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Eshelby's Inclusion
In continuum mechanics, Eshelby's inclusion problem refers to a set of problems involving ellipsoidal elastic inclusions in an infinite elastic body. Analytical solutions to these problems were first devised by John D. Eshelby in 1957.Eshelby (1957).Eshelby (1959). Eshelby started with a thought experiment on the possible stress, strain, and displacement fields in a linear elastic body containing an inclusion. In particular, he considered the situation in which the inclusion has undergone a transformation (such as twinning or localized thermal expansion) but its change in shape and size are restricted because of the surrounding material. In that situation, the inclusion and the surrounding material remains in a stressed state. Also the strain states in the body and the inclusion are potentially inhomogeneous and complicated. Eshelby found that the resulting elastic field can be found using a "sequence of imaginary cutting, straining and welding operations." Eshelby's findin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inclusion Plain
Inclusion or Include may refer to: Sociology * Social inclusion, aims to create an environment that supports equal opportunity for individuals and groups that form a society. ** Inclusion (disability rights), promotion of people with disabilities sharing various aspects of life and life as a whole with those without disabilities. ** Inclusion (education), to do with students with special educational needs spending most or all of their time with non-disabled students Science and technology * Inclusion (mineral), any material that is trapped inside a mineral during its formation * Inclusion bodies, aggregates of stainable substances in biological cells * Inclusion (cell), insoluble non-living substance suspended in a cell's cytoplasm * Inclusion (taxonomy), combining of biological species * Include directive, in computer programming Mathematics * Inclusion (set theory), or subset * Inclusion (Boolean algebra), the Boolean analogue to the subset relation * Inclusion map, or inclusi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystal Twinning
Crystal twinning occurs when two or more adjacent crystals of the same mineral are oriented so that they share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals that are tightly bonded to each other. The surface along which the lattice points are shared in twinned crystals is called a composition surface or twin plane. Crystallographers classify twinned crystals by a number of twin laws. These twin laws are specific to the crystal structure. The type of twinning can be a diagnostic tool in mineral identification. Deformation twinning, in which twinning develops in a crystal in response to a shear stress, is an important mechanism for permanent shape changes in a crystal.Courtney, Thomas H. (2000) ''Mechanical Behavior of Materials'', 2nd ed. McGraw Hill. Definition Twinning is a form of symmetrical intergrowth between two or more adjacent crystals of the same mineral. It differs from the ordinary random i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 models in the 19th century. Explanation A continuum model assumes that the substance of the object fills the space it occupies. Modeling objects in this way ignores the fact that matter is made of atoms, and so is not continuous; however, on length scales much greater than that of inter-atomic distances, such models are highly accurate. These models can be used to derive differential equations that describe the behavior of such objects using physical laws, such as mass conservation, momentum conservation, and energy conservation, and some information about the material is provided by constitutive relationships. Continuum mechanics deals with the physical properties of solids and fluids which are independent of any particular coordinate sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Micromechanics
Micromechanics (or, more precisely, micromechanics of materials) is the analysis of composite or heterogeneous materials on the level of the individual constituents that constitute these materials. 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 does not capture the physics for all heterogeneous materials. Micromechanics goal is to predict the anisotropic response of the heterogeneous material on the b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The Royal Society A
''Proceedings of the Royal Society'' is the main research journal of the Royal Society. The journal began in 1831 and was split into two series in 1905: * Series A: for papers in physical sciences and mathematics. * Series B: for papers in life sciences. Many landmark scientific discoveries are published in the Proceedings, making it one of the most historically significant science journals. The journal contains several articles written by the most celebrated names in science, such as Paul Dirac, Werner Heisenberg, Ernest Rutherford, Erwin Schrödinger, William Lawrence Bragg, Lord Kelvin, J.J. Thomson, James Clerk Maxwell, Dorothy Hodgkin and Stephen Hawking. In 2004, the Royal Society began ''The Journal of the Royal Society Interface'' for papers at the interface of physical sciences and life sciences. History The journal began in 1831 as a compilation of abstracts of papers in the ''Philosophical Transactions of the Royal Society'', the older Royal Society publication, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effective Medium Approximations
