Project objectives - Piezoelectricity can be defined as an interaction between two phenomena: the direct piezoelectric effect (a mechanical deformation generates an electric field in the material), and the inverse piezoelectric effect (the application to the material of an electric field or of a potential difference generates a deformation), cf. T. Ikeda, Fundamentals of Piezoelectricity, Oxford University Press, Oxford, 1990. Therefore, a single piezoelectric device is both an actuator and a sensor, and consequently, piezoelectric materials belong to a class of smart or intelligent materials, that are very important in many applications, as for example, biomechanics, biomedicine, structural mechanics, etc. The scope of this project is essentially to acquire a better mathematical knowledge of some particular piezoelectric models, as adaptive rod models and composite laminated plate models. This research project will lead to a better understanding of the mechanical and electric behavior of these problems, and consequently an improvement, in the future, of real-life applications.

Scientific research will be developed, under the following headings: i) asymptotic and variational methods, for the mathematical formulation, and related questions of existence and regularity of solutions, ii) discretization schemes, using finite element and finite difference methods, iii) analysis of error estimates, iv) algorithms to solve the discrete problems, as deterministic optimization algorithms and evolutionary algorithms, v) adapting programs, as finite element and optimization software.

Members List - Isabel Maria Narra de Figueiredo, principal investigator (CMUC, Department of Mathematics, University of Coimbra, Portugal), Carlos Manuel Franco Leal (CMUC, Department of Mathematics, University of Coimbra), Georg Stadler (CMUC, Department of Mathematics, University of Coimbra), José António Carvalho (Department of Mathematics, University of Coimbra), Pedro Nuno Ferreira Pinto Oliveira (Department of Production and Systems, University of Minho, Portugal), Lino Costa (Department of Production and Systems, University of Minho, Portugal), Rogério Augusto da Costa Pereira Leal (Department of Mechanical Engineering, University of Coimbra, Portugal), Cecília Maria Martins Agostinho Soares Pinto (Department of Mathematics, Viseu Polytechnical Institute, Portugal), Luis Manuel Ferreira Roseiro (Department of Mechanical Engineering, Coimbra Superior Engineering Institute, Portugal), Urbano Manuel Oliveira Ramos (Department of Mechanical Engineering, Coimbra Superior Engineering Institute, Portugal).

Outcomes and Activities of the Project :

• Research Articles

• Communications in Scientific Meetings

• Seminars

• Computational Applications

• Event Organizations

• PhD Thesis