Hosford Yield Criterion
The Hosford yield criterion is a function that is used to determine whether a material has undergone plastic yielding under the action of stress. Hosford yield criterion for isotropic plasticity The Hosford yield criterion for isotropic materials is a generalization of the von Mises yield criterion. It has the form : \tfrac, \sigma_2-\sigma_3, ^n + \tfrac, \sigma_3-\sigma_1, ^n + \tfrac, \sigma_1-\sigma_2, ^n = \sigma_y^n \, where \sigma_i, i=1,2,3 are the principal stresses, n is a material-dependent exponent and \sigma_y is the yield stress in uniaxial tension/compression. Alternatively, the yield criterion may be written as : \sigma_y = \left(\tfrac, \sigma_2-\sigma_3, ^n + \tfrac, \sigma_3-\sigma_1, ^n + \tfrac, \sigma_1-\sigma_2, ^n\right)^ \,. This expression has the form of an ''L''''p'' norm which is defined as :\ \, x\, _p=\left(, x_1, ^p+, x_2, ^p+\cdots+, x_n, ^p\right)^ \,. When p = \infty, the we get the ''L''∞ norm, :\ \, x\, _\infty=\max \left\. Compar ...
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Hosford Plane Stress
Hosford (also spelled ''Horsford'') is a name of English origin. It may refer to: People *Chauncey Hosford, Oregon pioneer. *Edward Columbus Hosford, American architect *Henry Hosford Gurley, Congressman from Louisiana *Kyle Hosford, Irish basketball player *Robert Flournoy Hosford, Florida politician Other *Hosford-Abernethy, Portland, Oregon, a neighborhood *Hosford yield criterion, a physics equation *John Hosford House, a historic building in Ohio *Hosford, Florida Hosford is an unincorporated community and census-designated place in Liberty County, Florida, United States. Its population was 650 as of the 2010 census. It is located at the junction of State Road 20 and State Road 65. Hosford has a post of ...

Face-centred Cubic
In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals. There are three main varieties of these crystals: *Primitive cubic (abbreviated ''cP'' and alternatively called simple cubic) *Body-centered cubic (abbreviated ''cI'' or bcc) *Face-centered cubic (abbreviated ''cF'' or fcc, and alternatively called ''cubic close-packed'' or ccp) Each is subdivided into other variants listed below. Although the ''unit cells'' in these crystals are conventionally taken to be cubes, the primitive unit cells often are not. Bravais lattices The three Bravais lattices in the cubic crystal system are: The primitive cubic lattice (cP) consists of one lattice point on each corner of the cube; this means each simple cubic unit cell has in total one lattice point. Each atom at a lattice point is then shared equally between eight adjacent cubes, ...
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Solid Mechanics
Solid mechanics, also known as mechanics of solids, is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents. Solid mechanics is fundamental for civil, aerospace, nuclear, biomedical and mechanical engineering, for geology, and for many branches of physics such as materials science. It has specific applications in many other areas, such as understanding the anatomy of living beings, and the design of dental prostheses and surgical implants. One of the most common practical applications of solid mechanics is the Euler–Bernoulli beam equation. Solid mechanics extensively uses tensors to describe stresses, strains, and the relationship between them. Solid mechanics is a vast subject because of the wide range of solid materials available, such as steel, wood, concrete, biological materials, textiles, geological ...
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Plasticity (physics)
In physics and materials science, plasticity, also known as plastic deformation, is the ability of a solid material to undergo permanent Deformation (engineering), deformation, a non-reversible change of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the material itself. In engineering, the transition from Elasticity (physics), elastic behavior to plastic behavior is known as Yield (engineering), yielding. Plastic deformation is observed in most materials, particularly metals, soils, Rock (geology), rocks, concrete, and foams. However, the physical mechanisms that cause plastic deformation can vary widely. At a crystalline scale, plasticity in metals is usually a consequence of dislocations. Such defects are relatively rare in most crystalline materials, but are numerous in some and part of their crystal structure; in such cases, plastic crystallinity can res ...
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Yield (engineering)
In materials science and engineering, the yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as plastic deformation. The yield strength or yield stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically. The yield strength is often used to determine the maximum allowable load in a mechanical component, since it represents the upper limit to forces that can be applied without producing permanent deformation. In some materials, such as aluminium, there is a gradual onset of non-linear behavior, making the precise yield point difficult to determine. In such a case, the offset yiel ...
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Yield Surface
A yield surface is a five-dimensional surface in the six-dimensional space of stresses. The yield surface is usually convex and the state of stress of ''inside'' the yield surface is elastic. When the stress state lies on the surface the material is said to have reached its yield point and the material is said to have become plastic. Further deformation of the material causes the stress state to remain on the yield surface, even though the shape and size of the surface may change as the plastic deformation evolves. This is because stress states that lie outside the yield surface are non-permissible in rate-independent plasticity, though not in some models of viscoplasticity.Simo, J. C. and Hughes, T,. J. R., (1998), Computational Inelasticity, Springer. The yield surface is usually expressed in terms of (and visualized in) a three-dimensional principal stress space ( \sigma_1, \sigma_2 , \sigma_3), a two- or three-dimensional space spanned by stress invariants ( I_1, J_2, J_3 ...
