Anelasticity

Anelasticity is a property of materials that describes their behaviour when undergoing deformation. Its formal definition does not include the physical or atomistic mechanisms but still interprets the anelastic behaviour as a manifestation of internal relaxation processes. It's a special case of elastic behaviour. Considering first an ideal elastic material, Hooke's law defines the relation between stress and strain as: The constant is called the modulus of elasticity (or just modulus) while its reciprocal is called the modulus of compliance (or just compliance). There are three postulates that define the ideal elastic behaviour: (1) the strain response to each level of applied stress (or vice versa) has a unique equilibrium value; (2) the equilibrium response is achieved instantaneously; (3) the response is linear These conditions may be lifted in various combinations to describe different types of behaviour, summarized in the following table: Anelasticity is therefore by the existence of a part of time dependent reaction, in addition to the elastic one in the material considered. It is also usually a very small fraction of the total response and so, in this sense, the usual meaning of “anelasticity” as “without elasticity” is improper in a physical sense. The formal definition of linearity is: “If a given stress history produces the strain , and if a stress gives rise to , then the stress will give rise to the strain .” The postulate of linearity is used because of its practical usefulness. The theory would become much more complicated otherwise, but in cases of materials under low stress this postulate can be considered true. In general, the change of an external variable of a thermodynamic system causes a response from the system called thermal relaxation that leads it to a new equilibrium state. In the case of mechanical changes, the response is known as anelastic relaxation, and in the same formal way can be also described for example dielectric or magnetic relaxation.