Solid mechanics is the branch of physics and mathematics that concern the behavior of solid matter under external actions (e.g., external forces, temperature changes, applied displacements, etc.). It is part of a broader study known as continuum mechanics. Since antiquity, people have tried to understand the behavior of matter: why unsupported objects drop to the ground, why different materials have different properties, and so forth. ... Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations related to: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has media related to: Mathematics Interactive Mathematics Miscellany and Puzzles â A collection of articles on various math topics, with interactive Java... In physics, a force is an external cause responsible for any change of a physical system. ... Continuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i. ...
There are several standard models for how solid materials respond to stress:
Elastic – a material has a rest shape and its shape departs away from the rest shape due to stress. The amount of departure from rest shape is called strain, the departure itself is called deformation. The resistance to deformation is called Young's modulus. Linearly elastic materials can be described by the 3-dimensional elasticity equations. A spring obeying Hooke's law is a one-dimensional linear version of a general elastic body.
Plastic – a material that, when the stress exceeds a threshold, changes its rest shape in response. The material commonly known as "plastic" is named after this property.
See also viscosity and thermoplasticity. in Economics see elasticity (economics) in Materials Science the word elastomer refers to a material which is very elastic, like rubber. ... In any branch of science dealing with materials and their behaviour, strain is the geometrical expression of deformation caused by the action of stress on a physical body. ... In engineering mechanics, deformation is a change in shape due to an applied force. ... The modulus of elasticity can also be measured in other units of pressure, for example pounds per square inch (psi). ... 3-D elasticity is one of three methods of structural analysis. ... In physics, Hookes law of elasticity is an approximation which states that if a spring is elongated by some distance, x, the restoring force exherted by the spring, F, is proportional to x by a constant factor, k. ... A viscoelastic material is one in which: hysteresis is seen in the stress-strain curve. ... Friction is the force that opposes the relative motion or tendency of such motion of two surfaces in contact. ... In physics and materials science, plasticity is a property of a material to undergo a non-reversible change of shape in response to an applied force. ... Plastic is a term that covers a range of synthetic or semisynthetic polymerization products. ... The pitch drop experiment at the University of Queensland. ... A thermoplastic is a plastic that softens when heated and hardens again when cooled. ...
One of the most common practical applications of Solid Mechanics is the Euler-Bernoulli beam equation The elementary Euler-Bernoulli beam theory is a simplfication of the linear isotropic theory of elasticity which allows quick calculation of the load-carrying capacity and deflection of common structural elements called beams. ...
Solid mechanics extensively uses tensors to describe stresses, strains, and the relationship between them. In mathematics, a tensor is a certain kind of geometrical entity, or alternatively generalized quantity. The tensor concept includes the ideas of scalars, vectors, and linear operators. ...
Typically, solid mechanics uses linear models to relate stresses and strains (see linear elasticity). However, true materials exhibit non-linear behavior. The word linear comes from the Latin word linearis, which means created by lines. ... // Linear elasticity The linear theory of elasticity models the macroscopic mechanical properties of solids assuming small deformations. ... To do: 20th century mathematics chaos theory, fractals Lyapunov stability and non-linear control systems non-linear video editing See also: Aleksandr Mikhailovich Lyapunov Dynamical system External links http://www. ...
For more specific definitions of stress, strain, and the relationship between them, please see strength of materials. Strength of materials is the scientific area of applied mechanics for the study of the strength of engineering materials and their mechanical behavior in general (such as stress, deformation, strain and stress-strain relations). ...
J.E. Marsden, T.J. Hughes, Mathematical Foundations of Elasticity, Dover, ISBN 0486678652
P.C. Chou, N. J. Pagano, Elasticity: Tensor, Dyadic, and Engineering Approaches, Dover, ISBN 0486669580
R.W. Ogden, Non-linear Elastic Deformation, Dover, ISBN 0486696480
S. Timoshenko and J.N. Goodier," Theory of elasticity", 2d ed., New York, McGraw-Hill, 1951.
A.I. Lurie, "Theory of Elasticity", Springer, 1999.
L.B. Freund, "Dynamic Fracture Mechanics", Cambridge University Press, 1990.
R. Hiil, "The Mathematical Theory of Plasticity", Oxford University, 1950.
J. Lubliner, "Plasticity Theory", Macmillan Publishing Company, 1990.
Categories: Continuum mechanics | Structural engineering Image File history File links Wikibooks-logo-en. ... Wikibooks logo Wikibooks, previously called Wikimedia Free Textbook Project and Wikimedia-Textbooks, is a sister project to Wikipedia and is part of the Wikimedia Foundation, begun on July 10, 2003. ... Lev Davidovich Landau (ÐÐµÌÐ² ÐÐ°Ð²Ð¸ÌÐ´Ð¾Ð²Ð¸Ñ ÐÐ°Ð½Ð´Ð°ÌÑ) (January 22, 1908 â April 1, 1968) was a prominent Soviet physicist and winner of the Nobel Prize for Physics whose broad field of work included the theory of superconductivity and superfluidity, quantum electrodynamics, nuclear physics and particle physics. ... Evgeny Mikhailovich Lifshitz (ÐÐ²Ð³ÐµÐ½Ð¸Ð¹ ÐÐ¸Ñ Ð°Ð¹Ð»Ð¾Ð²Ð¸Ñ ÐÐ¸ÑÑÐ¸Ñ) (February 21, 1915 â October 29, 1985) was a Russian physicist. ...
Mechanics of Materials, Bedford, A. and Liechti, K. Mechanics of Materials, Beer, F. and Johnston E. Mechanics of Materials, Craig, R. Mechanics of Materials, Gere, J. Mechanics of Materials, Vol 1 and 2, Hearn, E. Mechanics of Materials, Hibbeler, R. Mechanics of Materials, Riley, W. et al., 1998
Mechanics of Solid Materials, Lemaitre, J. and Chaboche, J. Mechanics of Solids, Fenner, R. Mechanics of Solids, Lardner, T. and Archer, R. Mechanics of Solids, Ross, C. Mechanics of Solids and Fluids, Ziegler, F., 1995
Mechanics of Solids and Structures, Rees, D. Mesomechanical Constitutive Modeling, Kafka, V., 2001
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