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Hill Yield Criteria
The Hill yield criterion developed by Rodney Hill, is one of several yield criteria for describing anisotropic plastic deformations. The earliest version was a straightforward extension of the von Mises yield criterion and had a quadratic form. This model was later generalized by allowing for an exponent ''m''. Variations of these criteria are in wide use for metals, polymers, and certain composites. Quadratic Hill yield criterion The quadratic Hill yield criterion has the form : F(\sigma_-\sigma_)^2 + G(\sigma_-\sigma_)^2 + H(\sigma_-\sigma_)^2 + 2L\sigma_^2 + 2M\sigma_^2 + 2N\sigma_^2 = 1 ~. Here ''F, G, H, L, M, N'' are constants that have to be determined experimentally and \sigma_ are the stresses. The quadratic Hill yield criterion depends only on the deviatoric stresses and is pressure independent. It predicts the same yield stress in tension and in compression. Expressions for ''F'', ''G'', ''H'', ''L'', ''M'', ''N'' If the axes of material anisotropy are assum ...
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R-value (plasticity)
R-value or rvalue may refer to: * R-value (insulation) in building engineering, the efficiency of insulation of a house * R-value (soils) in geotechnical engineering, the stability of soils and aggregates for pavement construction * R-factor (crystallography), a measure of the agreement between the crystallographic model and the diffraction data * ''R''0 or ''R'' number, the basic reproduction number in epidemiology * In computer science, a pure value which cannot be assigned to * In statistics, the Pearson product-moment correlation coefficient, or simply ''correlation coefficient'' * In solid mechanics, the Lankford coefficient See also * L-value (other) * R rating (other) * R-factor Plasmid-mediated resistance is the transfer of antibiotic resistance genes which are carried on plasmids. Plasmids possess mechanisms that ensure their independent replication as well as those that regulate their replication number and guarantee st ...

Body-centered Cubic
In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals. There are three main varieties of these crystals: *Primitive cubic (abbreviated ''cP'' and alternatively called simple cubic) *Body-centered cubic (abbreviated ''cI'' or bcc) *Face-centered cubic (abbreviated ''cF'' or fcc, and alternatively called ''cubic close-packed'' or ccp) Each is subdivided into other variants listed below. Although the ''unit cells'' in these crystals are conventionally taken to be cubes, the primitive unit cells often are not. Bravais lattices The three Bravais lattices in the cubic crystal system are: The primitive cubic lattice (cP) consists of one lattice point on each corner of the cube; this means each simple cubic unit cell has in total one lattice point. Each atom at a lattice point is then shared equally between eight adjacent cubes, ...
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Von Mises Yield Criterion
The maximum distortion criterion (also von Mises yield criterion) states that yielding of a ductile material begins when the second invariant of deviatoric stress J_2 reaches a critical value. It is a part of plasticity theory that mostly applies to ductile materials, such as some metals. Prior to yield, material response can be assumed to be of a nonlinear elastic, viscoelastic, or linear elastic behavior. In materials science and engineering von Mises yield criterion is also formulated in terms of the von Mises stress or equivalent tensile stress, \sigma_\text. This is a scalar value of stress that can be computed from the Cauchy stress tensor. In this case, a material is said to start yielding when the von Mises stress reaches a value known as yield strength, \sigma_\text. The von Mises stress is used to predict yielding of materials under complex loading from the results of uniaxial tensile tests. The von Mises stress satisfies the property where two stress states with equa ...
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Hill Yield Criteria
The Hill yield criterion developed by Rodney Hill, is one of several yield criteria for describing anisotropic plastic deformations. The earliest version was a straightforward extension of the von Mises yield criterion and had a quadratic form. This model was later generalized by allowing for an exponent ''m''. Variations of these criteria are in wide use for metals, polymers, and certain composites. Quadratic Hill yield criterion The quadratic Hill yield criterion has the form : F(\sigma_-\sigma_)^2 + G(\sigma_-\sigma_)^2 + H(\sigma_-\sigma_)^2 + 2L\sigma_^2 + 2M\sigma_^2 + 2N\sigma_^2 = 1 ~. Here ''F, G, H, L, M, N'' are constants that have to be determined experimentally and \sigma_ are the stresses. The quadratic Hill yield criterion depends only on the deviatoric stresses and is pressure independent. It predicts the same yield stress in tension and in compression. Expressions for ''F'', ''G'', ''H'', ''L'', ''M'', ''N'' If the axes of material anisotropy are assum ...
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Hosford Aniso Plane Stress
Hosford (also spelled ''Horsford'') is a name of English origin. It may refer to: People *Chauncey Hosford, Oregon pioneer. *Edward Columbus Hosford, American architect *Henry Hosford Gurley, Congressman from Louisiana *Kyle Hosford, Irish basketball player *Robert Flournoy Hosford, Florida politician Other *Hosford-Abernethy, Portland, Oregon, a neighborhood *Hosford yield criterion, a physics equation *John Hosford House, a historic building in Ohio *Hosford, Florida Hosford is an unincorporated community and census-designated place in Liberty County, Florida, United States. Its population was 650 as of the 2010 census. It is located at the junction of State Road 20 and State Road 65. Hosford has a post of ...