Yield Surface
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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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Solid Mechanicss
Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structural rigidity and resistance to a force applied to the surface. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire available volume like a gas. The atoms in a solid are bound to each other, either in a regular geometric lattice (crystalline solids, which include metals and ordinary ice), or irregularly (an amorphous solid such as common window glass). Solids cannot be compressed with little pressure whereas gases can be compressed with little pressure because the molecules in a gas are loosely packed. The branch of physics that deals with solids is called solid-state physics, and is the main branch of condensed matter physics (which also includes liquids). Materials sc ...
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Tresca Guest Yield Surface 3D
Tresca may refer to: * Carlo Tresca (1879–1943), Italian-born American anarchist * Henri Tresca (1814–1885), French mechanical engineer {{surname ...
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Drucker Prager
Drucker (; {{IPA-de, ˈdʁʊkɐ, lang) is a surname of German and Jewish origin, and may refer to: Surname *Adam Drucker (born 1977), American rapper and poet, known by the stage name Doseone *Adolphus Drucker (1868–1903), Dutch-born English politician * Amy Drucker (1873–1951), British artist * Daniel C. Drucker (1918–2001), American engineer and academic * Daniel J. Drucker (born 1956), Canadian endocrinologist *Gerald Drucker (1925–2010), British bassist and photographer * Iosif Druker (1822–1879), Russian Jewish violin virtuoso, known by the popular name Stempenyu *Itzhak Drucker (born 1947), Israeli footballer *Léa Drucker (born 1972), French actress * Leon Drucker (born 1961), American bassist, known by the stage name of Lee Rocker, son of Stanley * Leopold Drucker (1903–1988), Austrian footballer and coach * Linda Ryke-Drucker, American poker player * Hendrik Lodewijk Drucker (1857–1917), Dutch politician * Jason Drucker (born 2005), American child actor * Jean ...
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MH Surface 2D
MH or mH may refer to: Businesses and organizations * Malaysia Airlines, by IATA airline designator * Menntaskólinn við Hamrahlíð, a gymnasium in Reykjavík, Iceland * Miami Heat, an NBA basketball team Places * Mahalle, (abbreviated mh. on maps) a Turkish residential district * Maharashtra, a state of western India (ISO 3166-2 code MH) * Marshall Islands (ISO 3166-1 alpha-2 country code and postal symbol MH) * County Meath, Ireland (code MH) * Montserrat (FIPS PUB 10-4 territory code MH) People Politics * Mohammad Hatta, 1st Vice President of Indonesia, 3rd Prime Minister of Indonesia, 4th Minister of Defense of Indonesia and 4th Foreign Minister of Indonesia Musicians * Michael Hutchence, frontman and lead singer of Australian rock band INXS Technologists * Michael Hood, internet researcher Science and technology * .mh, the Internet country code top-level domain for Marshall Islands * Malignant hyperthermia, in medicine * Masked hypertension, the phenomenon whe ...
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MH Yield Surface 3D
MH or mH may refer to: Businesses and organizations * Malaysia Airlines, by IATA airline designator * Menntaskólinn við Hamrahlíð, a gymnasium in Reykjavík, Iceland * Miami Heat, an NBA basketball team Places * Mahalle, (abbreviated mh. on maps) a Turkish residential district * Maharashtra, a state of western India (ISO 3166-2 code MH) * Marshall Islands (ISO 3166-1 alpha-2 country code and postal symbol MH) * County Meath, Ireland (code MH) * Montserrat (FIPS PUB 10-4 territory code MH) People Politics * Mohammad Hatta, 1st Vice President of Indonesia, 3rd Prime Minister of Indonesia, 4th Minister of Defense of Indonesia and 4th Foreign Minister of Indonesia Musicians * Michael Hutchence, frontman and lead singer of Australian rock band INXS Technologists * Michael Hood, internet researcher Science and technology * .mh, the Internet country code top-level domain for Marshall Islands * Malignant hyperthermia, in medicine * Masked hypertension, the phenomenon whe ...
