Mechanical characterization of an incompressible, strain-hardening, transversely isotropic material.

A strain energy approach for the characterization of strain-hardening, transversely isotropic materials was developed and validated through a combination of indentation and uniaxial extension experiments. These experiments were utilized because they can also be applied to directly measure the mechanical properties of many living tissues, including muscle. Model materials with transversely isotropic mechanical properties broadly representative of biological tissues were utilized in the experiments. These organogels were made from acrylic triblock copolymer solutions with an aligned cylindrical domain morphology. The strain energy function used here was proposed recently by Hegde et al., and is based on the three independent linear elastic constants for a transversely isotropic material, along with two additional strain-hardening parameters. These five parameters were determined for the model material by indentation with a blade indenter aligned both parallel and perpendicular to the unique axis of the gel, and by uniaxial extension of the material along the directions parallel and perpendicular to the unique axis. The effect on the indentation curves of an applied tensile pre-stress applied along the unique axis was also investigated. Finite element modeling was used to generate interpolated functions that allow the elastic constants, along with their uncertainty, to be obtained from the experimental data in a straightforward manner. These parameters were then used to predict the wave speeds in pre-stressed material that would be measured by shear wave elastography, a commonly used technique for non-invasively characterizing the mechanical properties of biological tissues.