Sezione F7 Meccanica del continuo

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MATERIAL FORCES INHOMOGENEOUS FERROELECTRIC CRYSTALS G. A. Maugin Loboratoire de Modélization en Mécanique Université Pierre et Marie Curie Paris, France L. Restuccia University of Messina Department of Mathematics Messina, Italy Abstract Within the framework of the theory of inhomogeneities ([1]), a systematic construction of the canonical balance laws of so-called pseudomomentum ([2]) and energy are formulated in the case of thermoelastic ferroelectrics ([3], [4]). This exploits the notion of material forces on the material manifold. In order to describe the microstructure of those media the local electric polarization density per unit mass is considered as an additional degree of freedom which possesses its own dynamics and inertia. Together with the polarization gradients (describing nonlocal interactions responsible for electric ordering phenomenologically) it is introduced in the free-energy density. The canonical form of the energy and pseudomomentum balance plays a crucial role in applications related to fracture (computation of the so-called energy-release rate and in phase-transition fronts (energy dissipated at the front). References [1] Maugin G.A. (1993), Material inhomogeneities in elasticity, Chapman and Hall, London. [2] Maugin G.A., Trimarco C. (1992), Pseudomomentum and material forces in nonlinear elasticity: Variational formulations and application to brittle fracture, Acta Mechanica, 94 1–28. [3] Maugin G.A., Pouget J. (1980), Electroacoustic equations for one-domain ferroelectric bodies, J. Acoust. Soc. Am. 68 (2), 575–587. [4] Maugin G.A., (1988), Continuum Mechanics and Electromagnetic Solids, North-Holland, Amsterdam. [5] Maugin G.A., (1997), Thermomechanics of inhomogeneous-heterogeneous systems: application to the irreversible progress of two- and three-dimensional defects. ARI 50, 41–56. [6] Descalu C.,Maugin G.A., (1994), Energy-release rates and path-independent integrals in electroelastic crack propagation. Int. J. Engng. Sci. 32, 755–765. [7] Maugin G.A., Trimarco C., (1997), Driving force on phase transition fronts in thermoelastic crystals. Mathematics and Mechanics of Solids, 2, 199–214. 1
XVII Congresso U.M.I. Milano, 8-13 settembre 2003 Analytical results for scattering problems in wave propagation Edoardo Scarpetta Dipartimento di Ingegneria dell’Informazione e Matematica Applicata - Università di Salerno In the context of wave propagation through damaged (elastic) solids, an analytical approach to study the normal penetration of a scalar plane wave into a periodic array of defects with arbitrary shape is developed. Starting from an integral representation of the wave field and the scattering parameters already known in the literature for purely numerical treatments, we apply simple (but uniform) approximations valid in the so-called one-mode regime so as to derive some auxiliary integral equations independent on frequency. The problem is thus reduced to a 13×13 (or 22×22) linear system, whose solution leads to explicit analytical formulas for the above field and parameters. Numerical resolution of the main integral equations for assigned shapes provide values for some constants, so that several graphs showing comparison with previous and exact (numerical) results can be set up. via Ponte don Melillo, 84084 Fisciano (SA) E-mail address: scarpett@diima.unisa.it 1991 Mathematics Subject Classification. 73D25. Questa ricerca è stata svolta nell’ambito delle attività del Gruppo Nazionale per la Fisica Matematica dell’INdAM
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