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Lode Coordinates
Lode coordinates (z,r,\theta) or Haigh–Westergaard coordinates (\xi,\rho,\theta).Menetrey, Philippe; Willam, K. J.; 1995, "Triaxial Failure Criterion for Concrete and its Generalization", ''Structural Journal'', American Concrete Institute, Volume 92, Issue 3, pages 311-318, DOI: 10.14359/1132 are a set of Invariants of tensors, tensor invariants that span the space of Real number, real, Symmetric tensor, symmetric, second-order, 3-dimensional tensors and are Isomorphism, isomorphic with respect to Stress space, principal stress space. This Right-hand rule, right-handed Orthogonality, orthogonal coordinate system is named in honor of the German scientist Dr. Walter Lode because of his seminal paper written in 1926 describing the effect of the middle principal stress on metal plasticity. Other examples of sets of tensor invariants are the set of principal stresses (\sigma_1, \sigma_2, \sigma_3) or the set of kinematic invariants (I_1, J_2, J_3). The Lode coordinate system can be d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Even And Odd Functions
In mathematics, an even function is a real function such that f(-x)=f(x) for every x in its domain. Similarly, an odd function is a function such that f(-x)=-f(x) for every x in its domain. They are named for the parity of the powers of the power functions which satisfy each condition: the function f(x) = x^n is even if ''n'' is an even integer, and it is odd if ''n'' is an odd integer. Even functions are those real functions whose graph is self-symmetric with respect to the and odd functions are those whose graph is self-symmetric with respect to the origin. If the domain of a real function is self-symmetric with respect to the origin, then the function can be uniquely decomposed as the sum of an even function and an odd function. Early history The concept of even and odd functions appears to date back to the early 18th century, with Leonard Euler playing a significant role in their formalization. Euler introduced the concepts of even and odd functions (using La ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henri Tresca
Henri Édouard Tresca (12 October 1814 – 21 June 1885) was a French mechanical engineer, and a professor at the Conservatoire National des Arts et Métiers in Paris. Work on plasticity He is the father of the field of plasticity, or non-recoverable deformations, which he explored in an extensive series of experiments begun in 1864. He stated one of the first criterion of material failure, that now bears his name. The criterion specifies that a material would flow plastically if \ \sigma_=\sigma_1-\sigma_3 > \sigma_ Tresca's criterion is one of two main failure criteria used today for ductile materials. The second important criterion is due to Richard von Mises. See comparison on the image left: Design of the International Prototype Metre Tresca was also among the designers of the prototype metre bar that served as the first standard of length for the metric system. After the Convention of the Metre had been signed in 1875, the International Bureau of Weights and Mea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stress (physics)
In continuum mechanics, stress is a physical quantity that describes Force, forces present during Deformation (physics), deformation. For example, an object being pulled apart, such as a stretched elastic band, is subject to Tension (physics), ''tensile'' stress and may undergo Elongation (materials science), elongation. An object being pushed together, such as a crumpled sponge, is subject to Compression (physics), ''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 (physics), dimension of force per area, with SI Units, SI units of newtons per square meter (N/m2) or Pascal (unit), pascal (Pa). Stress expresses the internal forces that neighbouring particles of a continuous material exert on each other, while Strain (mechanics), ''strain'' is the measure of the relative deformation (mechanics), deformation of the material. For example, when a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 resul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. For most metals, such as aluminium and cold-worked steel, there is a gradual onset of non-linear behavior, and no precise yield point. In such a case, the offset yield p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tresca Yield Criterion
A yield surface is a five-dimensional surface in the six-dimensional space of Stress (mechanics), stresses. The yield surface is usually convex polytope, 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 (engineering), yield point and the material is said to have become Plasticity (physics), 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 plasticity (physics), 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 Stress (physics)#Principal stresses ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
