CNRS Navier Laboratory

Paris, France

CNRS Navier Laboratory

Paris, France
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Caroli C.,University Pierre and Marie Curie | Lemaitre A.,CNRS Navier Laboratory
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2017

We examine how the distribution of contour lengths and the high-stretch stiffening of individual chain segments affect the macroscopic shear modulus of flexible polymer gels, using a two-dimensional numerical model in which polymer segments form a triangular network and disorder is introduced by varying their contour lengths. We show that, in the relevant parameter range: (i) the nonaffine contribution to the shear modulus is negligible, i.e., the Born approximation is satisfactory, and (ii) the shear modulus is dominated by the contribution originating from equilibrium chain tensions. Moreover, mechanical equilibration at the nodes induces specific correlations between the end-to-end distances and contour lengths of chain segments, which must be properly accounted for to construct reasonable estimates of chain pressure and shear modulus. © 2017 American Physical Society.

Corfdir A.,CNRS Navier Laboratory | Bonnet G.,University Paris Est Creteil
Engineering Analysis with Boundary Elements | Year: 2017

It is well known that the 2D Laplace Dirichlet boundary value problem with a specific contour has a degenerate scale for which the boundary integral equation (BIE) has several solutions. We study here the case of the Robin condition (i.e. convection condition for thermal conduction problems), and show that this problem has also one degenerate scale. The cases of the interior problem and of the exterior problem are quite different. For the Robin interior problem, the degenerate scale is the same as for the Dirichlet problem. For the Robin exterior problem, the degenerate scale is always larger than for the Dirichlet problem and has some asymptotic properties. The cases of several simple boundaries like ellipse, equilateral triangle, square and rectangle are numerically investigated and the results are compared with the analytically predicted asymptotic behavior. An important result is that avoiding a contour leading to a degenerate Robin problem cannot be achieved as simply as in the case of Dirichlet boundary condition by introducing a large reference scale into the Green's function. © 2017 Elsevier Ltd

Roussel N.,University Paris Est Creteil | Ovarlez G.,CNRS Navier Laboratory | Garrault S.,French National Center for Scientific Research | Brumaud C.,University Paris Est Creteil
Cement and Concrete Research | Year: 2012

In this paper, we show that the thixotropic behavior of standard fresh cement pastes may find two origins. We first clarify the ambiguity in literature concerning the critical strain of fresh cement pastes, thanks to a detailed analysis of their macroscopic behavior. We show that the largest critical strain can be associated to the network of colloidal interactions between cement particles whereas the smallest critical strain can be associated to the early hydrates, which form preferentially at the contact points between cement grains. From the study of the structuration kinetics, we show that there exists a short term thixotropy due to colloidal flocculation along with a long term thixotropy (of practical interest) due to the ongoing hydrates nucleation. From dimensional considerations, we moreover suggest why the apparent yield stress of the mixture left at rest can be approximated as a linear function of time. © 2011 Elsevier Ltd. All rights reserved.

Shen W.Q.,Lille Laboratory of Mechanics | Shao J.F.,Lille Laboratory of Mechanics | Dormieux L.,CNRS Navier Laboratory | Kondo D.,University Pierre and Marie Curie
Computational Materials Science | Year: 2012

In the framework of limit analysis theory, we derive closed-form expressions of approximate criteria for ductile porous materials whose plastically compressible matrix obeys to an elliptic criterion. The general methodology is based on limit analysis of a hollow sphere subjected to a uniform strain rate boundary conditions. We first consider a porous medium with a Green type matrix and establish the corresponding macroscopic yield function. Then, the obtained results are used in order to investigate double porous materials whose solid phase at the microscale (the smallest scale) obeys a von Mises criterion. The results are assessed by comparing them with numerical data, and with recently published results. © 2012 Elsevier B.V. All rights reserved.

He Z.,Lille Laboratory of Mechanics | He Z.,CNRS Navier Laboratory | Dormieux L.,CNRS Navier Laboratory | Kondo D.,University Pierre and Marie Curie
International Journal of Plasticity | Year: 2013

In the present study, we investigate the strength properties of ductile porous materials reinforced by rigid particles. The microporous medium is constituted of a Drucker-Prager solid phase containing spherical voids; its behavior is described by means of an elliptic criterion (issued from a modified secant moduli approach) whose corresponding support function is determined. The latter is then implemented in a limit analysis approach in which a careful attention is paid for the contribution of the inclusion matrix-interface. This delivers parametric equations of the effective strength properties of the porous material reinforced by rigid particles. The predictions are compared to available results obtained by means of variational homogenization methods successively applied for micro-to-meso and then for meso-to-macro scales transitions. Moreover, additional static solutions are derived and compared to the kinematics limit analysis ones in order to prove the accuracy of the strength predictions under isotropic loading. Thereafter, the theoretical predictions (by the two methods) under shear loading are assessed by comparison with experimental data. The influences of mineralogical compositions and porosity are also discussed. Finally, we derive an approximate closed-form expression of the macroscopic strength which proves to be very accurate. Then, we examine in Appendix the particular case of a von Mises solid phase of the porous matrix for which our results are compared to the available estimates. © 2013 Elsevier Ltd. All rights reserved.

