Structural stability study for porous Cosserat media

References

• J.W. Nunziato, and S.C. Cowin, A nonlinear theory of materials with voids, Arch. Rational Mech. Anal., vol. 72, no. 2, pp. 175–201, 1979. DOI: 10.1007/BF00249363.
   Web of Science ®Google Scholar
• S.C. Cowin, and J.W. Nunziato, Linear elastic materials with voids, J. Elast., vol. 13, no. 2, pp. 125–147, 1983. DOI: 10.1007/BF00041230.
   Web of Science ®Google Scholar
• M.A. Goodman, and S.C. Cowin, A continuum theory of granular material, Arch. Rational Mech. Anal., vol. 44, no. 4, pp. 249–266, 1972. DOI: 10.1007/BF00284326.
   Web of Science ®Google Scholar
• D. Iesan, A theory of thermoelastic material with voids, Acta Mech., vol. 60, pp. 67–89, 1986.
   Web of Science ®Google Scholar
• D. Ieşan, and R. Quintanilla, Non-linear deformations of porous elastic solids, Int. J. Nonlinear Mech., vol. 49, pp. 57–65, 2013. DOI: 10.1016/j.ijnonlinmec.2012.08.005.
   Web of Science ®Google Scholar
• G. Iovane, and F. Passarella, Saint-Venant’s principle in dynamic porous thermoelastic media with memory for heat flux, J. Therm. Stresses, vol. 27, no. 11, pp. 983–999, 2004. DOI: 10.1080/01495730490498502.
   Web of Science ®Google Scholar
• M.I .A. Othman, and M. Marin, Effect of thermal loading due to laser pulse on thermo-elastic porous medium under G-N theory, Results Phys., vol. 7, pp. 3863–3872, 2017. DOI: 10.1016/j.rinp.2017.10.012.
   Web of Science ®Google Scholar
• M. Marin, On existence and uniqueness in thermoelasticity of micropolar bodies, C. R. Acad. Sci. Paris, Serie II, B, vol. 321, no. 12, pp. 375–480, 1995.
   Google Scholar
• M. Marin, R. Ellahi, S. Vlase, and M.M. Bhatti, On the decay of exponential type for the solutions in a dipolar elastic body, J. Taibah Univ. Sci., vol. 14, no. 1, pp. 534–540, 2020. DOI: 10.1080/16583655.2020.1751963.
   Web of Science ®Google Scholar
• A.C. Eringen, Theory of thermo-microstretch elastic solids, Int. J. Eng. Sci., vol. 28, no. 12, pp. 1291–1301, 1990. DOI: 10.1016/0020-7225(90)90076-U.
   Web of Science ®Google Scholar
• A.C. Eringen, Microcontinuum Field Theories, Springer, New York, 1999.
   Google Scholar
• R.D. Mindlin, Micro-structure in linear elasticity, Arch. Rational Mech. Anal., vol. 16, no. 1, pp. 51–78, 1964. DOI: 10.1007/BF00248490.
   Web of Science ®Google Scholar
• A.E. Green, and R.S. Rivlin, Multipolar continuum mechanics, Arch. Rational Mech. Anal., vol. 17, no. 2, pp. 113–147, 1964. DOI: 10.1007/BF00253051.
   Web of Science ®Google Scholar
• E. Fried, and M.E. Gurtin, Thermomechanics of the interface between a body and its environment, Continuum Mech. Thermodyn., vol. 19, no. 5, pp. 253–271, 2007. DOI: 10.1007/s00161-007-0053-x.
   Web of Science ®Google Scholar
• M. Marin, and C. Marinescu, Thermoelasticity of initially stressed bodies. Asymptotic equipartition of energies, Int. J. Eng. Sci., vol. 36, no. 1, pp. 73–86, 1998. DOI: 10.1016/S0020-7225(97)00019-0.
   Web of Science ®Google Scholar
• A.E. Abouelregal, and M. Marin, The response of nanobeams with temperature-dependent properties using state-space method via modified couple stress theory, Symmetry, vol. 12, no. 8, p. 1276, 2020. DOI: 10.3390/sym12081276.
