The mixed initial-boundary value problem in the context of elasticity of porous bodies having a dipolar structure is considered. By means of a semigroup of contractions, we can obtain some results regarding the existence and uniqueness of solutions for this mixed problem, after proving the equivalence between this problem and a Cauchy problem attached to an abstract equation of evolution. Also, by means of this Cauchy problem, we deduce two continuous dependence results, regarding the supply terms of the original mixed problem and upon initial data.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Nunziato, J.W., Cowin, S.C.: Linear elastic materials with voids. J. Elast. 13, 125–147 (1983)
Cowin, S.C.: Bone Poroelasticity. J. Biomech. 32, 217–238 (1999)
Goodman, M.A., Cowin, S.C.: A continuum theory for granular materials. Arch. Ration. Mech. Anal. 44, 249–266 (1972)
Nunziato, J.W., Cowin, S.C.: A nonlinear theory of elastic materials with voids. Arch. Ration. Mech. Anal. 72, 175–201 (1979)
Iesan, D.: A theory of thermoelastic materials with voids. Acta Mech. 60, 67–89 (1986)
Eringen, A.C.: Theory of thermo-microstretch elastic solids. Int. J. Eng. Sci. 28, 1291–1301 (1990)
Eringen, A.C.: Microcontinuum Field Theories. Springer, New York (1999)
Marin, M.: On the minimum principle for dipolar materials with stretch. Nonlinear Anal. Real World Appl. 10, 1572–1578 (2009)
Abbas, I., Marin, M.: Analytical solution of thermoelastic interaction in a half-space by pulsed laser heating. Phys. E Low Dimens. Syst. Nanostruct. 87, 254–260 (2017)
Othman, M.I.A., Marin, M.: Effect of thermal loading due to laser pulse on thermo-elastic porous medium under GN theory. Results Phys. 7, 3863–3872 (2017)
Bhatti, M.M. et al.: Swimming of Motile Gyrotactic Microorganisms and Nanoparticles in Blood Flow Through Anisotropically Tapered Arteries, Front. Phys., 8, 1–12(2020), Art. No. 95
Khan, A.A., et al.: Effects of chemical reaction on third-grade MHD fluid flow under the influence of heat and mass transfer with variable reactive index. Heat Trans. Res. 50(11), 1061–1080 (2019)
Grot, R.: Thermodynamics of a continuum with microstructure. Int. J. Eng. Sci. 7, 801–814 (1969)
Mindlin, R.D.: Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16, 51–78 (1964)
Green, A.E., Rivlin, R.S.: Multipolar continuum mechanics. Arch. Ration. Mech. Anal. 17, 113–147 (1964)
Fried, E., Gurtin, M.E.: Thermomechanics of the interface between a body and its environment. Contin. Mech. Therm. 19(5), 253–271 (2007)
Marin, M., Nicaise, S.: Existence and stability results for thermoelastic dipolar bodies with double porosity. Contin. Mech. Therm. 28(6), 1645–1657 (2016)
Teodorescu-Draghicescu, H., Vlase, S., et al.: Advanced pultruded glass fibers-reinforced isophtalic polyester resin. Mater. Plast. 52(1), 62–64 (2015)
Marin, M., Lupu, M.: On harmonic vibrations in thermoelasticity of micropolar bodies. J. Vib. Control 4(5), 507–518 (1998)
Niculita, C., Vlase, S., et al.: Optimum stacking in a multi-ply laminate used for the skin of adaptive wings. Optoelectron. Adv. Mat. 5(11), 1233–1236 (2011)
Marin, M., Stan, G.: Weak solutions in Elasticity of dipolar bodies with stretch. Carpathian J. Math. 29(1), 33–40 (2013)
Marin, M., Agarwal, R.P., Mahmoud, S.R., Modeling a microstretch thermo-elastic body with two temperatures, Abstr. Appl. Anal., : 1–7, (2013), p. 583464. Art, ID (2013)
Adams, R.A.: Sobolev Spaces. Academic Press, New York (1975)
Fichera, G.: Existence theorems in elasticity, Handbuch der Physik, vol. VIa-2. Springer, Berlin (1972)
Marin, M., Öchsner, A.: Complements of Higher Mathematics. Springer, Cham (2018)
Hlavacek, I., Necas, J.: On inequalities of Korn’s type. Arch. Ration. Mech. Anal. 36, 305–334 (1980)
Pazy, A.: Semigroups of Linear Operators and Applications. Springer, New York (1983)
Marin, M., Öchsner, A.: Essentials of Partial Differential Equations. Springer, Cham (2019)
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Communicated by Andreas Öchsner.
About this article
Cite this article
Marin, M., Öchsner, A., Ellahi, R. et al. A semigroup of contractions in elasticity of porous bodies. Continuum Mech. Thermodyn. 33, 2027–2037 (2021). https://doi.org/10.1007/s00161-021-00992-7
- Equations of evolution
- Porous bodies
- Continuous dependence