Solid mechanics

Solid mechanics

Solid mechanics is the branch of mechanics, physics, and mathematics that concerns 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. One of the most common practical applications of solid mechanics is the Euler-Bernoulli beam equation. Solid mechanics extensively uses tensors to describe stresses, strains, and the relationship between them.

Relationship to continuum mechanics

As shown in the following table, solid mechanics inhabits a central place within continuum mechanics. The field of rheology presents an overlap between solid and fluid mechanics.

 Continuum mechanics The study of the physics of continuous materials Solid mechanics The study of the physics of continuous materials with a defined rest shape. Elasticity Describes materials that return to their rest shape after an applied stress. Plasticity Describes materials that permanently deform after a sufficient applied stress. Rheology The study of materials with both solid and fluid characteristics. Fluid mechanics The study of the physics of continuous materials which take the shape of their container. Non-Newtonian fluids Newtonian fluids

Response models

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. 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. This region of deformation is known as the linearly elastic region.

It is most common for analysts in solid mechanics to use linear material models, due to ease of computation. However, real materials often exhibit non-linear behavior. As new materials are used and old ones are pushed to their limits, non-linear material models are becoming more common.

There are three models that describe how a solid responds to an applied stress:

1. Elastically – When an applied stress is removed, the material returns to its undeformed state. Linearly elastic materials, those that deform proportionally to the applied load, can be described by the linear elasticity equations such as Hooke's law.
2. Viscoelastically – These are materials that behave elastically, but also have damping: when the stress is applied and removed, work has to be done against the damping effects and is converted in heat within the material resulting in a hysteresis loop in the stress–strain curve. This implies that the material response has time-dependence.
3. Plastically – Materials that behave elastically generally do so when the applied stress is less than a yield value. When the stress is greater than the yield stress, the material behaves plastically and does not return to its previous state. That is, deformation that occurs after yield is permanent.

References

• L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics: Theory of Elasticity Butterworth-Heinemann, ISBN 0-7506-2633-X
• J.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.

Wikimedia Foundation. 2010.

Look at other dictionaries:

• solid mechanics — solid mechanics, mechanics that deals with bodies at rest or in motion, as distinguished from fluid mechanics …   Useful english dictionary

• Mechanics — This article is about an area of scientific study. For other uses, see Mechanic (disambiguation). Mechanics (Greek Μηχανική) is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and… …   Wikipedia

• Mechanics — Me*chan ics, n. [Cf. F. m[ e]canique.] That science, or branch of applied mathematics, which treats of the action of forces on bodies. [1913 Webster] Note: That part of mechanics which considers the action of forces in producing rest or… …   The Collaborative International Dictionary of English

• Solid-state physics — Solid state physics, the largest branch of condensed matter physics, is the study of rigid matter, or solids. The bulk of solid state physics theory and research is focused on crystals, largely because the periodicity of atoms in a crystal mdash; …   Wikipedia

• mechanics — /meuh kan iks/, n. 1. (used with a sing. v.) the branch of physics that deals with the action of forces on bodies and with motion, comprised of kinetics, statics, and kinematics. 2. (used with a sing. v.) the theoretical and practical application …   Universalium

• Solid — Continuum mechanicsA solid object is in the states of matter characterized by resistance to deformation and changes of volume. At the microscopic scale, a solid has these properties : * The atoms or molecules that compose the solid are packed… …   Wikipedia

• Solid Body Picross — Infobox VG title= caption= developer= publisher=Nintendo designer= engine= released= 2009 genre=Nonogram modes=Single player ratings= platforms = Nintendo DS media= requirements= input= Solid Body Picross is a puzzle video game being made by… …   Wikipedia

• mechanics — Synonyms and related words: Newtonian physics, acoustics, aerophysics, applied physics, art, astrophysics, basic conductor physics, biophysics, chemical physics, craft, cryogenics, crystallography, cytophysics, electron physics, electronics,… …   Moby Thesaurus

• solids, mechanics of — ▪ physics Introduction       science concerned with the stressing (stress), deformation (deformation and flow), and failure of solid materials and structures.       What, then, is a solid? Any material, fluid or solid, can support normal forces.… …   Universalium

• Continuum mechanics — Continuum mechanics …   Wikipedia