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Generalized Method Of Cells
Micromechanics (or, more precisely, micromechanics of materials) is the analysis of heterogeneous materials including of composite, and anisotropic and orthotropic materials on the level of the individual constituents that constitute them and their interactions. Aims of micromechanics of materials Heterogeneous materials, such as composites, solid foams, polycrystals, or bone, consist of clearly distinguishable constituents (or ''phases'') that show different mechanical and physical material properties. While the constituents can often be modeled as having isotropic behaviour, the microstructure characteristics (shape, orientation, varying volume fraction, ..) of heterogeneous materials often leads to an anisotropic behaviour. Anisotropic material models are available for linear elasticity. In the nonlinear regime, the modeling is often restricted to orthotropic material models which do not capture the physics for all heterogeneous materials. An important goal of mi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analysis
Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 BC), though ''analysis'' as a formal concept is a relatively recent development. The word comes from the Ancient Greek (''analysis'', "a breaking-up" or "an untying" from ''ana-'' "up, throughout" and ''lysis'' "a loosening"). From it also comes the word's plural, ''analyses''. As a formal concept, the method has variously been ascribed to René Descartes ('' Discourse on the Method''), and Galileo Galilei. It has also been ascribed to Isaac Newton, in the form of a practical method of physical discovery (which he did not name). The converse of analysis is synthesis: putting the pieces back together again in a new or different whole. Science and technology Chemistry The field of chemistry uses analysis in three ways: to i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stress (mechanics)
In continuum mechanics, stress is a physical quantity that describes forces present during deformation. For example, an object being pulled apart, such as a stretched elastic band, is subject to ''tensile'' stress and may undergo elongation. An object being pushed together, such as a crumpled sponge, is subject to ''compressive'' stress and may undergo shortening. The greater the force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Stress has dimension of force per area, with SI units of newtons per square meter (N/m2) or pascal (Pa). Stress expresses the internal forces that neighbouring particles of a continuous material exert on each other, while ''strain'' is the measure of the relative deformation of the material. For example, when a solid vertical bar is supporting an overhead weight, each particle in the bar pushes on the particles immediately below it. When a liquid is in a closed container under pressure, each ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elastic Modulus
An elastic modulus (also known as modulus of elasticity (MOE)) is a quantity that describes an object's or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. Definition The elastic modulus of an object is defined as the slope of its stress–strain curve in the elastic deformation region: A stiffer material will have a higher elastic modulus. An elastic modulus has the form: :\delta \ \stackrel\ \frac where stress is the force causing the deformation divided by the area to which the force is applied and strain is the ratio of the change in some parameter caused by the deformation to the original value of the parameter. Since strain is a dimensionless quantity, the units of \delta will be the same as the units of stress. Elastic constants and moduli Elastic constants are specific parameters that quantify the stiffness of a material in response to applied stresses and are fundamental in defining the elastic pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Upper And Lower Bounds
In mathematics, particularly in order theory, an upper bound or majorant of a subset of some preordered set is an element of that is every element of . Dually, a lower bound or minorant of is defined to be an element of that is less than or equal to every element of . A set with an upper (respectively, lower) bound is said to be bounded from above or majorized (respectively bounded from below or minorized) by that bound. The terms bounded above (bounded below) are also used in the mathematical literature for sets that have upper (respectively lower) bounds. Examples For example, is a lower bound for the set (as a subset of the integers or of the real numbers, etc.), and so is . On the other hand, is not a lower bound for since it is not smaller than every element in . and other numbers ''x'' such that would be an upper bound for ''S''. The set has as both an upper bound and a lower bound; all other numbers are either an upper bound or a lower bound for tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zvi Hashin
Zvi Hashin (; 1929–29 October 2017) was an Israeli mechanical engineer. He was a professor for engineering sciences at Tel Aviv University. In 2012, he won the Benjamin Franklin Medal in Mechanical Engineering, for his research on micro-mechanics of failure of fibre-reinforced plastic Fibre-reinforced plastic (FRP; also called fibre-reinforced polymer, or in American English ''fiber'') is a composite material made of a polymer matrix reinforced with fibres. The fibres are usually glass (in fibreglass), carbon (in carbon-fibre .... Publications * Z. Hashin, Failure criteria for unidirectional fiber composites, J. Appl. Mech.,47, 329–334 (1980). References External links * http://www.eng.tau.ac.il/~hashin/ 1929 births 2017 deaths Academic staff of Tel Aviv University Israeli mechanical engineers Israel Prize in technology and engineering recipients Benjamin Franklin Medal (Franklin Institute) laureates Technion – Israel Institute of Technology alumni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isotropy
