In this paper we employ the Nunziato–Cowin theory for elastic materials with voids in order to investigate the bending of plates made from a porous material. We first present the fundamental equations and formulate the boundary initial value problem. Then, we establish some existence and uniqueness results concerning the solution in both equilibrium and dynamic theory. Finally, we apply the theory presented to solve a bending problem for a circular plate with voids.
Nunziato, J. W. and Cowin, S. C.A nonlinear theory of elastic materials with voids . Archive for Rational Mechanics and Analysis,72, 175–201 (1979).
2.
Cowin, S. C. and Nunziato, J. W.Linear elastic materials with voids . Journal of Elasticity,13, 125–147 (1983).
3.
Capriz, G. and Podio–Guidugli, P.Materials with spherical structures . Archive for Rational Mechanics and Analysis,75, 269–279 (1981).
4.
Capriz, G.Continua with Microstructure,Springer Tracts in Natural Philosophy, Vol. 35, C. Truesdell (Ed.), Springer, New York , 1989.
5.
Cowin, S. C.A note on the problem of pure bending in the linear theory of elastic materials with voids . Journal of Elasticity,14, 227–233 (1984).
6.
Cowin, S. C.The viscoelastic behavior of linear elastic materials with voids . Journal of Elasticity,15, 185–192 (1985).
7.
Ieşan, D.Some theorems in the theory of elastic materials with voids . Journal of Elasticity,15, 215–224 (1985).
8.
Ieşsan, D.A theory of thermoelastic materials with voids . Acta Mechanica,60, 67–89 (1986).
9.
Ciarletta, M. and Ieşsan, D.Non-classical Elastic Solids,Pitman Research Notes in Mathematics, Vol. 293, Longman Scientific and Technical, New York , 1993.
10.
Mindlin, R. D.Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates . Journal of Applied Mechanics,18, 31–38 (1951).
11.
Eringen, A. C.Theory of micropolar plates . ZAMP, 18, 12–30 (1967).
12.
Lagnese, J. E. and Lions, J. L.Modelling, Analysis and Control of Thin Plates,Collection RMA, Vol. 6, Masson, Paris , 1989.
13.
Constanda, C.A Mathematical Analysis of Bending of Plates with Transverse Shear Deformation,Pitman Research Notes in Mathematics, Vol. 215, Longman Scientific and Technical, New York , 1990.
14.
Ciarlet, P. G.Mathematical Elasticity. II: Theory of Plates, Elsevier, Amsterdam , 1997.
15.
BÎrsan, M.A bending theory of porous thermoelastic plates . Journal of Thermal Stresses, 26, 67–90 (2003).
16.
BÎrsan, M.On the bending of plates in the theory of elastic material with voids . Analele Ştiinţtifice Univ.‘Al.I. Cuza’ Iaşi, Serie Matematica, 49, 61–76 (2003).
17.
Scarpetta, E.Minimum principles for the bending problem of elastic plates with voids . International Journal of Engineering Science, 40, 1317–1327 (2002).
18.
Hlaváčcek, I. and Hlavácek, M.On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses: I. Cosserat continuum . Aplikace Matematiky, 14, 387–410 (1969).
19.
Nečcas, J.Les Methodes Directes en Théorie des Equations Elliptiques, Academia, Prague , 1967.
20.
Duvaut, G. and Lions, J. L.Inequalities in Mechanics and Physics, Springer, Berlin , 1976.
21.
Brezis, H.Analyse Fonctionelle. Théorie et Applications, Masson, Paris , 1992.
