Solid mechanics (also known as the theory of elasticity) is a branch of physics, which governs the response of solid material to applied stress (e.g., external forces). It is part of a broader study known as continuum mechanics.

There are several standard models for how solid materials respond to stress:

1. 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. A spring obeying Hooke's law is a one-dimensional linear version of a general elastic body.
2. Viscoelastic -- a material that is elastic, but also has damping.
3. 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.

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, true materials exhibit non-linear behavior.

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

References

• L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics: Theory of Elasticity Butterworth-Heinemann, ISBN 075062633X
• 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.