Joseph Pastor

New bounds for the height limit of a vertical slope

Using the finite element method, the static and kinematic methods of limit analysis provide tools to solve many stability problems in mechanics of continuous media. The classic problem of the height limit of a Tresca or Mises vertical slope subjected to the action of gravity stems naturally from this theory in plane strain. Although the exact solution to this problem remains unknown, the present work has produced precise bounds using the static and kinematic approaches conjointly: the height limit is now between 3·760 and 3·786 C/ γ, γ being the weight per unit volume and C the soil cohesion. These tests also show that both methods, used on current workstations with industrial optimization codes such as XPRESS or OSL, are capable of solving any plane problem of limit loads in geotechnics or in structural calculus. Copyright

Dynamic analysis of piezoelectric fiber composite in an active beam using homogenization and finite element methods

The purpose of this work is to point out the improvement, which could be achieved through use of piezoelectric fiber composite elements in place of piezoelectric patch elements, in structural vibration systems. Therefore, we review the homogenization method for prediction of the overall properties of piezoelectric fiber composite and we propose the Periodic Medium Homogenization model. The results indicated a good correlation between our proposed model and the MoriTanaka approach. Then we considered the cases of incorporated bulk piezoelectric and piezoelectric fiber composite in two epoxy cantilevered beams loaded by static and dynamic forces. The numerical results show that, with the piezoelectric fiber composite, one can adapt the electromechanical coupling coefficient for a specific task by simply changing the fiber content. The results also suggest that increasing fiber content above 35% for the analyzed beam, will effectively result in reduced performance of the active structure.

Résistance de plaques multiperforées: comparaison calcul—expérience

This study concerns the strength prediction of heterogeneous ductile materials. On the one hand, we use the limit analysis theory with the kinematic and static methods and, on the other hand, the h...

Limit Analysis of a Soil Reinforced by Micropile Group: A Decomposition Approach

The behavior of soils reinforced by micropile networks is still not fully understood due to the lack of accurate modelling capabilities. Particularly, the complex geometry of large soil-micropile systems makes accurate calculation of the bearing capacity of the reinforced soil a computational challenge. This complexity requires highly detailed and finely discretized models to achieve reasonable accuracy using direct numerical methods. Such models lead to large scale numerical optimization problems that are hardly tractable using a personal computer.

Limit Analysis and Conic Programming for Gurson-Type Spheroid Problems

In his famous 1977-paper, Gurson used the kinematic approach of Limit Analysis (LA) about the hollow sphere model with a von Mises solid matrix. The computation led to a macroscopic yield function of the “Porous von Mises”-type materials. Several extensions have been further proposed in the literature, such as those accounting for void shape effects by Gologanu et al. (J. Eng. Mater. Technol. 116:290–297, 1994; Continuum Micromechanics, Springer, Berlin, 1997), among others. To obtain pertinent lower and upper bounds to the exact solutions in terms of LA, we have revisited our existing kinematic and static 3D-FEM codes for spherical cavities to take into account the model with confocal spheroid cavity and boundary. In both cases, the optimized formulations have allowed to obtain an excellent efficiency of the resulting codes. A first comparison with the Gurson criterion does not only show an improvement of the previous results but points out that the real solution to the hollow sphere model problem depends on the third invariant of the stress tensor. A second series of tests is presented for oblate cavities, in order to analyze the above-mentioned works in terms of bound and efficiency.

Gurson Model and Conic Programming for Pressure-Sensitive Materials

In this talk we analyze the yield criterion of a porous material containing cylindrical and spherical cavities on the basis of the Gurson mechanical model where the matrix is pressuresensitive. Both limit analysis (LA) methods are used to determine as closely as possible the corresponding macroscopic criterion, by using conic programming formulations. For a Drucker-Prager matrix the case of cylindrical cavities is investigated in generalized plane strain, and the results compared with those of previous works for von Mises matrices. Then we study the case of a Coulomb matrix for spherical cavities under axisymmetrical conditions. Due to the constraining character of the axisymmetry, specific analytical solutions are superimposed on the numerical fields. Among other results, a comparison with an ad hoc translated “modified Cam-Clay criterion” points out that it might be considered as a satisfactory approximation, except that it does not account for the corner of our criterion on the isotropic compressive axis, unlike the original Cam-Clay criterion.

Limit Analysis and Macroscopic Strength of Porous Materials with Coulomb Matrix

The paper is devoted to the numerical Limit Analysis of a hollow spheroidal model with a Coulomb solid matrix. In a first part the hollow spheroid model is presented, together with its axisymmetric FEM discretization and its mechanical position. Then, after an adaptation of a previous static code, an original mixed (but fully kinematic) approach dedicated to the axisymmetric problem was elaborated with a specific quadratic velocity field associated to the triangular finite element. Despite the less good conditioning inherent to the axisymmetric modelization, the final conic mixed code appears very efficient, allowing to take into account numerical meshes highly refined. After a first validation in the case of spherical cavities and isotropic loadings, for which the exact solution is known, numerical bounds of the macroscopic strength are provided for both cases of spherical and spheroidal voids. Effects of the friction angle as well as that of the void aspect ratio are fully illustrated.

A Quasi-periodic Approximation Based Model Reduction for Limit Analysis of Micropile Groups

The behavior of soils reinforced by micropile networks is still not fully understood due to the lack of accurate modelling capabilities. Particularly, the complex geometry of large soil-micropile systems makes accurate calculation of the bearing capacity of the reinforced soil a computational challenge. This complexity requires highly detailed and finely discretized models to achieve reasonable accuracy using direct numerical methods. Such models lead to large scale numerical optimization problems that are hardly tractable using a personal computer.

Finite Element Limit Analysis and Porous Mises-Schleicher Material

By using the kinematic approach of limit analysis (LA) for a hollow sphere whose solid matrix obeys the von Mises criterion, Gurson (J. Eng. Mater. Technol. 99:2–15, 1977) derived a macroscopic criterion of ductile porous medium. The relevance of such criterion has been widely confirmed in several studies and in particular in Trillat and Pastor (Eur. J. Mech. A, Solids 24:800–819, 2005) through numerical lower and upper bound formulations of LA. In the present paper, these formulations are extended to the case of a pressure dependent matrix obeying the parabolic Mises-Schleicher criterion. This extension has been made possible by the use of a specific component of the conic optimization. We first provide the basics of LA for this class of materials and of the required conic optimization; then, the LA hollow sphere model and the resulting static and mixed kinematic codes are briefly presented. The obtained numerical bounds prove to be very accurate when compared to available exact solutions in the particular case of isotropic loadings. A second series of tests is devoted to assess the upper bound and approximate criterion established by Lee and Oung (J. Appl. Mech. 67:288–297, 2000), and also the criterion proposed by Durban et al. (Mech. Res. Commun. 37:636–641, 2010). As a matter of conclusion, these criteria can be considered as admissible only for a slight tension/compression asymmetry ratio for the matrix; in other words, our results show that the determination of the macroscopic criterion of the “porous Mises-Schleicher” material still remains an open problem.