Incremental mechanics of collagen gels: new experiments and a new viscoelastic model

Paired incremental uniaxial step (i.e., relaxation) and ramp tests were conducted simultaneously on four (nominally) identical samples of type I collagen gel, over a direct strain range 0 < epsilon < 0.2. The paired step and ramp responses could not both be predicted by a simple viscoelastic constitutive relation (either linear or Fung-type), but could be predicted reasonably accurately by a general nonlinear viscoelastic relation with a strain-dependent relaxation spectrum, of the form sigma(t) = f(t)-infinity g(t-tau,epsilon)[d(epsilon)(tau)/d(tau)]d(tau). Based on a four-term exponential-series approximation, we measured the stiffness moduli and time constants of the relaxation function, g(t,epsilon), for the four gel samples that we tested, and found that the time constants were independent of strain but the moduli increased strongly with strain. Further, we found that the time constants did not vary across the four gels, but the moduli varied by a factor of about 2 across the gels. Some additional tests show features of the response of collagen gels to cycles of application and removal of loading.