| Continuum mechanics |
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| Conservation of mass Conservation of momentum Navier–Stokes equations |
Solid mechanics is the branch of mechanics, physics, and mathematics that concerns the behavior of solid matter under external actions (e. Continuum mechanics is a branch of Mechanics that deals with the analysis of the Kinematics and mechanical behavior of materials modeled as a continuum e The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov - Lavoisier law says that the Mass of In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product The Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous Fluid substances such Mechanics ( Greek) is the branch of Physics concerned with the behaviour of physical bodies when subjected to Forces or displacements Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and g. , external forces, temperature changes, applied displacements, etc. In Physics, a force is whatever can cause an object with Mass to Accelerate. ). It is part of a broader study known as continuum mechanics. Continuum mechanics is a branch of Mechanics that deals with the analysis of the Kinematics and mechanical behavior of materials modeled as a continuum e
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 deformation, the proportion of deformation to original size is called strain. In Materials science, deformation is a change in the shape or size of an object due to an applied force. If the applied stress is sufficiently low (or the imposed strain is small enough), almost all solid materials behave in such a way that the strain is directly proportional to the stress; the coefficient of the proportion is called the modulus of elasticity or Young's modulus. An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically (i In Solid mechanics, Young's modulus (E is a measure of the Stiffness of an isotropic elastic material This region of deformation is known as the linearly elastic region.
Major topics
There are several standard models for how solid materials respond to stress:
- Elastic – Linearly elastic materials can be described by the linear elasticity equations. A material is said to be elastic if it deforms under stress (e Linear elasticity is the mathematical study of how solid objects deform and become internally stressed due to prescribed loading conditions A spring obeying Hooke's law is a one-dimensional linear version of a general elastic body. In Mechanics, and Physics, Hooke's law of elasticity is an approximation that states that the amount by which a material body is deformed (the By definition, when the stress is removed, elastic deformation is fully recovered.
- Viscoelastic – a material that is elastic, but also has damping: on loading, as well as on unloading, some work has to be done against the damping effects. Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Friction is the Force resisting the relative motion of two Surfaces in contact or a surface in contact with a fluid (e This work is converted in heat within the material. This results in a hysteresis loop in the stress–strain curve. A system with hysteresis can be summarised as a system that may be in any number of states independent of the inputs to the system
- Plastic – a material that, when the stress exceeds a threshold (yield stress), permanently changes its rest shape in response. The material commonly known as "plastic" is named after this property. Plastic is the general common term for a wide range of synthetic or semisynthetic organic solid materials suitable for the manufacture of industrial products Plastic deformation is not recovered on unloading, although generally the elastic deformation up to yield is.
One of the most common practical applications of Solid Mechanics is the Euler-Bernoulli beam equation. Euler-Bernoulli beam theory, or just beam theory, is a simplification of the linear Theory of elasticity which provides a means of calculating the load-carrying
Solid mechanics extensively uses tensors to describe stresses, strains, and the relationship between them. History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually
Typically, solid mechanics uses linear models to relate stresses and strains (see linear elasticity). The word linear comes from the Latin word linearis, which means created by lines. Linear elasticity is the mathematical study of how solid objects deform and become internally stressed due to prescribed loading conditions However, real materials often exhibit non-linear behavior. This article describes the use of the term nonlinearity in mathematics
For more specific definitions of stress, strain, and the relationship between them, see strength of materials. In Materials science, the strength of a material refers to the material's ability to resist an applied force
See also
References
- L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics: Theory of Elasticity Butterworth-Heinemann, ISBN 0-7506-2633-X
- J. Applied mechanics is a branch of the Physical sciences and the practical application of Mechanics. Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress. A thermoplastic is a Plastic that Melts to a liquid when heated and freezes to a Brittle, very Glassy state when cooled sufficiently Materials Science or Materials Engineering is an interdisciplinary field involving the properties of matter and its applications to various areas of Science and In Solid mechanics, the chord modulus is the slope of the chord drawn between any two specified points on the stress-strain curve Lev Davidovich Landau ( Russian language: Ле́в Дави́дович Ланда́у ( January 22, 1908 &ndash April 1, 1968 Evgeny Mikhailovich Lifshitz (Евгений Михайлович Лифшиц February 21 1915 &ndash October 29 1985) was a leading Soviet E. Marsden, T. J. Hughes, Mathematical Foundations of Elasticity, Dover, ISBN 0-486-67865-2
- P. C. Chou, N. J. Pagano, Elasticity: Tensor, Dyadic, and Engineering Approaches, Dover, ISBN 0-486-66958-0
- R. W. Ogden, Non-linear Elastic Deformation, Dover, ISBN 0-486-69648-0
- S. Timoshenko and J. N. Goodier," Theory of elasticity", 3d ed. , New York, McGraw-Hill, 1970.
- A. I. Lurie, "Theory of Elasticity", Springer, 1999.
- L. B. Freund, "Dynamic Fracture Mechanics", Cambridge University Press, 1990.
- R. Hill, "The Mathematical Theory of Plasticity", Oxford University, 1950.
- J. Lubliner, "Plasticity Theory", Macmillan Publishing Company, 1990.
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