Development of a rheological constitutive relation for a soft biological tissue

A rheological constitutive relation in shear for an apple cortex tissue has been developed based upon creep experiments on solid cylindrical samples of the soft tissue obtained from a specified location of the apple and subjected to constant torques of various magnitudes and duration using a specially developed multiaxial loading device. Results indicate that the material displays non-linear viscoelastic properties which can be characterized by a multiple integral relation between the torque and the unit angle of twist. Using this relation the creep response of the material under two step and three step torque histories and the history with torque linearly varying with time was predicted and found to agree well with experimental results. Finally, the paper describes a method for obtaining the constitutive relation in shear from the developed unit angle of twist-torque equation. The shear constitutive relation for the tissue has been found to be of the integral type with two kernal functions specifying the rheological response.