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Acoustoelastic Effect
The acoustoelastic effect is how the sound velocities (both longitudinal and shear wave velocities) of an elastic material change if subjected to an initial static stress field. This is a non-linear effect of the constitutive relation between mechanical stress and finite strain in a material of continuous mass. In classical linear elasticity theory small deformations of most elastic materials can be described by a linear relation between the applied stress and the resulting strain. This relationship is commonly known as the generalised Hooke's law. The linear elastic theory involves second order elastic constants (e.g. \lambda and \mu) and yields constant longitudinal and shear sound velocities in an elastic material, not affected by an applied stress. The acoustoelastic effect on the other hand include higher order expansion of the constitutive relation (non-linear elasticity theory) between the applied stress and resulting strain, which yields longitudinal and shear sound velo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sound Velocity
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as well as the medium through which a sound wave is propagating. At , the speed of sound in air is about . The speed of sound in an ideal gas depends only on its temperature and composition. The speed has a weak dependence on frequency and pressure in ordinary air, deviating slightly from ideal behavior. In colloquial speech, ''speed of sound'' refers to the speed of sound waves in air. However, the speed of sound varies from substance to substance: typically, sound travels most slowly in gases, faster in liquids, and fastest in solids. For example, while sound travels at in air, it travels at in water (almost 4.3 times as fast) and at in iron (almost 15 times as fast). In an exceptionally stiff material such as diamond, sound travels at , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Armco
AK Steel Holdings Corporation was a steelmaking company headquartered in West Chester Township, Butler County, Ohio. The company, whose name was derived from the initials of Armco, its predecessor company, and Kawasaki Steel Corporation, was acquired by Cleveland-Cliffs in 2020. AK Steel operated eight steel plants and two tube manufacturing plants in Ashland, Kentucky; Butler, Pennsylvania; Coshocton, Ohio; Dearborn, Michigan; Mansfield, Ohio; Middletown, Ohio; Rockport, Indiana; and Zanesville, Ohio. The company had manufacturing operations in the United States, Canada and Mexico, and facilities in Western Europe. AK Steel produced flat-rolled carbon, stainless and electrical steel products, primarily for the automotive, infrastructure and manufacturing sectors, including electrical power, and distributors and converters markets. The company also provided carbon and stainless steel tubing products, die design and tooling, and hot- and cold-stamped components. Of AK Steel's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Strain
In continuum mechanics, the finite strain theory—also called large strain theory, or large deformation theory—deals with deformations in which strains and/or rotations are large enough to invalidate assumptions inherent in infinitesimal strain theory. In this case, the undeformed and deformed configurations of the continuum are significantly different, requiring a clear distinction between them. This is commonly the case with elastomers, plastically-deforming materials and other fluids and biological soft tissue. Displacement The displacement of a body has two components: a rigid-body displacement and a deformation. * A rigid-body displacement consists of a simultaneous translation (physics) and rotation of the body without changing its shape or size. * Deformation implies the change in shape and/or size of the body from an initial or undeformed configuration \kappa_0(\mathcal B) to a current or deformed configuration \kappa_t(\mathcal B) (Figure 1). A change in the confi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deformation (mechanics)
In physics, deformation is the continuum mechanics transformation of a body from a ''reference'' configuration to a ''current'' configuration. A configuration is a set containing the positions of all particles of the body. A deformation can occur because of external loads, intrinsic activity (e.g. muscle contraction), body forces (such as gravity or electromagnetic forces), or changes in temperature, moisture content, or chemical reactions, etc. Strain is related to deformation in terms of ''relative'' displacement of particles in the body that excludes rigid-body motions. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered. In a continuous body, a deformation field results from a stress field due to applied forces or because of some changes in the temperature field of the body. The rel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deformation (engineering)
In engineering, deformation refers to the change in size or shape of an object. ''Displacements'' are the ''absolute'' change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain is the ''relative'' internal change in shape of an infinitesimally small cube of material and can be expressed as a non-dimensional change in length or angle of distortion of the cube. Strains are related to the forces acting on the cube, which are known as stress, by a stress-strain curve. The relationship between stress and strain is generally linear and reversible up until the yield point and the deformation is elastic. The linear relationship for a material is known as Young's modulus. Above the yield point, some degree of permanent distortion remains after unloading and is termed plastic deformation. The determination of the stress and strain throughout a solid object is given by the field of strength of materials and for a structure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Material Objectivity
