Abstract
The Poisson's ratio of a material is strictly defined only for small strain linear elastic behavior. In practice, engineering strains are often used to calculate Poisson's ratio in place of the mathematically correct true strains with only very small differences resulting in the case of many engineering amterials. The engineering strain definition is often used even in the inelastic region, for example, in metals during plastic yielding. However, for highly nonlinear elastic materials, such as many biomaterials, smart materials and microstructured materials, this convenient extension may be misleading, and it becomes advantageous to define a strainvarying Poisson's function. This is analogous to the use of a tangent modulus for stiffness. An important recent application of such a Poisson's function is that of auxetic materials that demonstrate a negative Poisson's ratio and are often highly strain dependent. In this paper, the importance of the use of a Poisson's function in appropriate circumstances is demonstrated. Interpretation methods for coping with error-sensitive data or small strains are also described.
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Abbreviations
- e :
-
engineering strain (also known as nominal or Cauchy)
- l 0 :
-
starting length
- l i :
-
length
- ε:
-
true strain (also known as Hencky strain)
- εint :
-
instantaneous true strain
- εlog :
-
log transform true strain
- εtot :
-
total instantaneous true strain
- ν:
-
Poisson's ratio or function
- νeng :
-
Poisson's ratio (engineering strain)
- νint :
-
Poisson's ratio (instantaneous true strain)
- νlog :
-
Poisson's ratio (log transform true strain)
- νtot :
-
Poisson's function (total instantaneous true strain)
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Smith, C.W., Wootton, R.J. & Evans, K.E. Interpretation of experimental data for Poisson's ratio of highly nonlinear materials. Exp Mech 39, 356–362 (1999). https://doi.org/10.1007/BF02329817
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DOI: https://doi.org/10.1007/BF02329817