Poromechanics is a branch of

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

and specifically

continuum mechanics Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such m ...

and

acoustics Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician ...

that studies the behaviour of fluid-saturated

porous media A porous medium or a porous material is a material containing pores (voids). The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid (liquid or gas). The skeletal material is usu ...

. A porous medium or a porous material is a

solid Solid is one of the State of matter#Four fundamental states, four fundamental states of matter (the others being liquid, gas, and Plasma (physics), plasma). The molecules in a solid are closely packed together and contain the least amount o ...

referred to as

matrix Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** ''The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchis ...

) permeated by an interconnected network of pores (voids) filled with a

fluid In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...

(

liquid A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, a ...

gas Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...

). 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

rocks In geology, rock (or stone) is any naturally occurring solid mass or aggregate of minerals or mineraloid matter. It is categorized by the minerals included, its chemical composition, and the way in which it is formed. Rocks form the Earth's ...

soils Soil, also commonly referred to as earth or dirt, is a mixture of organic matter, minerals, gases, liquids, and organisms that together support life. Some scientific definitions distinguish ''dirt'' from ''soil'' by restricting the former term ...

biological tissue In biology, tissue is a biological organizational level between cells and a complete organ. A tissue is an ensemble of similar cells and their extracellular matrix from the same origin that together carry out a specific function. Organs are ...

s including

heart The heart is a muscular organ in most animals. This organ pumps blood through the blood vessels of the circulatory system. The pumped blood carries oxygen and nutrients to the body, while carrying metabolic waste such as carbon dioxide t ...

and

cancellous bone A bone is a rigid organ that constitutes part of the skeleton in most vertebrate animals. Bones protect the various other organs of the body, produce red and white blood cells, store minerals, provide structure and support for the body, and ...

, and man-made materials such as

foam Foams are materials formed by trapping pockets of gas in a liquid or solid. A bath sponge and the head on a glass of beer are examples of foams. In most foams, the volume of gas is large, with thin films of liquid or solid separating the reg ...

s and

ceramic A ceramic is any of the various hard, brittle, heat-resistant and corrosion-resistant materials made by shaping and then firing an inorganic, nonmetallic material, such as clay, at a high temperature. Common examples are earthenware, porcelain ...

s can be considered as porous media. Porous media whose solid matrix is

elastic Elastic is a word often used to describe or identify certain types of elastomer, elastic used in garments or stretchable fabrics. Elastic may also refer to: Alternative name * Rubber band, ring-shaped band of rubber used to hold objects togeth ...

and the fluid is

viscous The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inter ...

are called poroelastic. A poroelastic medium is characterised by its

porosity Porosity or void fraction is a measure of the void (i.e. "empty") spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure ...

, permeability 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 is a branch of soil physics and applied 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 (usually air and wat ...

, and in particular in the works of

Karl von Terzaghi Karl von Terzaghi (October 2, 1883 – October 25, 1963) was an Austrian mechanical engineer, geotechnical engineer, and geologist known as the "father of soil mechanics and geotechnical engineering". Early life In 1883, he was born the first ch ...

, 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 (May 25, 1905 – September 12, 1985) was a Belgian-American applied physicist. He made contributions in thermodynamics, aeronautics, geophysics, earthquake engineering, and electromagnetism. Particularly, he was accredited as ...

(1905–1985), a Belgian-American engineer. In a series of papers published between 1935 and 1962 Biot developed the theory of dynamic

poroelasticity Poroelasticity is a field in materials 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 d ...

(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

linear theory In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the nonlinear case. As a mathematical abstraction or ...

of poroelasticity are derived from the equations of

linear elasticity Linear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mech ...

for a solid matrix, the

Navier–Stokes equations In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician Geo ...

for a viscous fluid, and

Darcy's law Darcy's law is an equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of e ...

for a flow of fluid through a porous matrix. One of the key findings of the theory of poroelasticity is that in poroelastic media there exist three types of elastic

wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...

s: 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 __NOTOC__ Yakov Il'ich Frenkel (russian: Яков Ильич Френкель; 10 February 1894 – 23 January 1952) was a Soviet physicist renowned for his works in the field of condensed matter physics. He is also known as Jacov Frenkel, frequ ...

and

Fritz Gassmann Fritz Gassmann (1899–1990) was a Swiss mathematician and geophysicist. Life His Ph.D. advisors at ETH Zurich were George Pólya and Hermann Weyl. He was a geophysics professor at the ETH Zurich. Legacy Gassmann is the eponym for the Gas ...

. 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. 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.

References

External links

Poronet - PoroMechanics Internet Resources Network

APMR - Acoustical Porous Material Recipes
Continuum mechanics Acoustics Applied and interdisciplinary physics Porous media

See also

References

Further reading

External links