Poromechanics
Encyclopedia
Poromechanics is a branch of physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

 and specifically continuum mechanics
Continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modelled as a continuous mass rather than as discrete particles...

 and acoustics
Acoustics
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...

 that studies the behaviour of fluid-saturated porous media
Porous medium
A porous medium is a material containing pores . The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid...

. A porous medium or a porous material
Material
Material is anything made of matter, constituted of one or more substances. Wood, cement, hydrogen, air and water are all examples of materials. Sometimes the term "material" is used more narrowly to refer to substances or components with certain physical properties that are used as inputs to...

 is a solid
Solid
Solid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...

 (often called matrix) permeated by an interconnected network of pores
Porosity
Porosity or void fraction is a measure of the void spaces in a material, and is a fraction of the volume of voids over the total volume, between 0–1, or as a percentage between 0–100%...

 (voids) filled with a fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....

 (liquid
Liquid
Liquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...

 or gas
Gas
Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...

). Usually both solid matrix and the pore network (also known as the pore space) are assumed to be continuous, so as to form two interpenetrating continua such as in a sponge. Many natural substances such as rocks
Rock (geology)
In geology, rock or stone is a naturally occurring solid aggregate of minerals and/or mineraloids.The Earth's outer solid layer, the lithosphere, is made of rock. In general rocks are of three types, namely, igneous, sedimentary, and metamorphic...

, soils, biological tissue
Biological tissue
Tissue is a cellular organizational level intermediate between cells and a complete organism. A tissue is an ensemble of cells, not necessarily identical, but from the same origin, that together carry out a specific function. These are called tissues because of their identical functioning...

s, and man made materials such as foam
Foam
-Definition:A foam is a substance that is formed by trapping gas in a liquid or solid in a divided form, i.e. by forming gas regions inside liquid regions, leading to different kinds of dispersed media...

s and ceramic
Ceramic
A ceramic is an inorganic, nonmetallic solid prepared by the action of heat and subsequent cooling. Ceramic materials may have a crystalline or partly crystalline structure, or may be amorphous...

s can be considered as porous media. Porous media whose solid matrix is elastic
Elasticity (physics)
In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....

 and the fluid is viscous are called poroelastic. A poroelastic medium is characterised by its porosity
Porosity
Porosity or void fraction is a measure of the void spaces in a material, and is a fraction of the volume of voids over the total volume, between 0–1, or as a percentage between 0–100%...

, permeability
Permeability (fluid)
Permeability in fluid mechanics and the earth sciences is a measure of the ability of a porous material to allow fluids to pass through it.- Units :...

 as well as the properties of its constituents (solid matrix and fluid).

The concept of a porous medium originally emerged in soil mechanics
Soil mechanics
Soil mechanics is a branch of engineering mechanics that describes the behavior of soils. It differs from fluid mechanics and solid mechanics in the sense that soils consist of a heterogeneous mixture of fluids and particles but soil may also contain organic solids, liquids, and gasses and other...

, and in particular in the works of Karl von Terzaghi
Karl von Terzaghi
Karl von Terzaghi was an Austrian civil engineer and geologist, called the father of soil mechanics.-Early life:...

, the father of soil mechanics. However a more general concept of a poroelastic medium, independent of its nature or application, is usually attributed to Maurice Anthony Biot
Maurice Anthony Biot
Maurice Anthony Biot was a Belgian-American physicist and the founder of the theory of poroelasticity.Born in Antwerp, Belgium, Biot studied at Catholic University of Leuven in Belgium where he received a bachelor's degrees in philosophy , mining engineering and electrical engineering , and...

 (1905–1985), a Belgian-American engineer. In a series of papers published between 1935 and 1957 Biot developed the theory of dynamic poroelasticity (now known as Biot theory) which gives a complete and general description of the mechanical behaviour of a poroelastic medium. Biot's equation
Equation
An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign , for examplex + 3 = 5\,asserts that x+3 is equal to 5...

s of the linear theory of poroelasticity are derived from
  • Equations of linear elasticity
    Linear elasticity
    Linear elasticity is the mathematical study of how solid objects deform and become internally stressed due to prescribed loading conditions. Linear elasticity models materials as continua. Linear elasticity is a simplification of the more general nonlinear theory of elasticity and is a branch of...

     for the solid matrix,
  • Navier–Stokes equations for the viscous fluid, and
  • Darcy's law
    Darcy's law
    Darcy's law is a phenomenologically derived constitutive equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on the results of experiments on the flow of water through beds of sand...

     for the flow
    Fluid dynamics
    In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

     of fluid through the porous matrix.


One of the key findings of the theory of poroelasticity is that in poroelastic media there exist three types of elastic waves
WAVES
The WAVES were a World War II-era division of the U.S. Navy that consisted entirely of women. The name of this group is an acronym for "Women Accepted for Volunteer Emergency Service" ; the word "emergency" implied that the acceptance of women was due to the unusual circumstances of the war and...

: 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 Yakov Frenkel
Yakov Frenkel
Yakov Il'ich Frenkel, was a Soviet physicist renowned for his works in the field of solid-state physics. He is also known as Jacov Frenkel....

 and Fritz Gassmann
Fritz Gassmann
Fritz Gassmann was a Swiss mathematician and geophysicist. Gassmann is the eponym for the Gassmann triple and Gassmann's equation. His Ph.D. advisors at ETH Zurich were George Polya and Hermann Weyl. He was a geophysics professor at the ETH Zurich....

.

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