Roussel N.,CNRS Navier Laboratory
Kuei Suan Jen Hsueh Pao/Journal of the Chinese Ceramic Society | Year: 2015

By going through rational and micro-mechanical arguments on particle/particle and particle/fluid interactions, we first provide here a conceptual diagram of predominant interactions within flowing cement pastes under simple shear in steady state as a function of shear rate and solid volume fraction. Within this frame, we then focus on the last four years advances in the understanding of the main changes in the underlying physics occurring when the most common polymers used in the cement construction industry are added to a cement suspension. We finally discuss the upscaling between cement paste rheology and concrete fresh properties. © 2015, Chinese Ceramic Society. All right reserved.

Bleyer J.,CNRS Navier Laboratory | De Buhan P.,CNRS Navier Laboratory
European Journal of Mechanics, A/Solids | Year: 2016

This work investigates the formulation of lower and upper bound finite elements for the yield design (or limit analysis) of shell structures. The shell geometry is first discretized into triangular planar facets so that previously developed lower bound equilibrium and upper bound kinematic plate finite elements can be coupled to membrane elements. The other main novelty of this paper relies on the formulation of generalized strength criteria for shells in membrane-bending interaction via an implicit upscaling procedure. This formulation provides a natural strategy for constructing lower and upper bound approximations of the exact shell strength criterion and are particularly well suited for a numerical implementation using second-order cone programming tools. By combining these approximate strength criteria to the previously mentioned finite elements, rigorous lower and upper bound ultimate load estimates for shell structures can be computed very efficiently. Different numerical examples illustrate the accuracy as well as the generality and versatility of the proposed approach. © 2016 Elsevier Masson SAS. All rights reserved.

Pouya A.,CNRS Navier Laboratory
Advances in Water Resources | Year: 2012

Governing equations for flow in three-dimensional heterogeneous and anisotropic porous media containing fractures or cracks with infinite transverse permeability are described. Fractures are modeled as zero thickness curve surfaces with the possibility of multiple intersections. It is assumed that flow obeys to an anisotropic Darcy's law in the porous matrix and to a Poiseuille type law in fractures. The mass exchange relations at fractures intersections are carefully investigated as to establish a complete mathematical formulation for the flow problem in a fractured porous body. A general potential solution, based on singular integral equations, is established for steady state flow in an infinite fractured body with uniform and isotropic matrix permeability. The main unknown variable in the equations is the pressure field on the crack surfaces, reducing thus from three to two the dimension of the numerical problem. A general transformation lemma is then given that allows extending the solution to matrices with anisotropic permeability. The results lead to a simple and efficient numerical method for modeling flow in three-dimensional fractured porous bodies. © 2011 Elsevier Ltd.

Coussot P.,CNRS Navier Laboratory | Ovarlez G.,CNRS Navier Laboratory
European Physical Journal E | Year: 2010

Jammed systems all have a yield stress. Among these materials some have been shown to shear-band but it is as yet unclear why some materials develop shear-band and some others do not. In order to rationalize existing data concerning the flow characteristics of jammed systems and in particular understand the physical origin of such a difference, we propose a simple approach for describing the steady flow behaviour of yield stress fluids, which retains only basic physical ingredients. Within this framework we show that in the liquid regime the behaviour of jammed systems turns from that of a simple yield stress fluid (exhibiting homogeneous flows) to a shear-banding material when the ratio of a characteristic relaxation time of the system to a restructuring time becomes smaller than 1, thus suggesting a possible physical origin of these trends. © 2010 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.

Shen W.Q.,Lille Laboratory of Mechanics | Kondo D.,CNRS Jean Le Rond d'Alembert Institute | Dormieux L.,CNRS Navier Laboratory | Shao J.F.,Lille Laboratory of Mechanics
Mechanics of Materials | Year: 2013

The present paper is devoted to a micro-macro model of plastic deformation in Callovo Oxfordian argillite. This material is composed of a porous clay matrix which is reinforced by linear elastic mineral grains. The clay matrix is itself constituted of a solid phase containing a distribution of pores. The solid phase of clay matrix is described by a pressure sensitive plastic model. By means of a two step homogenization procedure, a macroscopic plastic criterion is formulated to estimate the nonlinear behavior of the clayey rock taking into account influences of pores and of mineral inclusions. Both associated and non-associated macroscopic plastic flow rules depending if the solid phase is associated or not. The mechanical behavior of the clayey rock in conventional triaxial compression tests is studied with the proposed micro-macro model. It is shown that the non-associated plastic flow rule of the solid phase is an essential mechanism for the description of the macroscopic plastic deformation of the clayey rock. Comparisons between the predicted results and experimental data show that the proposed model is able to capture the main features of the mechanical behavior of the studied material.© 2012 Elsevier Ltd. All rights reserved.

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