   Google Scholar
• M.L. Scutaru, and S. Vlase, New analytical method based on dynamic response of planar mechanical elastic systems, Boundary Value Probl., vol. 2020, no. 1, pp. 1–16, 2020.
   Web of Science ®Google Scholar
• S. Vlase, and C. Năstac, M. MARIN, and M. MIHĂLCICĂ, A method for the study of the vibration of mechanical bars systems with symmetries, Acta Tech. Napocensis, Ser. Appl. Math. Mech. Eng., vol. 60, no. 4, pp. 539–544, 2017.
   Google Scholar
• F. Alzahrani, and A. Hobiny, I. Abbas, and M. Marin, An eigenvalues approach for a two-dimensional porous medium based upon weak, normal and strong thermal conductivities, Symmetry, vol. 12, no. 5, p. 848, 2020. DOI: 10.3390/sym12050848.
   Google Scholar
• M. Marin, E. Carrera, and S. Vlase, A reciprocal relation with application in the study of the dislocations, Mech. Adv. Mater. Struct., vol. 29, no. 27, pp. 6330–6335, 2022. DOI: 10.1080/15376494.2021.1975854.
   Web of Science ®Google Scholar
• R.J. Knops, and L.E. Payne, Improved estimates for contiunous data dependence in linear elastodynamics, Math. Models Meth. Appl. Sci., vol. 103, pp. 535–559, 1988.
   Google Scholar
• L.E. Payne, and B. Straughan, Structural stability for the Darcy equations of flow in porous media, Proc. R Soc. London A, vol. 454, no. 1974, pp. 1691–1698, 1998. DOI: 10.1098/rspa.1998.0227.
   Web of Science ®Google Scholar
• K.A. Ames, and B. Straughan, Non-Standard and Improperly Posed Problems, Academic Press, New York, 1997.
   Google Scholar
• E. Carrera, and V.V. Zozulya, Carrera unified formulation (CUF) for the micropolar beams: Analytical solutions, Mech. Adv. Mater. Struct., vol. 28, no. 6, pp. 583–607, 2021. DOI: 10.1080/15376494.2019.1578013.
   Web of Science ®Google Scholar
• E. Carrera, and V.V. Zozulya, Carrera unified formulation (CUF) for the micropolar plates and shells. I. Higher order theory, Mech. Adv. Mater. Struct., vol. 29, no. 6, pp. 773–795, 2022. DOI: 10.1080/15376494.2020.1793241.
   Web of Science ®Google Scholar
• E. Carrera, and V.V. Zozulya, Carrera unified formulation (CUF) for the micropolar plates and shells. II. Complete linear expansion case, Mech. Adv. Mater. Struct., vol. 29, no. 6, pp. 796–815, 2022. DOI: 10.1080/15376494.2020.1793242.
   Web of Science ®Google Scholar
• D. Atta, A.E. Abouelregal, and F. Alsharari, Thermoelastic analysis of functionally graded nanobeams via fractional heat transfer model with nonlocal kernels, Mathematics, vol. 10, no. 24, p. 4718, 2022.
   Web of Science ®Google Scholar
• A.E. Abouelregal, and H.M. Sedighi, Elastic thermal deformation of an infinite copper material due to cyclic heat supply using higher-order nonlocal thermal modeling, Metals, vol. 12, p. 1927, 2022.
   Web of Science ®Google Scholar
• I.E. Ahmed, A.E. Abouelregal, D, and M. Mostafa, Photo-carrier dynamics in a rotating semiconducting solid sphere under modification of the GN-III model without singularities, Arch. Appl. Mech., vol. 92, no. 8, pp. 2351–2370, 2022. DOI: 10.1007/s00419-022-02180-8.
   Web of Science ®Google Scholar
• G. Fichera, Existence theorems in elasticity, in Handbuch der Physik, vol. VI a/2, S. Flügge, Ed. Berlin: Springer, 1972.
   Google Scholar