Continuum mechanics 
 Key topics  Conservation of mass Conservation of momentum NavierStokes equations  Classical mechanics  Stress · Strain · Tensor
 Solid mechanics  Solids · Elasticity Plasticity · Hooke's law Rheology · Viscoelasticity Continuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i. ...
Image File history File links File links The following pages link to this file: Bernoullis equation ...
The law of conservation of mass/matter, also known as law of mass/matter conservation (or the LomonosovLavoisier law), states that the mass of a closed system of substances will remain constant, regardless of the processes acting inside the system. ...
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ...
The NavierStokes equations, named after ClaudeLouis Navier and George Gabriel Stokes, are a set of equations which describe the motion of fluid substances such as liquids and gases. ...
Classical mechanics (also called Newtonian mechanics) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ...
Stress is a measure of force per unit area within a body. ...
This article is about the deformation of materials. ...
In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multidimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ...
Solid mechanics is the branch of physics and mathematics that concern the behavior of solid matter under external actions (e. ...
For other uses, see Solid (disambiguation). ...
Elasticity is a branch of physics which studies the properties of elastic materials. ...
Hookes law accurately models the physical properties of common mechanical springs for small changes in length. ...
Rheology is the study of the deformation and flow of matter under the influence of an applied stress. ...
Viscoelasticity, also known as anelasticity, describes materials that exhibit both viscous and elastic characteristics when undergoing plastic deformation. ...
 Fluid mechanics  Fluids · Fluid statics Fluid dynamics · Viscosity · Newtonian fluids NonNewtonian fluids Surface tension  Scientists  Newton · Stokes · others Fluid mechanics is the subdiscipline of continuum mechanics that studies fluids, that is, liquids and gases. ...
A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ...
Fluid statics (also called hydrostatics) is the science of fluids at rest, and is a subfield within fluid mechanics. ...
Fluid dynamics is the subdiscipline of fluid mechanics dealing with fluids (liquids and gases) in motion. ...
Viscosity is a measure of the resistance of a fluid to deform under shear stress. ...
A Newtonian fluid (named for Isaac Newton) is a fluid that flows like waterâ€”its shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. ...
A nonNewtonian fluid is a fluid in which the viscosity changes with the applied strain rate. ...
In physics, surface tension is an effect within the surface layer of a liquid that causes that layer to behave as an elastic sheet. ...
Sir Isaac Newton FRS (4 January 1643 â€“ 31 March 1727) [ OS: 25 December 1642 â€“ 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ...
Sir George Gabriel Stokes, 1st Baronet (13 August 1819â€“1 February 1903) was an Irish mathematician and physicist, who at Cambridge made important contributions to fluid dynamics (including the NavierStokes equations), optics, and mathematical physics (including Stokes theorem). ...
 This box: view • talk • edit  “plastic material” redirects here. For the material used in manufacturing, see plastic. In physics and materials science, plasticity is a property of a material to undergo a nonreversible change of shape in response to an applied force. For example, a solid piece of metal or plastic being bent or pounded into a new shape displays plasticity as permanent changes occur within the material itself. By contrast, a permanent crease in a sheet of paper or a reshaping of wet clay is due to a rearrangement of separate fibers or particles. In engineering, the transition from elastic behavior to plastic behavior is called yield. Look up plasticity in Wiktionary, the free dictionary. ...
This article or section does not cite any references or sources. ...
This is a discussion of a present category of science. ...
The Materials Science Tetrahedron, which often also includes Characterization at the center Materials science or Materials Engineering is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering. ...
Yield strength, or the yield point, is defined in engineering and materials science as the stress at which a material begins to plastically deform. ...
Explanation
For many ductile metals, tensile loading applied to a sample will cause it to behave in an elastic manner. Each increment of load is accompanied by a proportional increment in extension, and when the load is removed, the piece returns exactly to its original size. However, once the load exceeds some threshold (the yield strength), the extension increases more rapidly than in the elastic region, and when the load is removed, some amount of the extension remains. A generic graph displaying this behavior is below. Ductility is the physical property of being capable of sustaining large plastic deformations without fracture (in metals, such as being drawn into a wire). ...
