Solids
  
  • Thomas Jesse D.
  • Triantafyllidis Nicolas
  • Vivek A.
  • Daehn Glenn S.
  • Bradley John R.
  International Journal of Fracture, Springer Verlag, 2010, 163, pp.pp. 67-83. In fracture and fragmentation research the technique of electromagnetic forming, which uses electromagnetic (Lorentz) body forces to shape metallic parts, is finding significant use due to the high velocity, high strain rate loading it can impart without contact on workpieces. The same process is also becoming increasingly relevant formanufacturing processes in sheet metal forming, where this technique offers several advantages: speed, repeatability, non-contact loading, reduced springback and considerable ductility increase in several metals. Current modeling techniques for these coupled electromagnetic and thermomechanical processes are not based on coupled variational principles that can simultaneously account for electromagnetic and mechanical effects. Typically, separate solutions to the electromagnetic (Maxwell) and motion (Newton) equations are combined in staggered or lock-step methods, sequentially solving the mechanical and electromagnetic problems. To address this issue, Thomas and Triantafyllidis (J Mech Phys Solids 57:1391-1416, 2009) have recently introduced a fully coupled Lagrangian (reference configuration) variational principle, involving the magnetic field potential and the displacement field as independent variables. The corresponding Euler-Lagrange equations areMaxwell's and Newton's equations in the reference configuration under the eddy current approximation. This novel approach is used here to simulate free expansion experiments of AA6063-T6 aluminum tubes. A viscoplastic constitutive model, developed independently by the authors (Thomas et al. Acta Mater 55:2863-2873, 2007) for necking experiments in tubes of the same aluminum alloy, is used in the simulations. The measured electric currents and tube deformation--the latter obtained by Photon Doppler Velocimetry--show reasonably good agreement with the corresponding simulations, which are obtained using a variational integration numerical scheme that results in an efficient staggered solution algorithm.
• Hybrid Experimental-numerical Analysis of Basic Ductile Fracture Experiments for Sheet Metals
  
  • Mohr Dirk
  • Dunand M.
  International Journal of Solids and Structures, Elsevier, 2010, 47 (9), pp.1130-1143. A basic ductile fracture testing program is carried out on specimens extracted from TRIP780 steel sheets including tensile specimens with a central hole and circular notches. In addition, equi-biaxial punch tests are performed. The surface strain fields are measured using two- and three-dimensional digital image correlation. Due to the localization of plastic deformation during the testing of the tensile specimens, finite element simulations are performed of each test to obtain the stress and strain histories at the material point where fracture initiates. Error estimates are made based on the differences between the predicted and measured local strains. The results from the testing of tensile specimens with a central hole as well as from punch tests show that equivalent strains of more than 0.8 can be achieved at approximately constant stress triaxialities to fracture of about 0.3 and 0.66, respectively. The error analysis demonstrates that both the equivalent plastic strain and the stress triaxiality are very sensitive to uncertainties in the experimental measurements and the numerical model assumptions. The results from computations with very fine solid element meshes agree well with the experiments when the strain hardening is identified from experiments up to very large strains (10.1016/j.ijsolstr.2009.12.011)
  DOI : 10.1016/j.ijsolstr.2009.12.011
• Micromechanical Investigation of the Hydromechanical Behaviors of Carbonates Contribution of In-Situ Strain Field Measurement By Means of SEM And Optic Digital Image Correlation
  
  • Dautriat Jérémie
  • Bornert Michel
  • Gland Nicolas
  • Dimanov Alexandre
  • Raphanel Jean
  • Vizika Olga
  Petrophysics – The SPWLA Journal of Formation Evaluation and Reservoir Description, The Society of Petrophysicists and Well Log Analysts (SPWLA), 2010, 51 (6), pp.388-398. In a previous study (Dautriat et al., 2008), we have studied the macroscopic hydro-mechanical behavior of a moderately heterogeneous carbonate reservoir analogue, undergoing triaxial testing along several proportional stress paths, ranging from hydrostatic compression -to-axial compression. Evolutions of permeabilities and compressibilities during loading have been measured and correlated and the yield envelope has been determined. Structural heterogeneities have been shown to strongly affect the initiation of brittle and plastic damages. There is a trend to interpret the macroscopic response in term of micro-mechanisms without actual observation and identification. While post-mortem characterization techniques (HPMI, SEM and XR CT / μ-CT images) inform qualitatively on the damage mechanisms activated at the grain and aggregate scales, a quantitative and continuous micromechanical investigation is needed to follow the history of the deformation and the localization during compression. We have therefore performed in-situ observations during loading at different scales. First, small samples have been deformed by simple compression inside a SEM, in order to identify the physical deformation and damage micro-mechanisms responsible for the evolutions of the transport properties. Then, larger samples have been subjected to axial compression in a hydraulic press and have been observed by optical methods, in order to better understand the complex interactions governing the macroscopic behavior. Observations of the micro-mechanisms during mechanical tests are difficult for geomaterials because the levels of deformation are low (below the percent), but feasible with some care and appropriate recording devices; different regions of small parallelipipedic samples have been imaged using different magnifications to focus either on grain or contact, or to visualize the aggregates. Direct optical observations on bigger cylindrical samples, mechanically loaded on conventional UCS testing machines, have also been performed at two different scales by means of high resolution digital cameras. On one side, the full sample is imaged (≈20μm resolution) in order to characterize the overall response. On the opposite spot side, a centimetric area has been considered (≈3μm resolution), at which scale the composite nature of the rock made of microporous and dense calcite grains is revealed. Those two scales imaging experiments have been combined with efficient Digital Image Correlation (DIC) post-treatments, able to detect very small displacements and evolutions of the microstructures (strain accuracy better than 10-3). The comparisons of SEM images taken stepwise, reveal deformations hardly detectable by conventional observations, such as: opening or closure of pre-existing microcracks, nucleation of new microcracks and relative movements at grain interfaces. Different strain accommodation regimes are also observed in dense and microporous grains, respectively brittle and diffuse. The movies at sample scale show that the heterogeneity of strain is correlated to the local distribution of the aggregates, which confirms the post-mortem observations.
• X-ray tomographic characterization of the macroscopic porosity of chemical vapor infiltration SIC/SIC composites: effects on the elastic behavior
  