In materials science, effective medium approximations (EMA) or effective medium theory (EMT) pertain to analytical or theoretical modeling that describes the macroscopic properties of composite materials. EMAs or EMTs are developed from averaging the multiple values of the constituents that directly make up the composite material. At the constituent level, the values of the materials vary and are inhomogeneous. Precise calculation of the many constituent values is nearly impossible. However, theories have been developed that can produce acceptable approximations which in turn describe useful parameters including the effective permittivity and permeability of the materials as a whole. In this sense, effective medium approximations are descriptions of a medium (composite material) based on the properties and the relative fractions of its components and are derived from calculations, and effective medium theory.T.C. Choy, "Effective Medium Theory", Oxford University Press, (2016) 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Composite Material
A composite material (also called a composition material or shortened to composite, which is the common name) is a material which is produced from two or more constituent materials. These constituent materials have notably dissimilar chemical or physical properties and are merged to create a material with properties unlike the individual elements. Within the finished structure, the individual elements remain separate and distinct, distinguishing composites from mixtures and solid solutions. Typical engineered composite materials include: *Reinforced concrete and masonry *Composite wood such as plywood *Reinforced plastics, such as fibre-reinforced polymer or fiberglass *Ceramic matrix composites ( composite ceramic and metal matrices) *Metal matrix composites *and other advanced composite materials There are various reasons where new material can be favoured. Typical examples include materials which are less expensive, lighter, stronger or more durable when compared with commo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenstrain
In continuum mechanics an eigenstrain is any mechanical deformation in a material that is not caused by an external mechanical stress, with thermal expansion often given as a familiar example. The term was coined in the 1970s by Toshio Mura, who worked extensively on generalizing their mathematical treatment. A non-uniform distribution of eigenstrains in a material (e.g., in a composite material) leads to corresponding eigenstresses, which affect the mechanical properties of the material. Overview Many distinct physical causes for eigenstrains exist, such as crystallographic defects, thermal expansion, the inclusion of additional phases in a material, and previous plastic strains. All of these result from internal material characteristics, not from the application of an external mechanical load. As such, eigenstrains have also been referred to as “stress-free strains” and “inherent strains”. When one region of material experiences a different eigenstrain than its surro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 mechanics. The fundamental "linearizing" assumptions of linear elasticity are: infinitesimal strains or "small" deformations (or strains) and linear relationships between the components of stress and strain. In addition linear elasticity is valid only for stress states that do not produce yielding. These assumptions are reasonable for many engineering materials and engineering design scenarios. Linear elasticity is therefore used extensively in structural analysis and engineering design, often with the aid of finite element analysis. Mathematical formulation Equations governing a linear elastic boundary value problem are based on three tensor partial differential equations for the balance of linear momentum and six infinitesimal strain- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 models in the 19th century. Explanation A continuum model assumes that the substance of the object fills the space it occupies. Modeling objects in this way ignores the fact that matter is made of atoms, and so is not continuous; however, on length scales much greater than that of inter-atomic distances, such models are highly accurate. These models can be used to derive differential equations that describe the behavior of such objects using physical laws, such as mass conservation, momentum conservation, and energy conservation, and some information about the material is provided by constitutive relationships. Continuum mechanics deals with the physical properties of solids and fluids which are independent of any particular coordinate sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Displacement Vector
In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory. A displacement may be identified with the translation that maps the initial position to the final position. A displacement may be also described as a '' relative position'' (resulting from the motion), that is, as the final position of a point relative to its initial position . The corresponding displacement vector can be defined as the difference between the final and initial positions: s = x_\textrm - x_\textrm = \Delta In considering motions of objects over time, the instantaneous velocity of the object is the rate of change of the displacement as a function of time. The instantaneous speed, then, is distinct from velocity, or the time rate of chan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinitesimal Strain Theory
In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller (indeed, infinitesimally smaller) than any relevant dimension of the body; so that its geometry and the constitutive properties of the material (such as density and stiffness) at each point of space can be assumed to be unchanged by the deformation. With this assumption, the equations of continuum mechanics are considerably simplified. This approach may also be called small deformation theory, small displacement theory, or small displacement-gradient theory. It is contrasted with the finite strain theory where the opposite assumption is made. The infinitesimal strain theory is commonly adopted in civil and mechanical engineering for the stress analysis of structures built from relatively stiff elastic materials like concrete and steel, since a common goal in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
