Irini Djeran-Maigre

Velocities, dispersion, and energy of SH-waves in anisotropic laminated plates

A mathematical model is worked out for analyzing propagation ability and the specific energy of horizontally polarized shear surface waves (SH-waves) in multilayered plates. All the layers are assumed to have monoclinic symmetry. Different types of boundary conditions imposed on the outer surfaces of plates are considered. Analytic solutions for one- and two-layered plates are presented.

Modélisation du comportement mécanique des argilites de l'Est

ABSTRACT The aim of this work is to propose a poroplastic damage model, in according to experimental results, for claystone (Aublivé-Conil, 2003). Firstly, an anisotropic elastoplastic damage model is formulated to describe the material degradations. Finally, this model is rewritten in order to reproduce the damage influence on the hydromechanical behaviour of the material. With some micromechanical analysis results the expression of the Biot coefficient tensor in function of the damage variable is obtained.

A PERFECTLY MATCHED LAYER FOR SEISMIC WAVE PROPAGATION IN UNBOUNDED DOMAIN BY USING HETEROGENEOUS MULTI-TIME STEP SUBDOMAIN METHODS.

Abstract. In the framework of the Finite Element Method, Perfectly Matched Layer (or PML) is recognized as a very effective tool for reproducing unbounded domains (Basu et al. [13]). Nonetheless, the computation time required by the PML may be large, especially when an explicit time integration scheme is adopted for dealing with the wave propagation problem both in the domain of interest and in the PML medium (Basu et al. [13]). The paper proposed to investigate subdomain strategies enabling to choose the appropriate time integration scheme in the PML with its own time step, independently on the choice of the explicit time scheme in the domain of interest associated with a fine time step satisfying the stability criterion (CFL condition). The investigated subdomain strategy, proposed by Gravouil and Combescure [14], is based on the Schur dual approach, characterized by the introduction of Lagrange multipliers at the interface between subdomains for ensuring the velocity continuity.

Soliton-Like Lamb Waves in Layered Media

Solitons, or by the original terminology waves of translation, were for the first time observed and described by Scott Russel (1845) as a special kind of the hydrodynamic waves that can arise and propagate in narrow channels. Solitons are: (i) solitary waves, resembling propagation of the wave front of shock waves; (ii) these waves can propagate without considerable attenuation, or (iii) change of form; or (iv) diminution of their speed; see, Craik (2004). It was shown later on, that motion of these waves can be described by a non-linear KdV differential equation; see the work by the originators of the KdV-equation Korteweg and de Vries (1885) and the subsequent works by Lax (1968), Miles (1981), and Zwillinger (1997), where some of the analytical solutions are presented and the main properties of the KdV equation are analyzed. Herein, we analyze the long-wave limits of Lamb waves propagating in multilayered elastic anisotropic plates at vanishing frequency 0   , or in terms of the wave number r , at 0 r  . These vanishing frequency Lamb waves satisfy conditions (i) – (iv), and thus, resemble the solitons. But, in contrast to the genuine solitons in hydrodynamics or their nonlinear analogues propagating in elastic solids; see, Eckl et al. (2004), Kawahara (1972), Kliakhandler, Porubov, and Verlande (2000), Planat and Hoummady (1989), Porubov et al. (1998), Samsonov (2001), our soliton-like waves are described by linear vectorial differential equations, known as the Christoffel equations for Lamb waves. Studies of Lamb waves, as solutions of linear equations of motion for the infinite plates, and the corresponding soliton-like linear waves traveling with the finite phase speed at vanishing frequency have quite a long history. Presumably, the first asymptotic analysis of the waves propagating at vanishing frequency in an isotropic plate with the traction-free outer planes was performed by Gogoladze (1947). He obtained an analytical expression for the phase speed of such a wave by asymptotic analysis of the approximate equation of motion related to the theory of plates based on the Bernoulli – Euler hypotheses. Later on, the similar approach and a more elaborate one allowing to consider plates with different boundary conditions at outer planes, but still based on the approximated theories of plates, were exploited by Mindlin (1951a, b, 1958, 1960), Mindlin and Medick (1959), Mindlin and Onoe (1957), Onoe (1955), and Tolstoy and Usdin (1953). The latter authors reported highly intricate behavior of the disperse curves in the vicinity of the zero frequency. See also a more recent work by Pagneux and Maurel (2001), where the dispersion relations in the complex

An homogenization iterative process for nonlinear materials applied to compacted clays

In previous works an homogenization iterative approach has been successfully proposed to predict the linear behavior of reinforced and porous materials. This homogenization process consists to construct the Representative Elementary Volume of the heterogeneous media, by adding gradually to the matrix, low heterogeneity proportions until reaching the final rate of heterogeneity of the material following a process closed to the differential scheme method [1]. At any intermediate step of this process, an homogenization is carried out by any classical explicit method and the obtained effective behavior becomes the matrix of the following step. The equivalent homogeneous behavior is reached after convergence of the succession of intermediate homogeneous media. A significant result shows that the application of this iterative process to different homogenization approaches like dilute approximation, Hashin’s bound, self consistent method, and even the morphological representative pattern leads to the same behavior even for significant rates of heterogeneities or porosities [2].