This article does not cite any references or sources. ...
Look up elastic in Wiktionary, the free dictionary. ...
Yield strength, or the yield point, is defined in engineering and materials science as the stress at which a material begins to plastically deform. ...
Plasticity is a property of materials to undergo large deformation without fracture. This is found in most metals, and in general is a good description of a large class of materials. Perfect plasticity is a property of materials to undergo large shear deformation without any increase of (shear) stress. Plastic materials that are not perfectly plastic are viscoplastic. Microscopically, plasticity is a consequence of dislocations. In materials science, a dislocation is a crystallographic defect, or irregularity, within a crystal structure. ...
Mathematical descriptions of Plasticity Deformation theory There are several mathematical descriptions of Plasticity. One is deformation theory (see e.g. Hooke's law) where the stress tensor (of order d in d dimensions) is a function of the strain tensor. Although this description is accurate when a small part of matter is subjected to increasing loading (such as strain loading), this theory can not account for irreversibility. Hookes law accurately models the physical properties of common mechanical springs for small changes in length. ...
Generic stressstrain graph for a ductile material. ...
The image above represents a shear stress component with respect to a shear strain component, under increasing strain loading. Ductile materials can sustain large plastic deformations without fracture. However, even ductile metals will fracture when the strain becomes large enough  this is as a result of workhardening of the material, which causes it to become brittle. Heat treatment such as annealing can restore the ductility of a worked piece, so that shaping can continue. Ductility is the physical property of being capable of sustaining large plastic deformations without fracture (in metals, such as being drawn into a wire). ...
In physics and materials science, plasticity is a property of a material to undergo a nonreversible change of shape in response to an applied force. ...
For fractures in geologic formations, see Rock fracture. ...
This article is about the deformation of materials. ...
A material is brittle if it is subject to fracture when subjected to stress i. ...
Heat treatment is a method used to alter the physical, and sometimes chemical, properties of a material. ...
Annealing, in metallurgy and materials science, is a heat treatment wherein a material is altered, causing changes in its properties such as strength and hardness. ...
Ductility is the physical property of being capable of sustaining large plastic deformations without fracture (in metals, such as being drawn into a wire). ...
Flow plasticity theory In 1934, Egon Orowan, Michael Polanyi and Geoffrey Ingram Taylor, roughly simultaneously, realized that the plastic deformation of ductile materials could be explained in terms of the theory of dislocations. The more correct mathematical theory of plasticity, flow plasticity theory, uses a set of nonlinear, nonintegrable equations to describe the set of changes on strain and stress with respect to a previous state and a small increase of deformation. Egon Orowan (in Hungarian Orován Egon) (August 2, 1901 — August 3, 1989) was an Hungarian/US physicist and metallurgist. ...
Michael Polanyi (born PolÃ¡nyi MihÃ¡ly) (March 11, 1891 â€“ February 22, 1976) was a Hungarianâ€“British polymath whose thought and work extended across physical chemistry, economics, and philosophy. ...
Sir Geoffrey Ingram Taylor (7 March 1886  27 June 1975) was a physicist, mathematician and expert on fluid dynamics and wave theory. ...
Elastic vs plastic failure If the stress exceeds a critical value, as was mentioned above, the material will undergo plastic, or irreversible, deformation. This critical stress can be tensile or compressive.
Tresca Criterion This criterion is based on the notion that when a material fails, it does so in shear, which is a relatively good assumption when considering metals. Given the principal stress state, we can use Mohr’s Circle to solve for the maximum shear stresses our material will experience and conclude that the material will fail if: σ_{1}  σ_{3} ≥ σ_{0} Where σ_{1} is the maximum normal stress, σ_{3} is the minimum normal stress, and σ_{0} is the stress under which the material fails in uniaxial loading. A yield surface may be constructed, which provides a visual representation of this concept. Inside of the yield surface, deformation is elastic. Outside of the surface, deformation is plastic. See Henri Tresca. Henri Tresca (1814â€“1884) was French Mechanical Engineer, professor of Conservatoire National des Arts et MÃ©tiers in Paris. ...
