Solid mechanics

Solid mechanics is the branch of 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.

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 Young's modulus. 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:

1. Hooke's law is a one-dimensional linear version of a general elastic body. By definition, when the stress is removed, elastic deformation is fully recovered.
2. hysteresis loop in the stress–strain curve.
3. plastic" is named after this property. 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.

Solid mechanics extensively uses tensors to describe stresses, strains, and the relationship between them.

Typically, solid mechanics uses linear models to relate stresses and strains (see linear elasticity). However, real materials often exhibit non-linear behavior.

For more specific definitions of stress, strain, and the relationship between them, please see strength of materials.

See also

• Applied mechanics
• Viscosity
• Thermoplasticity
• Materials science

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.