Poroelasticity

Definition

Poroelasticity is a field in material science and mechanics that studies the interaction between fluid flow and solids deformation within a linear porous medium and it is an extension of elasticity and porous medium flow (diffusion equation). The deformation of the medium influences the flow of the fluid and vice versa. The theory was proposed by Maurice Anthony Biot (1935, 1941)[1] as a theoretical extension of soil consolidation models developed to calculate the settlement of structures placed on fluid-saturated porous soils. The theory of poroelasticity has been widely applied in geomechanics,[2] hydrology,[3] biomechanics,[4] tissue mechanics,[5] cell mechanics,[6] and micromechanics.[7]

An intuitive sense of the response of a saturated elastic porous medium to mechanical loading can be developed by thinking about, or experimenting with, a fluid-saturated sponge. If a fluid- saturated sponge is compressed, fluid will flow from the sponge. If the sponge is in a fluid reservoir and compressive pressure is subsequently removed, the sponge will reimbibe the fluid and expand. The volume of the sponge will also increase if its exterior openings are sealed and the pore fluid pressure is increased. The basic ideas underlying the theory of poroelastic materials are that the pore fluid pressure contributes to the total stress in the porous matrix medium and that the pore fluid pressure alone can strain the porous matrix medium. There is fluid movement in a porous medium due to differences in pore fluid pressure created by different pore volume strains associated with mechanical loading of the porous medium.[5]

Types of Poroelasticity

The theories of poroelasticity can be divided into two categories: static (or quasi-static) and dynamic theories[8], just like mechanics can be divided into statics and dynamics. The static poroelasticity considers processes in which water movement and solid skeleton deformation occur simultaneously and affect each other. The static poroelasticity is predominant in the literature for poroelasticity; as a result, this term is used interchangeably with poroelasticity in many publications. This static poroelasticity theory is a generalization of the one-dimensional consolidation theory in soil mechanics. This theory was developed from Biot's work in 1941[1]. The dynamic poroelasticity is proposed for understanding the wave propagation in both the liquid and solid phases of saturated porous materials. The inertial and associated kinetic energy, which are not considered in static poroelasticity, are included. This is especially necessary when the speed of the movement of the phases in the porous material is considerable, e.g., when vibration or stress waves is present[9]. The dynamic poroelasticity was developed attributed to Biot's work on the propagation of elastic waves in fluid-saturated media[10][11].

Books

Some of the helpful references to studying theory of poroelasticity are Fundamentals of Poroelasticity,[12] Poroelasticity,[2] Theory of linear poroelasticity with applications to geomechanics and hydrogeology[3], Multiphysics in Porous Materials[9], Theory of Porous Media[13], and Poromechanics[14].

See also

References

  1. 1 2 Biot MA (1941-02-01). "General Theory of Three‐Dimensional Consolidation". Journal of Applied Physics. 12 (2): 155–164. doi:10.1063/1.1712886. ISSN 0021-8979.
  2. 1 2 Cheng AH (2016). Poroelasticity. Springer. doi:10.1007/978-3-319-25202-5.
  3. 1 2 Wang HF (2000). Theory of linear poroelasticity with applications to geomechanics and hydrogeology. Princeton University Press.
  4. ↑ Cowin SC (1999). "Bone poroelasticity". Journal of Biomechanics. 32 (3): 217–38. doi:10.1016/s0021-9290(98)00161-4. PMID 10093022.
  5. 1 2 Cowin SC, Doty SB (eds.). Tissue Mechanics. Springer. doi:10.1007/978-0-387-49985-7.
  6. ↑ Moeendarbary E, Valon L, Fritzsche M, Harris AR, Moulding DA, Thrasher AJ, Stride E, Mahadevan L, Charras GT (March 2013). "The cytoplasm of living cells behaves as a poroelastic material". Nature Materials. 12 (3): 253–61. doi:10.1038/nmat3517. PMC 3925878. PMID 23291707.
  7. ↑ Dormieux L, Kondo D, Ulm F. Microporomechanics. Wiley. doi:10.1002/0470032006.
  8. ↑ Liu, Zhen (Leo). "Multiphysics - Poroelasticity and Poromechanics". www.multiphysics.us. Retrieved 2018-10-03.
  9. 1 2 Multiphysics in Porous Materials | Zhen (Leo) Liu | Springer.
  10. ↑ Biot, M. A. (April 1962). "Mechanics of Deformation and Acoustic Propagation in Porous Media". Journal of Applied Physics. 33 (4): 1482–1498. doi:10.1063/1.1728759. ISSN 0021-8979.
  11. ↑ Biot, M. A. (March 1956). "Theory of Propagation of Elastic Waves in a Fluid‐Saturated Porous Solid. II. Higher Frequency Range". The Journal of the Acoustical Society of America. 28 (2): 179–191. doi:10.1121/1.1908241. ISSN 0001-4966.
  12. ↑ Detournay E, Cheng AH (1993). "Fundamentals of poroelasticity" (PDF). In Fairhurst C. Comprehensive Rock Engineering: Principles, Practice and Projects. II, Analysis and Design Method. Pergamon Press. pp. 113–171.
  13. ↑ Theory of Porous Media - Highlights in Historical Development and Current State | Reint de Boer | Springer.
  14. ↑ Coussy, Olivier (2003-12-09). "Poromechanics". doi:10.1002/0470092718.
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