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Tangent Modulus
{{Use dmy dates, date=November 2017 In solid mechanics, the tangent modulus is the slope of the stress– strain curve at any specified stress or strain. Below the proportional limit (the limit of the linear elastic regime) the tangent modulus is equivalent to Young's modulus. Above the proportional limit the tangent modulus varies with strain and is most accurately found from test data. The Ramberg–Osgood equation relates Young's modulus to the tangent modulus and is another method for obtaining the tangent modulus. The tangent modulus is useful in describing the behavior of materials that have been stressed beyond the elastic region. When a material is plastically deformed there is no longer a linear relationship between stress and strain as there is for elastic deformations. The tangent modulus quantifies the "softening" or "hardening" of material that generally occurs when it begins to yield. Although the material softens it is still generally able to sustain more load befor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 (mechanics), deformation under the action of forces, temperature changes, phase (chemistry), phase changes, and other external or internal agents. Solid mechanics is fundamental for civil engineering, civil, Aerospace engineering, aerospace, nuclear engineering, nuclear, Biomedical engineering, biomedical and mechanical engineering, for geology, and for many branches of physics and chemistry 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 prosthesis, dental prostheses and surgical implants. One of the most common practical applications of solid mechanics is the Euler–Bernoulli beam theory, Euler–Bernoulli beam equation. Solid mechanics extensively uses tensors to describe stresses, strains, and the r ... [...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] |
Strain (materials Science)
In mechanics, strain is defined as relative deformation, compared to a position configuration. 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. Strain has dimension of a length ratio, with SI base units of meter per meter (m/m). Hence strains are dimensionless and are usually expressed as a decimal fraction or a percentage. Parts-per notation is also used, e.g., parts per million or parts per billion (sometimes called "microstrains" and "nanostrains", respectively), corresponding to μm/m and nm/m. Strain can be formulated as the spatial derivative of displacement: \boldsymbol \doteq \cfrac\left(\mathbf - \mathbf\right) = \boldsymbol'- \boldsymbol, where is the identity tensor. The displacement of a body may be expressed in the form , where is the reference position of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Young's Modulus
Young's modulus (or the Young modulus) is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise. It is the modulus of elasticity for tension or axial compression. Young's modulus is defined as the ratio of the stress (force per unit area) applied to the object and the resulting axial strain (displacement or deformation) in the linear elastic region of the material. Although Young's modulus is named after the 19th-century British scientist Thomas Young, the concept was developed in 1727 by Leonhard Euler. The first experiments that used the concept of Young's modulus in its modern form were performed by the Italian scientist Giordano Riccati in 1782, pre-dating Young's work by 25 years. The term modulus is derived from the Latin root term '' modus'', which means ''measure''. Definition Young's modulus, E, quantifies the relationship between tensile or compressive stress \sigma (force per unit ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramberg–Osgood Relationship
The Ramberg–Osgood equation was created to describe the nonlinear relationship between stress and strain—that is, the stress–strain curve—in materials near their yield points. It is especially applicable to metals that ''harden'' with plastic deformation (see work hardening), showing a ''smooth'' elastic-plastic transition. As it is a phenomenological model, checking the fit of the model with actual experimental data for the particular material of interest is essential. Functional Relationship In its original form, the equation for strain (deformation) isRamberg, W., & Osgood, W. R. (1943). Description of stress–strain curves by three parameters. ''Technical Note No. 902'', National Advisory Committee For Aeronautics, Washington DC/ref> :\varepsilon = \frac + K \left(\frac \right)^ here : \varepsilon is strain, : \sigma is stress, : E is Young's modulus, and : K and n are constants that depend on the material being considered. In this form, and are not the same as t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buckling
In structural engineering, buckling is the sudden change in shape (Deformation (engineering), deformation) of a structural component under Structural load, load, such as the bowing of a column under Compression (physics), compression or the wrinkling of a plate under Shearing (physics), shear. If a structure is subjected to a gradually increasing load, when the load reaches a critical level, a member may suddenly change shape and the structure and component is said to have ''buckled''. Euler's critical load and Johnson's parabolic formula are used to determine the buckling stress of a column. Buckling may occur even though the Stress (mechanics), stresses that develop in the structure are well below those needed to cause Catastrophic failure, failure in the material of which the structure is composed. Further loading may cause significant and somewhat unpredictable deformations, possibly leading to complete loss of the member's load-carrying capacity. However, if the deformation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elasticity (physics)
In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to ''plasticity'', in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials. In metals, the Crystal structure, atomic lattice changes size and shape when forces are applied (energy is added to the system). When forces are removed, the lattice goes back to the original lower energy state. For rubber elasticity, rubbers and other polymers, elasticity is caused by the stretching of polymer chains when forces are applied. Hooke's law states that the force required to deform elastic objects should be Prop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ASTM
ASTM International, formerly known as American Society for Testing and Materials, is a standards organization that develops and publishes voluntary consensus technical international standards for a wide range of materials, products, systems and services. Some 12,575 apply globally. The headquarters is in West Conshohocken, Pennsylvania, about northwest of Philadelphia. It was founded in 1902 as the American Section of the International Association for Testing Materials. In addition to its traditional standards work, ASTM operates several global initiatives advancing additive manufacturing, advanced manufacturing, and emerging technologies, including the Additive Manufacturing Center of Excellence (AM CoE), the acquisition oWohlers Associatesfor market intelligence and advisory services, and the NIST-funded Standardization Center of Excellence (SCOE). History In 1898, a group of scientists and engineers, led by chemist, industry leader, and proponent of standardization Ch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
