Its formal definition does not include the physical or atomistic mechanisms but still interprets the anelastic behaviour as a manifestation of internal relaxation processes.
There are three postulates that define the ideal elastic behaviour: These conditions may be lifted in various combinations to describe different types of behaviour, summarized in the following table: (complete recoverability) Anelasticity is therefore by the existence of a part of time dependent reaction, in addition to the elastic one in the material considered.
So that the external manifestation of the internal relaxation behaviours is the stress strain relation, which in this case is time dependant.
These are called quasi-static, and in this case, anelastic materials exhibit creep, elastic aftereffect, and stress relaxation.
After a creep experiment has been run for a while, when stress is released the elastic spring-back is in general followed by a time dependent decay of the strain.
The ideal elastic solid returns to zero strain immediately, without any after-effect, while in the case of anelasticity total recovery takes time, and that is the aftereffect.
gives a measure of the fraction of energy lost per cycle due to anelastic behaviour, and so it is known as the internal friction of the material.
These can be divided into two categories: The response of a system in a forced-vibration experiment with a periodic force has a maximum of the displacement
falls to half maximum value, then: The loss angle that measures the internal friction can be obtained directly from the plot, since it is the width of the resonance peak at half-maximum.
The Boltzmann superposition principle states that every stress applied at a different time deforms the material as it if were the only one.
To obtain it the method of Laplace transforms can be used, or they can be related implicitly by: In this way though they are correlated in a complicated manner and it is not easy to evaluate one of these functions knowing the other.
The simplest one contains three elements (two springs and a dashpot) since that is the least number of parameters necessary for a stress–strain equation describing a simple anelastic solid.
This specific basic behaviour is of such importance that a material that exhibits it is called standard anelastic solid.
The most general one can be written as: For the specific case of anelasticity, which requires the existence of an equilibrium relation, additional restrictions must be placed on this equation.
To add internal friction to a model, the Newtonian dashpot is used, represented by a piston moving in an ideally viscous liquid.
However, taking a sample through a Debye peak by varying the frequency continuously is not possible with the more common resonance methods.
The next level of complexity in the description of an anelastic solid is a model containing n Voigt units in series with each other and with a spring.
Similarly, a model containing n Maxwell units all in parallel with each other and with a spring is also equivalent to a differential stress–strain equation of the same form.
The standard anelastic solid considered before is just a particular case of a one-line spectrum, that can be also called having a "single relaxation time".
Despite being historically uncommon, it has some great utility in solving practical problems regarding industrial production where knowledge and control of the microscopic structure of materials is becoming more and more important.
Unlike other chemical methods of analysis, mechanical spectroscopy is the only technique that can determine the quantity of interstitial elements in a solid solution.
Because of this, the octahedral positions stop being equivalent, and the larger ones will be occupied instead of the smallest ones, making the interstitial atom jump from one to the other.
By applying an alternating stress, the interstitial atom will keep jumping from one site to the other, in a reversible way, causing dissipation of energy and a producing a so-called Snoek peak.
Knowing the energy dissipation of a single event and the height of the Snoek peak can make possible to determine the concentration of atoms involved in the process.
High resolution microscopy show that material put under severe plastic deformation are characterized by significant distortions and dislocations over and near the grain boundaries.
Using steel AISI 304 as an example, an anomaly in the distribution of the elements in the alloy can cause a local increase in
, especially in areas with less nickel, and when usually martensite formation can only be induced by plastic deformation, around 9% can get formed anyway during cooling.
Ferromagnetic materials have specific anelastic effects that influence internal friction and dynamic modulus.
A non-magnetized ferromagnetic material forms Weiss domains, each one possessing a spontaneous and randomly directed magnetization.
The boundary zones, called Bloch walls, are about one hundred atoms long, and here the orientation of one domain gradually changes into the one of the adjacent one.