153:: a shear or transverse wave, and two types of longitudinal or compressional waves, which Biot called type I and type II waves. The transverse and type I (or fast) longitudinal wave are similar to the transverse and longitudinal waves in an elastic solid, respectively. The slow compressional wave, (also known as Biot’s slow wave) is unique to poroelastic materials. The prediction of the Biot’s slow wave generated some controversy, until it was experimentally observed by Thomas Plona in 1980. Other important early contributors to the theory of poroelasticity were
167:
Recent applications of poroelasticity to biology such as modeling of blood flows through the beating myocardium have also required an extension of the equations to nonlinear (large deformation) elasticity and the inclusion of inertia forces.
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as well as the properties of its constituents (solid matrix and fluid). The distribution of pores across multiple scales as well as the pressure of the fluid with which they are filled give rise to distinct elastic behaviour of the bulk.
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62:). Usually both solid matrix and the pore network, or pore space, are assumed to be continuous, so as to form two interpenetrating continua such as in a sponge. Natural substances including
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Conversion of energy from fast compressional and shear waves into the highly attenuating slow compressional wave is a significant cause of elastic wave attenuation in porous media.
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118:, the father of soil mechanics. However a more general concept of a poroelastic medium, independent of its nature or application, is usually attributed to
126:(now known as Biot theory) which gives a complete and general description of the mechanical behaviour of a poroelastic medium. Biot's equations of the
217:
MĂĽller TM, Gurevich B, Lebedev M (2010). "Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks: a review".
841:"General coupling of porous flows and hyperelastic formulations: from thermodynamics principles to energy balance and compatible time schemes"
783:
Rice JR, Cleary MP (1976). "Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents".
122:(1905–1985), a Belgian-American engineer. In a series of papers published between 1935 and 1962 Biot developed the theory of dynamic
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One of the key findings of the theory of poroelasticity is that in poroelastic media there exist three types of elastic
135:
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Plona T (1980). "Observation of a Second Bulk
Compressional Wave in a Porous Medium at Ultrasonic Frequencies".
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336:"Predictions of angle dependent tortuosity and elasticity effects on sound propagation in cancellous bone"
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517:"Theory of propagation of elastic waves in a fluid saturated porous solid. II Higher frequency range"
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475:"Theory of propagation of elastic waves in a fluid saturated porous solid. I Low frequency range"
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289:"A poroelastic model valid in large strains with applications to perfusion in cardiac modeling"
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Frenkel J (2005). "On the Theory of
Seismic and Seismoelectric Phenomena in a Moist Soil".
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Biot MA, Willis DG (1957). "The elastic coefficients of the theory of consolidation".
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Multiscale modeling of effective elastic properties of fluid-filled porous materials
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Theory of Linear
Poroelasticity with Applications to Geomechanics and Hydrogeology
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Propagation of Sound in Porous Media: Modelling Sound
Absorbing Materials
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can be considered as porous media. Porous media whose solid matrix is
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are called poroelastic. A poroelastic medium is characterised by its
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594:"Mechanics of deformation and acoustic propagation in porous media"
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Chapelle D, Gerbeau JF, Sainte-Marie J, Vignon-Clementel I (2010).
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Gassmann F (1951). "Elastic waves through a packing of spheres".
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International
Journal of Solids and Structures (2019) 162, 36-44
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AygĂĽn H, Attenborough K, Postema M, Lauriks W, Langton C (2009).
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Gassmann F (1951). "Ăśber die
Elastizität poröser Medien".
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Field of study combining physics, mechanics and acoustics
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The concept of a porous medium originally emerged in
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of poroelasticity are derived from the equations of
433:"General theory of three dimensional consolidation"
882:Poronet - PoroMechanics Internet Resources Network
524:The Journal of the Acoustical Society of America
482:The Journal of the Acoustical Society of America
34:that studies the behaviour of fluid-saturated
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343:Journal of the Acoustical Society of America
46:) permeated by an interconnected network of
38:. A porous medium or a porous material is a
887:APMR - Acoustical Porous Material Recipes
266:. Princeton: Princeton University Press.
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812:Bourbie T, Coussy O, Zinszner B (1987).
785:Reviews of Geophysics and Space Physics
707:10.1061/(ASCE)0733-9399(2005)131:9(879)
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730:(English translation available as pdf
912:Applied and interdisciplinary physics
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816:. Houston: Gulf Publication Company.
114:, and in particular in the works of
146:of fluid through a porous matrix.
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865:10.1016/j.euromechflu.2014.02.009
206:. Hoboken: John Wiley & Sons.
82:, and man-made materials such as
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845:European Journal of Mechanics B
839:Chapelle D, Moireau P (2014).
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834:. London: Chapman & Hall.
825:. Washington, DC: Hemisphere.
823:Dynamics of Multiphase Media
559:Journal of Applied Mechanics
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598:Journal of Applied Physics
440:Journal of Applied Physics
399:Theoretical Soil Mechanics
138:for a viscous fluid, and
814:Acoustics of Porous Media
313:10.1007/s00466-009-0452-x
134:for a solid matrix, the
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641:Applied Physics Letters
293:Computational Mechanics
136:Navier–Stokes equations
821:Nigmatulin RI (1990).
50:(voids) filled with a
408:10.1002/9780470172766
225:(5): 75A147–75A164.
120:Maurice Anthony Biot
902:Continuum mechanics
857:2014EJMF...46...82C
797:1976RvGSP..14..227R
758:1951Geop...16..673G
653:1980ApPhL..36..259P
610:1962JAP....33.1482B
571:1957JAM....24..594B
536:1956ASAJ...28..179B
494:1956ASAJ...28..168B
452:1941JAP....12..155B
402:. New York: Wiley.
396:Terzaghi K (1943).
305:2010CompM..46..101C
231:2010Geop...75A.147M
28:continuum mechanics
830:Allard JF (1993).
683:Journal of Physics
674:Frenkel J (1944).
248:20.500.11937/35921
94:and the fluid is
72:biological tissues
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189:References
74:including
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172:See also
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88:ceramics
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151:waves
84:foams
76:heart
68:soils
64:rocks
52:fluid
48:pores
40:solid
732:here
412:ISBN
359:PMID
268:ISBN
157:and
144:flow
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