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Granular Material
A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact (the most common example would be friction when grains collide). The constituents that compose granular material are large enough such that they are not subject to thermal motion fluctuations. Thus, the lower size limit for grains in granular material is about 1 μm. On the upper size limit, the physics of granular materials may be applied to ice floes where the individual grains are icebergs and to asteroid belts of the Solar System with individual grains being asteroids. Some examples of granular materials are snow, nuts, coal, sand, rice, coffee, corn flakes, fertilizer, and bearing balls. Research into granular materials is thus directly applicable and goes back at least to Charles-Augustin de Coulomb, whose law of friction was originally stated for granular materials. Granular materials are commercially important in applicat ...
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Soil
Soil, also commonly referred to as earth or dirt, is a mixture of organic matter, minerals, gases, liquids, and organisms that together support life. Some scientific definitions distinguish ''dirt'' from ''soil'' by restricting the former term specifically to displaced soil. Soil consists of a solid phase of minerals and organic matter (the soil matrix), as well as a porous phase that holds gases (the soil atmosphere) and water (the soil solution). Accordingly, soil is a three-state system of solids, liquids, and gases. Soil is a product of several factors: the influence of climate, relief (elevation, orientation, and slope of terrain), organisms, and the soil's parent materials (original minerals) interacting over time. It continually undergoes development by way of numerous physical, chemical and biological processes, which include weathering with associated erosion. Given its complexity and strong internal connectedness, soil ecologists regard soil as an ecosystem. Most ...
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Concrete
Concrete is a composite material composed of fine and coarse aggregate bonded together with a fluid cement (cement paste) that hardens (cures) over time. Concrete is the second-most-used substance in the world after water, and is the most widely used building material. Its usage worldwide, ton for ton, is twice that of steel, wood, plastics, and aluminum combined. Globally, the ready-mix concrete industry, the largest segment of the concrete market, is projected to exceed $600 billion in revenue by 2025. This widespread use results in a number of environmental impacts. Most notably, the production process for cement produces large volumes of greenhouse gas emissions, leading to net 8% of global emissions. Other environmental concerns include widespread illegal sand mining, impacts on the surrounding environment such as increased surface runoff or urban heat island effect, and potential public health implications from toxic ingredients. Significant research and development is ...
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Mohr–Coulomb Theory
Mohr–Coulomb theory is a mathematical model (see yield surface) describing the response of brittle materials such as concrete, or rubble piles, to shear stress as well as normal stress. Most of the classical engineering materials follow this rule in at least a portion of their shear failure envelope. Generally the theory applies to materials for which the compressive strength far exceeds the tensile strength. In geotechnical engineering it is used to define shear strength of soils and rocks at different effective stresses. In structural engineering it is used to determine failure load as well as the angle of fracture of a displacement fracture in concrete and similar materials. Coulomb's friction hypothesis is used to determine the combination of shear and normal stress that will cause a fracture of the material. Mohr's circle is used to determine which principal stresses will produce this combination of shear and normal stress, and the angle of the plane in which t ...
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Tresca Stress 2D
Tresca may refer to: * Carlo Tresca (1879–1943), Italian-born American anarchist * Henri Tresca (1814–1885), French mechanical engineer {{surname ...
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Mises Yield Surface 3D
Mises or von Mises may refer to: * Ludwig von Mises, an Austrian-American economist of the Austrian School, older brother of Richard von Mises ** Mises Institute, or the Ludwig von Mises Institute for Austrian Economics, named after Ludwig von Mises * Richard von Mises, an Austrian-American scientist and mathematician, younger brother of Ludwig von Mises ** Von Mises distribution, named after Richard von Mises ** Von Mises yield criterion, named after Richard von Mises * ''Dr. Mises'', pseudonym of Gustav Fechner, a German philosopher, physicist and experimental psychologist. {{DEFAULTSORT:Mises, von Jewish surnames Austrian noble families ...
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