Abstract
The present chapter presents a review of previous works of the authors on the subject of the dynamic analysis of gradient poroelastic solids and structures. First, the governing equations of motion of a fluid-saturated poroelastic medium with microstructural (for both the solid and fluid) and microinertia (for the solid) effects are derived. These equations are of an order of two degrees higher than in the classical case and consist of seven equations with seven unknowns in three-dimensions. Second, the propagation of plane harmonic waves in an infinitely extended medium is studied analytically for the low and high frequency range. This is accomplished by separating the equations of motion in their dilatational and rotational parts for which wave dispersion curves can be constructed. Third, a simple one-dimensional boundary value problem, that of the transient behavior of a gradient poroelastic soil column, is solved analytically/ numerically with the aid of numerical Laplace transform. Finally, on the basis of the above, conclusions are drawn and suggestions for future research are made.
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References
Biot, M.A.: General theory of three-dimensional consolidation. J. Appl. Phys. 12, 55–64 (1941)
Biot, M.A.: Theory of propagation of elastic waves in a fluid-saturated porous solid: I low frequency range; II higher frequency range. J. Acoust. Soc. Am. 28, 168–178, 179–191 (1956)
Schanz, M.: Poroelastodynamics: linear models, analytical solutions and numerical methods. Appl. Mech. Rev. ASME 62, 1–15 (2009)
Cheng, A.H.D.: Poroelasicity. Springer, Switzerland (2016)
Mindlin, R.D.: Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16, 51–78 (1964)
Vavva, M.G., Protopappas, V.C., Gergidis, L.N., Charalambopoulos, A., Fotiadis, D.L., Polyzos, D.: Velocity dispersion of guided waves propagating in a free gradient elastic plate: application to cortical bone. J. Acoust. Soc. Am. 125, 3414–3427 (2009)
Papargyri-Beskou, S., Polyzos, D., Beskos, D.E.: Wave dispersion in gradient elastic solids and structures: a unified treatment. Int. J. Solids Stuct. 46, 3751–3759 (2009)
Berryman, J.G., Thigpen, L.: Nonlinear and semi-linear dynamic poroelasticity with microstructure. J. Mech. Phys. Solids 33, 97–116 (1985)
Aifantis, E.C.: Microscopic processes and macroscopic response. In: Desai, C.S., Gallagher, R.H. (eds.) Mechanics of Engineering Materials, pp. 1–22. Wiley, Chichester (1984)
Vardoulakis, I., Aifantis, E.C.: On the role of microstructure in the behavior of solids: effects of higher order gradients and internal inertia. Mech. Mater. 18, 151–158 (1994)
Ehlers, W., Volk, W.: On shear band localization phenomena of liquid-saturated granular elastoplastic porous solid materials accounting for fluid viscosity and micropolar solid rotations. Mech. Cohes. Frict. Mater. 2, 301–320 (1997)
Ehlers, W., Volk, W.: On theoretical and numerical methods in the theory of porous media based on polar and non-polar elasto-plastic solid materials. Int. J. Solids Struct. 35, 4597–4617 (1998)
Sciarra, G., Dell’Isola, F., Ianiro, N., Mades, A.: A variational deduction of second gradient poroelasicity, Part I: general theory. J. Mech. Mater. Struct. 3, 507–526 (2008)
Madeo, A., Dell’Isola, F., Ianiro, N., Sciarra, G.: A variational deduction of second gradient poroelasticity II: an application to the consolidation problem. J. Mech. Mater. Stuct. 3, 607–625 (2008)
Papargyri-Beskou, S., Tsinopoulos, S.V., Beskos, D.E.: Transient dynamic analysis of a fluid-saturated porous gradient elastic column. Acta Mech. 222, 351–362 (2011)
Papargyri-Beskou, S., Polyzos, D., Beskos, D.E.: Wave propagation in 3-D poroelastic media including gradient effects. Arch. Appl. Mech. 82, 1569–1584 (2012)
Smyrlis, V.D., Pegios, I.P., Papargyri-Beskou, S.: On wave propagation in gradient poroelasicity. Soil Dyn. Earthq. Eng. 88, 72–75 (2016)
Serpieri, R., Travascio, F.: Variational Continuum Multiphase Poroelasticity. Springer International Publishing AG, Singapore (2017)
Beskos, D.E.: Dynamics of saturated rocks. I: equations of motion. J. Eng. Mech. ASCE 115(5), 982–995 (1989)
Beskos, D.E., Vgenopoulou, I., Providakis, C.P.: Dynamics of saturated rocks II: body waves. J. Eng. Mech. ASCE 115(5), 996–1016 (1989)
Durbin, F.: Numerical inversion of Laplace transform: an efficient improvement to Dubner and Abate’s method. Comput. J. 17, 371–376 (1974)
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Pegios, I.P., Papargyri-Beskou, S., Beskos, D.E. (2018). Dynamic Analysis of Gradient Poroelastic Solids and Structures. In: Altenbach, H., Jablonski, F., Müller, W., Naumenko, K., Schneider, P. (eds) Advances in Mechanics of Materials and Structural Analysis. Advanced Structured Materials, vol 80. Springer, Cham. https://doi.org/10.1007/978-3-319-70563-7_13
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