Von Mises Criterion This criterion is based on the Tresca criterion but takes into account the assumption that hydrostatic stresses do not contribute to material failure. Von Mises solves for an effective stress under uniaxial loading, subtracting out hydrostatic stresses, and claims that all effective stresses greater than that which causes material failure in uniaxial loading will result in plastic deformation. σ_{effective}² = 1/2 ((σ_{11} – σ_{22})² + (σ_{22} – σ_{33})² + (σ_{11} – σ_{33})²) + 3 (σ_{12}² + σ_{13}² + σ_{23}²) Again, a visual representation of the yield surface may be constructed using the above equation, which takes the shape of an ellipse. Inside the surface, materials undergo elastic deformation. Outside of the surface they undergo plastic deformation. See Von Mises stress Von Mises stress, , or simply Mises stress, is a scalar function of the components of the stress tensor that gives an appreciation of the overall magnitude of the tensor. ...
Atomic Mechanisms Slip Systems Crystalline materials contain uniform planes of atoms organized with longrange order. Planes may slip past each other along their closepacked directions, as is shown on the slip systems wiki page. The result is a permanent change of shape within the crystal and plastic deformation. The presence of dislocations increases the likelihood of planes slipping.
Shear Banding The presence of other defects within a crystal may entangle dislocations or otherwise prevent them from gliding. When this happens, plasticity is localized to particular regions in the material. For crystals, these regions of localized plasticity are called shear bands.
Crazing In amorphous materials, the discussion of “dislocations” is inapplicable, since the entire material lacks long range order. These materials can still undergo plastic deformation. Since amorphous materials, like polymers, are not wellordered, they contain a large amount of free volume, or wasted space. Pulling these materials in tension opens up these regions and can give materials a hazy appearance. This haziness is the result of crazing, where fibrils are formed within the material in regions of high hydrostatic stress. The material may go from an ordered appearance to a "crazy" pattern of strain and stretch marks.jkæ'
Martensitic materials Some materials, especially those prone to Martensitic transformations, deform in ways that are not well described by the classic theories of plasticity and elasticity. One of the bestknown examples of this is nitinol, which exhibits pseudoelasticity: deformations which are reversible in the context of mechanical design, but irreversible in terms of thermodynamics. Martensite in AISI 4140 steel 0. ...
A shape memory alloy (SMA) (also known as memory metal or smart wire) is a metal that remembers its geometry. ...
Nonequilibrium thermodynamics is a branch of thermodynamics concerned with studying timedependent thermodynamic systems, irreversible transformations and open systems. ...
Thermodynamics (from the Greek Î¸ÎµÏÎ¼Î·, therme, meaning heat and Î´Ï…Î½Î±Î¼Î¹Ï‚, dunamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ...
Cellular materials These materials plastically deform when the bending moment exceeds the fully plastic moment. This applies to open cell foams where the bending moment is exerted on the cell walls. The foams can be made of any material with a plastic yield point which includes rigid polymers and metals. This method of modeling the foam as beams is only valid if the ratio of the density of the foam to the density of the mater is less than 0.3. This is because beams yield axially instead of bending. In closed cell foams, the yield strength is increased if the material is under tension because of the membrane that spans the face of the cells.
See also The Liquid Limit, also known as the upper plastic limit, and the Atterberg limit, is the water content at which a soil changes from the liquid state to a plastic state. ...
A plastometer is a tool used to determine the flow properties of plastic materials. ...
References  R. Hill, The Mathematical Theory of Plasticity, Oxford University Press (1998).
 Jacob Lubliner, Plasticity Theory, Macmillan Publishing, New York (1990).
 L. M. Kachanov, Fundamentals of the Theory of Plasticity, Dover Books.
 A.S. Khan and S. Huang, Continuum Theory of Plasticity, Wiley (1995).
 J. C. Simo, T. J. Hughes, Computational Inelasticity, Springer.
 M. F. Ashby. Plastic Deformation of Cellular Materials. Encyclopedia of Materials: Science and Technology, Elsevier, Oxford, 2001, Pages 70687071.
 Van Vliet, K. J., 3.032 Mechanical Behavior of Materials, MIT (2006)
