Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
The modern materials undergoing large elastic deformations and exhibiting strong magnetostrictive effect are modelled here by free energy functionals for nonlinear and non-local magnetoelastic behaviour. The aim of this work is to prove a new theorem which claims that a sequence of free energy functionals of slightly compressible magnetostrictive materials with a non-local elastic behaviour, converges to an energy functional of a nearly incompressible magnetostrictive material. This convergence is referred to as a Γ -convergence. The non-locality is limited to non-local elastic behaviour which is modelled by a term containing the second gradient of deformation in the energy functional.
Rocznik
Tom
Strony
1025--1030
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
autor
- Institute of Fundamental Technological Research, Polish Academy of Sciences, 5B Pawińskiego St., 02-106 Warszawa, Poland Institute of Geophysics, Polish Academy of Sciences, 64 Księcia Janusza St., 01-452 Warszawa, Poland
autor
- Institute of Fundamental Technological Research, Polish Academy of Sciences, 5B Pawińskiego St., 02-106 Warszawa, Poland Institute of Geophysics, Polish Academy of Sciences, 64 Księcia Janusza St., 01-452 Warszawa, Poland
Bibliografia
- [1] C. Rodriguez, M. Rodriguez, I. Orue, J.L. Vilas, J.M. Barandiarn, M.L.F. Gubieda, and L.M. Leon, “New elastomer Terfenol-D magnetostrictive composites”, Sensors and Actuators A: Physical 149, 251-254 (2009).
- [2] D. Braes and P. Ming, “A finite element method for nearly incompressible elasticity problems”, Mathematics of Computations 74, 25-52 (2004).
- [3] H. Ghaemi, K. Behdinan, and A. Spence, “On the development of compressible pseudo-strain energy density function for elastomers, Part I. Theory and experiment”, J. Materials Process Techn. 178, 307-316 (2006).
- [4] P. Rybka and M. Luskin, “Existence of energy minimizers for magnetostrictive materials”, SIAM J. Math. Anal. 36, 2204-2019 (2005).
- [5] W. Bielski and B. Gambin, “Relationship between existence of energy minimizers of incompressible and nearly incompressible magnetostrictive materials”, Reports Math. Phys. 66, 147-157 (2010).
- [6] E. De Giorgi, “G-operators and -convergence”, Proc. Int. Congr. Math. 2, 1175-1191 (1984).
- [7] E. De Giorgi and T. Franzoni, “Su un tipo di convergenza variazionale”, Rend. Accad. Naz. Lincei, Roma LV III, 842-850 (1975).
- [8] H. Attouch, Convergence for Functions and Operators, Pitman, Boston, 1984.
- [9] A. Braides, -convergence for Beginners, Oxford University Press, Oxford, 2002.
- [10] G. Dal Maso, An Introduction to -convergence, Birkhauser, Boston, 1993.
- [11] P. Charrier, B. Dacorogna, B. Hanouzet, and P. Laborde, “An existence theorem for slightly compressible materials in nonlinear elasticity”, SIAM J. Math. Anal. 19, 70-85 (1988).
- [12] H. Le Dret, “Incompressible limit behaviour of slightly compressible nonlinear elastic materials”, Math. Mod. Num. Anal. 20, 315-340 (1986).
- [13] R. Rostamian, “Internal constraints in boundary value problems of continuum mechanics”, Indiana Univ. Math. J. 27, 637-656 (1978).
- [14] A. Giacomini and M. Ponsiglione, “Non-interpenetration of matter for SBV deformations of hyperelastic brittle materials”, Proc. Roy. Soc. Edinburgh Sect. A 138(5), 1019-1041 (2008).
- [15] Ph. Ciarlet and J. Neˇcas, “Injectivity and self-contact in nonlinear elasticity”, Arch. Rat. Mech. Analysis 97, 171-188 (1987).
- [16] J. Neˇcas, Les M´ethodes Directes en Th´eorie des Equations Elliptiques, Masson, Paris, 1997.
- [17] R. Adams, Sobolev Spaces, Academic Press, New York, 1975.
- [18] Ph. Ciarlet, Mathematical Elasticity, Volume I: Threedimensional Elasticity, Elsevier, Amsterdam, 1988.
- [19] T. Roubiˇcek, Relaxation in Optimization Theory and Variational Calculus, Walter de Gruyter, Berlin, 1997.
- [20] S. Doll and K. Schweizerhof, “On the development of volumetric strain energy functions”, J. Appl. Mech. 67, 17-21 (2000).
- [21] L. Daniel, O. Hubert, and R. Billardon, “Homogenisation of magneto-elastic behaviour: from the grain to the macro scale”, Comput. Appl. Math. 23, 1-24 (2004).
- [22] B. Gambin and J.J. Telega, “Effective properties of elastic solids with randomly distributed microcracks”, Mech. Res. Comm. 27, 697-706 (2000).
- [23] G. Milton, The Theory of Composites, Cambridge University Press, Cambridge 2002.
- [24] J.J. Telega and W. Bielski, “Flows in random porous media: effective models”, Computers and Geotechnics 30, 271-288 (2003).
- [25] B. Gambin, “Stochastic homogenization”, Control and Cybern. 23 (4), 672-676 (1994).
- [26] L.P. Liu, “Multiscale analysis and modeling of magnetostrictive composites”, Ph.D. Thesis, University of Minnesota, Minnesota, 2006.
- [27] L.P. Liu, R.D. James, and P.H. Leo, “Magnetostrictive composites in the dilute limit”, J. Mechanics and Physics of Solids 54, 951-974 (2006).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d44a17e6-8334-4a7f-a9fc-81d463286de5