Hi Jorgen,

First, thank you very much for providing such a professional platform for material modeling discussions. This is almost the only one that can provide useful information. Your kindness and expertise are greatly appreciated.

I have a few questions about biaxial test on soft tissue. Generally, for a biaxial test we can assume homogeneous deformation mode in the central region of the specimen as following

x1=lambda1*X1+kappa1*X2

x2=lambda2*X2+kappa2*X1

x3=lambda3*X3

So the deformation gradient F can be written as F=:

lambda1, kappa1, 0

kappa2, lambda1,0

0,0,lambda3

The Green-Lagrange strain can be calculated as:

E11=(lambda1^2+kappa2^2-1)/2

E22=(lambda2^2+kappa1^2-1)/2

E12=(lambda1*kappa1+lambda2*kappa2)/2

In biaxial test, if the specimen is stretched simultaneously and symmetrically along the two orthogonal directions, then it is reasonable to assume that the in-plane shearing is negligible.

[B]Now my question is about the exact meaning of negligible in-plane shearing. Specifically, it refers to

(1) E12=0 ?

or

(2) kappa1=0 and kappa2=0?[/B]

If it were the case of (1), then kappa1 and kappa2 are not necessarily be zero. Therefore even though the Lagrange stress P12=0, the true stress (sigma12) and 2nd P-K stress (S12) will not be zero. Is this correct mathematical description for symmetric biaxial testing?

If it were case (2), i.e., kappa1=kappa2=0, then E12=0, sigma12=S12=0. Is this correct description for biaxial testing?

[COLOR=Red]In summary, my first question is: between (1) and (2), which is the correct description of biaxial stretching test?[/COLOR]