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Large elastic strain - limits of Green strain

I am looking at problems of large deformation and large elastic strain in biological materials, using an analytical model that determines the current deformed state in a single step from the original undeformed state. The approach is to propose a strain energy function to allow the calculation of Piola-Kirchhoff 2 stresses which may then be converted to true Cauchy stresses via the usual mapping. Since I initially calculate PK2 stresses, the strain energy function must be a function of Green strain. However I am unclear as to the applicability of a function based on Green strain used in this way, since the stretch in a single analysis can be around 1.1 - 1.2, and Green strain will give quite different strain values, compared to say, logarithmic strain. Any thoughts or comments would be welcome.


Teng zhang's picture

We are taking the Continuum Mechanics course. There are many different types stress and strain measures. The problem should not be which types of strain measures to be used but be that choose the strain and stress which are pairs conjugate in power. For example, Cauchy stress/rate of deformation, PK2 stress/rate of green strain which I take from the book Nonlinear Finite Elements for Continua and Structures, with authors Ted Belytschko/Wing Kam Liu/Brian Moran, and more details can also be found in it. I have not finished the course and cannot give more sugestion in deepth. Hope this be a little usefull. I find that  Biswajit Banerjee  have post something related to your question whose link is as follows, which maybe helpful.

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