Walter Noll (January 7, 1925 June 6, 2017) was a mathematician, and Professor Emeritus at Carnegie Mellon University. He is best known for developing mathematical tools of classical mechanics, thermodynamics, and continuum mechanics. Biography Born in Berlin, Germany, Noll had his school education in a suburb of Berlin. In 1954, Noll earned a Ph.D. in Applied Mathematics from Indiana University under Clifford Truesdell. His thesis "On the Continuity of the Solid and Fluid States" was published both in '' Journal of Rational Mechanics and Analysis'' and in one of Truesdell's books. Noll thanks Jerald Ericksen for his critical input to the thesis. Noll has served as a visiting professor at the Johns Hopkins University, the University of Karlsruhe, the Israel Institute of Technology, the Institut National Polytechnique de Lorraine in Nancy, the University of Pisa, the University of Pavia, and the University of Oxford. In 2012 he became a fellow of the American Mathematical Socie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cauchy Elastic Material
In physics, a Cauchy-elastic material is one in which the stress at each point is determined only by the current state of deformation with respect to an arbitrary reference configuration.R. W. Ogden, 1984, ''Non-linear Elastic Deformations'', Dover, pp. 175–204. A Cauchy-elastic material is also called a simple elastic material. It follows from this definition that the stress in a Cauchy-elastic material does not depend on the path of deformation or the history of deformation, or on the time taken to achieve that deformation or the rate at which the state of deformation is reached. The definition also implies that the constitutive equations are spatially local; that is, the stress is only affected by the state of deformation in an infinitesimal neighborhood of the point in question, without regard for the deformation or motion of the rest of the material. It also implies that body forces (such as gravity), and inertial forces cannot affect the properties of the material. Finally, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering and mechanical engineering, but also in other complex fields such as meteorology. Historically, thermodynamics developed out of a desire to increase the efficiency of early steam engines, particularly through the work of French physicist Sadi Carnot (1824) who believed that engine efficiency was the key that could help France win the Napoleonic Wars. Scots-Irish physicist Lord Kelvin was the first to formulate a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isothermal
In thermodynamics, an isothermal process is a type of thermodynamic process in which the temperature ''T'' of a system remains constant: Δ''T'' = 0. This typically occurs when a system is in contact with an outside thermal reservoir, and a change in the system occurs slowly enough to allow the system to be continuously adjusted to the temperature of the reservoir through heat exchange (see quasi-equilibrium). In contrast, an ''adiabatic process'' is where a system exchanges no heat with its surroundings (''Q'' = 0). Simply, we can say that in an isothermal process * T = \text * \Delta T = 0 * dT = 0 * For ideal gases only, internal energy \Delta U = 0 while in adiabatic processes: * Q = 0. Etymology The adjective "isothermal" is derived from the Greek words "ἴσος" ("isos") meaning "equal" and "θέρμη" ("therme") meaning "heat". Examples Isothermal processes can occur in any kind of system that has some means of regulating the temperature, including hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polycrystalline
A crystallite is a small or even microscopic crystal which forms, for example, during the cooling of many materials. Crystallites are also referred to as grains. Bacillite is a type of crystallite. It is rodlike with parallel longulites. Structure The orientation of crystallites can be random with no preferred direction, called random texture, or directed, possibly due to growth and processing conditions. While the structure of a (single) crystal is highly ordered and its lattice is continuous and unbroken, amorphous materials, such as glass and many polymers, are non-crystalline and do not display any structures, as their constituents are not arranged in an ordered manner. Polycrystalline structures and paracrystalline phases are in-between these two extremes. Polycrystalline materials, or polycrystals, are solids that are composed of many crystallites of varying size and orientation. Most materials are polycrystalline, made of a large number crystallites held together by thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperelastic Material
A hyperelastic or Green elastic materialR.W. Ogden, 1984, ''Non-Linear Elastic Deformations'', , Dover. is a type of constitutive model for ideally elastic material for which the stress–strain relationship derives from a strain energy density function. The hyperelastic material is a special case of a Cauchy elastic material. For many materials, linear elastic models do not accurately describe the observed material behaviour. The most common example of this kind of material is rubber, whose stress-strain relationship can be defined as non-linearly elastic, isotropic and incompressible. Hyperelasticity provides a means of modeling the stress–strain behavior of such materials. The behavior of unfilled, vulcanized elastomers often conforms closely to the hyperelastic ideal. Filled elastomers and biological tissues are also often modeled via the hyperelastic idealization. Ronald Rivlin and Melvin Mooney developed the first hyperelastic models, the Neo-Hookean and Mooney–Ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compressible
In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure (or mean stress) change. In its simple form, the compressibility \kappa (denoted in some fields) may be expressed as :\beta =-\frac\frac, where is volume and is pressure. The choice to define compressibility as the negative of the fraction makes compressibility positive in the (usual) case that an increase in pressure induces a reduction in volume. The reciprocal of compressibility at fixed temperature is called the isothermal bulk modulus. Definition The specification above is incomplete, because for any object or system the magnitude of the compressibility depends strongly on whether the process is isentropic or isothermal. Accordingly, isothermal compressibility is defined: :\beta_T=-\frac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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