Experimental characterization and application of thermodynamically consistent viscoelastic models to describe the behavior of collagen dermal grafts

The mechanical behavior of collagen dermal grafts is nonlinear viscoelastic rather than elastic and a full description of the response to load requires a viscoelastic material model which is built on firm theoretical and experimental foundations. Experimentally, the mechanical behavior of dermal grafts has been studied using uniaxial and equibiaxial viscoelastic tests. In a uniaxial test, the instantaneous elastic response of the material and the subsequent relaxation behavior have been investigated by applying a step-like stretch fast enough to preclude the simultaneous stress relaxation and thereby allow separation of elastic and viscous responses of the material. The elastic response of dermal grafts is nonlinear with a highly compliant region followed by a stiff 'linear' region. In the highly compliant region the deformation is the result of a progressive reorientation of collagen fibers inside the fluid saturated glycosaminoglycan (GAG) matrix, whereas in the stiff linear region, collagen fibril extension is the principal mode of deformation.In the stress relaxation phase of the uniaxial test, the specimen was held at a constant strain while simultaneously measuring the change in stress. It was observed that rapid stress relaxation in dermal grafts generally occur within 10 to 12 seconds of the hold strain and a steady-state stress is reached in less than 3 minutes. In addition, the relaxation modulus and relaxation rates depend on strain level implying the presence of considerable viscoelastic nonlinearity that cannot be described by linear ad-hoc type constitutive theories.This work has considered three thermodynamically consistent constitutive theories to describe the experimentally observed behavior of dermal grafts. The quasilinear viscoelastic model (or QLV) has been shown to describe the strain dependent relaxation stress fairly well. However, the relaxation rate predicted by the QLV theory is significantly slower than what was actually observed during relaxation tests. The non-equilibrium thermoviscoelastic model predicted the relaxation and creep behaviors of dermal grafts from the same set of experimental data. The resulting model prediction agrees reasonably well with the long term relaxation and creep behaviors, but falls short in predicting the transient response. We have pointed out that such disparity in the transient response prediction can be alleviated by making the constants ksigma and klambda to vary with time rather than keeping them constant. Schapery's nonlinear constitutive theory, which is founded on the principle of irreversible thermodynamics, was able to describe the viscoelastic nonlinearity of dermal grafts in a much superior way than both thermoviscoelastic and quasilinear theories. The predictions are accurate in both stress and stress-relaxation rate.The thermodynamic consistency of these models arises from the fact that, given a set of data, they can be extended to include such state variables as temperature and humidity, which generally play a considerable role in defining the mechanical behavior of dermal grafts. Ad-hoc spring and dashpot models are not readily adaptable to provide such a robust mechanical description.Finally, a bubble-inflation test (or bulge test) has been carried out to investigate the equibiaxial stress-strain behavior of dermal grafts. In equibiaxial loading, the range of the highly compliant region is considerably shorter compared to a uniaxial test. However, the stiffness of the dermal grafts in equibiaxial loading is almost the same as the stiffness obtained from a comparable uniaxial test. This very important observation allows the use of a constant multiplicative factor to relate the stress-strain data from uniaxial tests to that of an equibiaxial test.