The strain-energy density function of the urinary bladder.

In previous articles we proposed a finite deformation theory of the urinary bladder. The present paper is the third article in a series of these works. Our aim is to study more carefully the strain-energy density function W of the urinary bladder, because the determination of this function W is one of the central problems in the finite deformation theory of a hyperelastic continuum. We found that, except for an infinitesimally small deformation region where Hook's law is valid, the third term in W of the Valanis-Landel type takes much smaller values than the other two terms, so that this term can be neglected. Hence, the formula giving the true stress t1 for the uniaxial extension test is reduced to the same one as the true stress t for the equal-biaxial extension test. This may be useful in practical applications.