Déformation

Déformation, or deformation, is the change in the shape, size, orientation, or internal structure of a body caused by external forces, temperature changes, phase transitions, or other effects. In science and engineering it is studied to predict performance and failure. A related concept is strain, the quantitative measure of deformation relative to a reference state. Deformation can be elastic, reversible, or plastic, permanent.

In solid mechanics, the deformation is described by field quantities such as the deformation gradient and strain tensors. For small deformations, linear elasticity applies, with stress proportional to strain through elastic moduli (Hooke's law). Materials may undergo shear, tension, compression, or bending, and the outcome depends on material properties and loading conditions. Large deformations require nonlinear models and can involve rotation and geometry changes.

In fluid mechanics, deformation refers to the distortion of fluid elements as they move. The rate of deformation is captured by the rate-of-deformation tensor, derived from velocity gradients. Viscous forces convert deformation into stress, governing flow behavior in Newtonian and non-Newtonian fluids.

In geology, deformation describes how rocks distort under tectonic forces, producing structures such as faults, folds, and metamorphic textures. Deformation can be distributed or localized and may involve complex interactions between mechanical and thermal processes.

In mathematics, deformation theory studies continuous families of objects, such as complex structures or algebraic varieties, to understand how small changes propagate. It uses cohomology and obstruction theory to describe possible deformations and their limits.