Hysteresivity
Hysteresivity derives from “hysteresis”, meaning “lag”. It is the tendency to react slowly to an outside force, or to not return completely to its original state. Whereas the area within a hysteresis loop represents energy dissipated to heat and is an extensive quantity with units of energy, the hysteresivity represents the fraction of the elastic energy that is lost to heat, and is an intensive property that is dimensionless.
Overview
When a force deforms a material it generates
In many inert and living materials, the relationship between elastic and frictional stresses turns out to be very nearly invariant (something unaltered by a transformation). In lung tissues, for example, the frictional stress is almost invariably between 0.1 and 0.2 of the elastic stress, where this fraction is called the hysteresivity, h, or, equivalently, the structural damping coefficient.[2] It is a simple phenomenological fact, therefore, that for each unit of peak elastic strain energy that is stored during a cyclic deformation, 10 to 20% of that elastic energy is taxed as friction and lost irreversibly to heat. This fixed relationship holds at the level of the whole lung[5] ,[6][7] isolated lung parenchymal tissue strips,[8] isolated smooth muscle strips,[2][9] and even isolated living cells.[10][11][12][13]
This close relationship between frictional and elastic stresses is called the structural damping law[1][2][4][14] or, sometimes, the constant phase model.[5] The structural damping law implies that frictional losses are coupled tightly to elastic stresses rather than to viscous stresses, but the precise molecular mechanical origin of this phenomenon remains unknown.[10][15] ' In
where:
- G*(f)= complex elastic modulus at frequency of oscillatory deformation, f
- G′ = the elastic modulus
- G′′ = the loss modulus
- j 2 = −1
This relationship can be rewritten as,
where:
- h = G′′/G′.
In systems conforming to the structural damping law, the hysteresivity h is constant with or insensitive to changes in oscillatory frequency, and the loss modulus G′′ (= hG′) becomes a constant fraction of the elastic modulus.
See also
References
- ^ ISSN 0022-460X.
- ^ PMID 2606848.
- ISSN 0033-5541.
- ^ PMID 5360349.
- ^ PMID 1537711.
- S2CID 12361807.
- ISSN 8750-7587.
- PMID 8482682.
- PMID 9018525.
- ^ S2CID 18895076.
- PMID 11580676.
- PMID 14682980.
- S2CID 39701905.
- ^ Fung Y. Biomechanics: Mechanical Properties of Living Tissues. New York:: Springer-Verlag, 1988.
- PMID 11007603.
Further reading
- Kaczka, David W.; Ingenito, Edward P.; Suki, Bela; Lutchen, Kenneth R. (1997-05-01). "Partitioning airway and lung tissue resistances in humans: effects of bronchoconstriction". Journal of Applied Physiology. 82 (5). American Physiological Society: 1531–1541. PMID 9134903.