Plasticity (physics)
Deformation theory

There are several mathematical descriptions of plasticity. One is deformation theory (see e.g. Hooke's law) where the Cauchy stress tensor (of order d-1 in d dimensions) is a function of the strain tensor. Although this description is accurate when a small part of matter is subjected to increasing loading (such as strain loading), this theory cannot account for irreversibility.

Ductile materials can sustain large plastic deformations without fracture. However, even ductile metals will fracture when the strain becomes large enough—this is as a result of work hardening of the material, which causes it to become brittle. Heat treatment such as annealing can restore the ductility of a worked piece, so that shaping can continue.
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