Diffraction of transverse horizontal waves in Fibonacci piezoelectric superlattices

The transfer matrix and global matrix techniques are used in the analysis of diffraction of transverse horizontal waves in piezoelectric superlattices. The system is composed of a set of different piezoelectric layers with quasiperiodic structure according to the Fibonacci sequence. The diffraction spectrum of different configurations of piezoelectric Fibonacci structures is studied. Numerical results for the diffraction spectrum for the piezoelectric Fibonacci superlattice are obtained and a comparison between the results of the transfer and global matrix methods is given, exhibiting the advantage of the latter.     

Elasticity and electro-magneto-elasticity of general-relativistic systems

This essay aims at demonstrating the interest for a genuine continuum mechanics and, more restrictively, elasticity of general-relativistic systems in cases where the Einsteinian gravitational picture cannot be deleted, e.g., in elastic gravitational-wave detectors and in the study of elastic oscillations of solid stars. The same foundations, constitutive theory, and methodology (superimposition of perturbations on finite initial states) apply to both cases, which also demand a generalization to comprehend electrodynamical-mechanical couplings, electroelasticity in the first case (use of piezoelectricity), and magnetoelasticity in the second case (presence of extremely intense magnetic fields).     

On shock waves and phase-transition fronts in continua

A R I - The canonical formalism that considers simultaneously the second law of thermodynamics and the balance of canonical momentum is used to incorporate the case of shock waves among those...     

Variational principles for nonlinear piezoelectric materials

Summary In the present paper, we consider the behavior of nonlinear piezoelectric materials by generalization for this case of the Hashin-Shtrikman variational principles. The new general formulation used here differs from others, because, it gives the possibility to evaluate the upper and lower Hashin-Shtrikman bounds for specific physical nonlinearities of piezoelectric materials. Geometrical nonlinearities are not considered.This work was sponsored by PAPIIT, DGAPA-UNAM IN103301. PNCB IBMFQ 09-2004 and, completed while one of the authors (RRR) was visiting the Laboratoire de Modélisation en Mécanique from Université Pierre et Marie Curie, Paris, while another one (G.A.M) benefited from the Max-Plank Award for International Cooperation (2002–2005).     

Electric and elastic multipole defects in finite piezoelectric media

In this paper, a piezoelectric analogy theorem is proposed, in which a piezoelectric body is represented as being composed of two fictitious bodies, an elastic body and a rigid dielectric body. An electric and elastic multipole approach for the treatment of various defects (dislocation, inhomogeneity, …) in finite piezoelectric media is then developed. It is shown that the electric and elastic coupling effects, the boundary effects, and the defects may be considered uniformly as sources of permanent and induced electric and elastic multipoles.     

A variational approach to a micro-structured theory of solid-fluid mixtures

Summary In this paper, we present a micro-structured model for describing global deformations of heterogeneous mixtures. In particular, for a saturated solid-fluid mixture, we regard the solid volume fraction as a microstructural parameter so as to enlarge the space of admissible deformations with respect to the classical theory of mixtures. According to the variational approach, the governing equations are obtained as the stationarity of a suitable action functional. The micro-structured model is then forced to establish a second-gradient mixture theory, by introducing among the considered state parameters a suitable internal constraint. Finally, we determine under which (integrability) conditions the additional balance laws, typically employed to close the theory of porous media endowed with the volume fraction, can fit the variational framework. The authors wish to thank Prof. Francesco dell'Isola from University of Rome La Sapienza for his constructive criticism about the variational approach to continuum mechanics and the interpretation of the volume-fraction balance law.     

A note on line forces in gradient elasticity

The theory of gradient elasticity is applied to line forces. Line forces acting on a point within the body and a concentrated normal force (Flamant problem) which acts on a half plane are studied. Closed analytical solutions which have a simple form are obtained for displacement fields of these forces. The gradient elasticity solutions are free from undesirable displacement singularities predicted by classical elasticity.     

A constitutive model for material growth and its application to three-dimensional finite element analysis

This paper describes a material model, in which the materials under consideration grow up in a particular direction while re-organizing themselves to the surroundings. The structural reorganization is modeled as the rearrangement of anisotropy. Two models are proposed; one is that the anisotropic vector is embedded just as in fiber-reinforced materials, and the other is that the vector behaves like a float. In order to apply the present model to boundary-value problems, a three-dimensional finite element formulation is obtained with reference to the total-Lagrangian approach. Here we evaluate the performance of the model in terms of anisotropic growth; (a) adaptation behavior of a quasi-isotropy in the initial state, and (b) monotonic growth in helical direction.     

Thermoelastic wave propagation in inhomogeneous media

Summary A novel approach to the modeling of thermoelastic wave propagation is presented, based on the thermodynamics of discrete systems. The first novelty includes the representation of integral balance laws for thermoelasticity in terms of contact quantities that describe the nonequilibrium state of elements. The next new aspect is a modification of the recently proposed wave-propagation algorithm, which is used as a tool for determining the contact quantities in a finite-volume scheme for the numerical simulation of two-dimensional thermoelastic wave propagation in inhomogeneous media. Such a modification is needed to provide the satisfaction of the thermodynamic consistency conditions between adjacent discrete elements. Results of computations for certain test problems show the efficiency and physical consistency of the algorithm. Received 11 November 1999; accepted for publication 2 May 2000