Weak solutions in elasticity of dipolar porous materials. (English) Zbl 1149.74009

Summary: We use some general results from the theory of elliptic equations in order to prove existence and uniqueness of generalized solutions for boundary value problems in elasticity of initially stressed bodies with voids (porous materials).


74A35 Polar materials
74B10 Linear elasticity with initial stresses
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74G25 Global existence of solutions for equilibrium problems in solid mechanics (MSC2010)
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
Full Text: DOI EuDML


[1] D. Ie\csan, “Thermoelastic stresses in initially stressed bodies with microstructure,” Journal of Thermal Stresses, vol. 4, no. 3-4, pp. 387-398, 1981.
[2] M. Marin, “Sur l/existence et l/unicité dans la thermoélasticité des milieux micropolaires,” Comptes Rendus de l/Académie des Sciences. Serie II, vol. 321, no. 12, pp. 475-480, 1995. · Zbl 0837.73017
[3] I. Hlavá\vcek and J. Ne\vcas, “On inequalities of Korn/s type. I: boundary-value problems for elliptic system of partial differential equations,” Archive for Rational Mechanics and Analysis, vol. 36, no. 4, pp. 305-311, 1970. · Zbl 0193.39001
[4] I. Ne\vcas, Les Méthodes Directes en Théorie des Équations Elliptiques, Academia, Prague, Czech Republic, 1967. · Zbl 1225.35003
[5] M. Marin, “On the nonlinear theory of micropolar bodies with voids,” Journal of Applied Mathematics, vol. 2007, Article ID 15745, 11 pages, 2007. · Zbl 1141.74007
[6] M. A. Goodman and S. C. Cowin, “A continuum theory for granular materials,” Archive for Rational Mechanics and Analysis, vol. 44, no. 4, pp. 249-266, 1972. · Zbl 0243.76005
[7] J. W. Nunziato and S. C. Cowin, “Linear elastic materials with void,” Journal of Elasticity, vol. 13, pp. 125-147, 1983. · Zbl 0523.73008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.