  • Gelebart Lionel
  • Chateau Camille
  • Bornert Michel
  • Crépin Jérôme
  • Boller Elodie
  International Journal of Applied Ceramic Technology, Wiley, 2010, 7, pp.348-360. This paper focuses on the characterization of the macroporosity, the porosity among the tows, observed in chemical vapor infiltration composites and on its effect on the thermo-mechanical behavior. The experimental characterization of macroporosity is performed using an X-ray tomography technique. Numerical 3D images are used to describe the distribution of macroporosity with respect to the position of the plies. It is clearly established that the stacking of the plies has a significant effect on the porosity distribution. As a consequence for the micromechanical modelling, a unique element that contains only one ply is not representative of the porosity distribution and is not sufficient to evaluate the "effective" mechanical properties; several volume elements (VE), called "statistical volume elements (SVE)," with at least two plies per VE have to be used in order to account for the variability of the stacking of the plies. Finally, such SVE are directly extracted from the tomographic image and the "effective" elastic behavior is evaluated from the average of the "apparent" behavior evaluated on each SVE. In spite of their quite important size, the "apparent" behaviors evaluated for each SVE exhibit important fluctuations. (10.1111/j.1744-7402.2009.02470.x)
  DOI : 10.1111/j.1744-7402.2009.02470.x
• Weak variations of Lipschitz graphs and stability of phase boundaries
  
  • Grabovsky Yury
  • Kucher Vladislav
  • Truskinovsky Lev
  Cont. Mech. Therm., 2010, 23, pp.87-123. In the case of Lipschitz extremals of vectorial variational problems, an important class of strong variations originates from smooth deformations of the corresponding non-smooth graphs. These seemingly singular variations, which can be viewed as combinations of weak inner and outer variations, produce directions of differentiability of the functional and lead to singularity-centered necessary conditions on strong local minima: an equality, arising from stationarity, and an inequality, implying configurational stability of the singularity set. To illustrate the underlying coupling between inner and outer variations, we study in detail the case of smooth surfaces of gradient discontinuity representing, for instance, martensitic phase boundaries in non-linear elasticity. (10.1007/s00161-010-0171-8)
  DOI : 10.1007/s00161-010-0171-8
• On the stick-slip waves under unilateral contact and Coulomb friction
  
  • Bui Hui Duong
  • Oueslati Abdelbacet
  Annals of Solid and Structural Mechanics, Springer Berlin Heidelberg, 2010, 1 (3-4), pp.159-172. In this paper, the construction of analytic solution of stick-slip waves propagating along the interface between an elastic half-space and a moving rigid one is investigated. The contact between the solids is governed by unilateral constraints and Coulomb friction law and the deformable body is loaded by remote uniform stresses t*yy<0, t*xy>0. The method of solution is based on the continuation of Radok's complex potentials within the framework of steady state elastodynamical problems. The governing equation combined with the boundary conditions are reduced to a Riemann-Hilbert problem with discontinuous coefficient. This approach for the stick-slip study is novel and differs from those in the literature, namely the series method and the Weertmann's dislocation formulation. We present the closed form solution of the Riemann-Hilbert problem and show that the principal unknowns are of number two: the wave celerity and the ratio of the slip length by the stick one. The considered loading introduces an additional velocity V* related to the elongation e*xx due to the normal stress t*yy. We show that if V* vanishes there is no solution. When V* is taken into account, it is possible to construct weakly singular solutions satisfying all stick-slip conditions except over a narrow zone at transition points: The shear stress is singular over a small zone and the normal stress exhibits a positive singularity over a very small zone in the slip region which implies a separation near the singular transition. (10.1007/s12356-010-0012-2)
  DOI : 10.1007/s12356-010-0012-2