In physics and geometry, isotropy () is uniformity in all orientations. Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe situations where properties vary systematically, dependent on direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. Mathematics Within mathematics, ''isotropy'' has a few different meanings: ; Isotropic manifolds: A manifold is isotropic if the geometry on the manifold is the same regardless of direction. A similar concept is homogeneity. ; Isotropic quadratic form: A quadratic form ''q'' is said to be isotropic if there is a non-zero vector ''v'' such that ; such a ''v'' is an isotropic vector or null vector. In complex geometry, a line through the origin in the direction of an is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Applied Mathematics And Mechanics
The ''Journal of Applied Mathematics and Mechanics'', also known as ''Zeitschrift für Angewandte Mathematik und Mechanik'' or ''ZAMM'' is a monthly peer-reviewed scientific journal dedicated to applied mathematics. It is published by Wiley-VCH on behalf of the Gesellschaft für Angewandte Mathematik und Mechanik. The editor-in-chief is Holm Altenbach ( Otto von Guericke University Magdeburg). According to the ''Journal Citation Reports'', the journal has a 2022 impact factor of 2.3. Publication history The journal's first issue appeared in 1921, published by the Verein Deutscher Ingenieure and edited by Richard von Mises. in the |
Stiffness
Stiffness is the extent to which an object resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. Calculations The stiffness, k, of a body is a measure of the resistance offered by an elastic body to deformation. For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as k = \frac where, * F is the force on the body * \delta is the displacement produced by the force along the same degree of freedom (for instance, the change in length of a stretched spring) Stiffness is usually defined under quasi-static conditions, but sometimes under dynamic loading. In the International System of Units, stiffness is typically measured in newtons per meter (N/m). In Imperial units, stiffness is typically measured in pounds (lbs) per inch. Generally speaking, deflections (or motions) of an infinitesima ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rule Of Mixtures
In materials science, a general rule of mixtures is a weighted mean used to predict various properties of a composite material . It provides a theoretical upper- and lower-bound on properties such as the elastic modulus, ultimate tensile strength, thermal conductivity, and electrical conductivity. In general there are two models, the ''rule of mixtures'' for axial loading (Voigt model), and the ''inverse rule of mixtures'' for transverse loading (Reuss model). For some material property E, the rule of mixtures states that the overall property in the direction parallel to the fibers could be as high as : E_\parallel = fE_f + \left(1-f\right)E_m The inverse rule of mixtures states that in the direction perpendicular to the fibers, the elastic modulus of a composite could be as low as :E_\perp = \left(\frac + \frac\right)^. where * f = \frac is the volume fraction of the fibers * E_\parallel is the material property of the composite parallel to the fibers * E_\perp is the materi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Woldemar Voigt
Woldemar Voigt (; 2 September 1850 – 13 December 1919) was a German mathematician and physicist. Biography Voigt was born in Leipzig, and died in Göttingen. He was a student of Franz Ernst Neumann. Voigt taught at the Georg August University of Göttingen and eventually went on to head the Mathematical Physics Department there. He was succeeded in 1914 by Peter Debye, who took charge of the theoretical department of the Physical Institute. Voigt worked on crystal physics, thermodynamics and electro-optics. His main work was the ''Lehrbuch der Kristallphysik'' (''Textbook on crystal physics''), first published in 1910. He discovered what is now called the Voigt effect in 1898. The word tensor in its current meaning was introduced by him in 1898. Voigt profile and Voigt notation are named after him. He was also an amateur musician and became known as a Bach expert (see External links). He was the first to suggest, in 1886, that Bach's Concerto for two harpsichords in C m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heat Conduction
Thermal conduction is the diffusion of thermal energy (heat) within one material or between materials in contact. The higher temperature object has molecules with more kinetic energy; collisions between molecules distributes this kinetic energy until an object has the same kinetic energy throughout. Thermal conductivity, frequently represented by , is a property that relates the rate of heat loss per unit area of a material to its rate of change of temperature. Essentially, it is a value that accounts for any property of the material that could change the way it conducts heat. Heat spontaneously flows along a temperature gradient (i.e. from a hotter body to a colder body). For example, heat is conducted from the hotplate of an electric stove to the bottom of a saucepan in contact with it. In the absence of an opposing external driving energy source, within a body or between bodies, temperature differences decay over time, and thermal equilibrium is approached, temperature becomin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nanomechanics
Nanomechanics is a branch of '' nanoscience'' studying fundamental ''mechanical'' (elastic, thermal and kinetic) properties of physical systems at the nanometer scale. Nanomechanics has emerged on the crossroads of biophysics, classical mechanics, solid-state physics, statistical mechanics, materials science, and quantum chemistry. As an area of nanoscience, nanomechanics provides a scientific foundation of nanotechnology. Nanomechanics is that branch of nanoscience which deals with the study and application of fundamental mechanical properties of physical systems at the nanoscale, such as elastic, thermal and kinetic material properties. Often, nanomechanics is viewed as a ''branch'' of nanotechnology, i.e., an applied area with a focus on the mechanical properties of ''engineered'' nanostructures and nanosystems (systems with nanoscale components of importance). Examples of the latter include nanomachines, nanoparticles, nanopowders, nanowires, nanorods, nanoribbons, nanot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
