From Wikipedia, the free encyclopedia
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.
Response
models
There are three models that describe how a solid responds to an
applied stress:
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.
- 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.
- 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.
- 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.
See also
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.