Solid Mechanics

Solid mechanics, 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 the part of a broader study known as continuum mechanics. One common practical application of solid mechanics is the Euler-Bernoulli beam equation. Solid mechanics uses tensors to describe stresses, strains, and the relationship between them.

Response models

A material with a rest shape and its shape departs away from the rest shape due to stress. The amount that is departed from rest shape is called deformation; the proportion of deformation to original size is called strain. If the amount of 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.

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

• Elastically – When the applied stress is removed, the material returns to its undeformed state. Linearly elastic objects, those that deform proportionally to the applied load, can be described by the linear elasticity equations such as Hooke's law.
• Viscoelastically – These are the 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 the material response has time-dependence.
• Plastically – Materials that are to behave elastically generally do so when the applied stress is less than a yield value. When the amount of stress is greater than the yield stress, the material behaves plastically and does not return to its previous state. That is the deformation that occurs after yield is permanent.