Simple uniaxial and uniform biaxial deformation of nearly isotropic incompressible tissues.

A method is developed for analyzing in a unified manner both uniaxial and uniform biaxial strain data obtained from nearly isotropic tissues. The formulation is a direct application of nonlinear elasticity theory pertaining to large deformations. The general relation between Eulerian stress (sigma) and extension ratio (lambda) in soft isotropic elastic bodies undergoing uniform deformation takes the simple form: sigma = ((lambda(3) - 1)/lambda) f(lambda), where f(lambda) must be determined for each material. The extension ratio may be either greater than 1.0 (uniaxial elongation), or lie between zero and 1.0 (uniform biaxial extension). Simple analytical functions for f(lambda) are most readily found for each tissue by plotting all data as (lambda(3) - 1)/lambdasigma vs. lambda. Of those tissues investigated in this way (dog pericardium and pleura, and cat mesentery and dura), all but pleura could be adequately described by a parabola: 1/f(lambda) = 1/k{[(lambda(M) - lambda)(lambda - lambda(m))]/[lambda(M) - lambda(m)}. In these instances, three material constants per tissue (K, lambda(M), lambda(m)) served to predict approximately the stresses attained during both small and large deformations, in strips and sheets alike. It was further found that the uniaxial strain asymptote (lambda(M)) was linearly related to the biaxial strain asymptote (Lambda(M)), thus effectively reducing the number of constants by one.