Dissipation characteristics of collagen fibrils, as determined from Gibbs-potential-based viscoelasticity combined with the Mooney–Rivlin model

Abstract

Collagen fibrils are fundamental structural elements of most biological tissues with mechanical functionality. While the rate-dependent and viscoelastic mechanical behavior of individual collagen fibrils is well agreed upon, the specific dissipation characteristics have been rarely studied explicitly. To this end, we employ a thermodynamically consistent viscoelasticity formulation based on the Gibbs potential. The latter is split into an elastic and viscous portion. The dissipation depends on the viscous portion of the total strain rate, while the elastic portion is linked, via a hypoelastic compliance tensor, to the objective stress rate of Jaumann type. This formulation is specified for volume-invariant Mooney–Rivlin hyperelasticity and fed with atomic force microscopy-based mechanical testing data. The dissipative strain rates are minimized and required to remain positive. As a general feature, dissipative phenomena turn out to be thixotropic. More specifically, two dissipative portions are obtained at elevated strain rates, one below and one above a stress level of 2 MPa. Both may occur in the “structured water matrix” surrounding the collagen molecules. Namely, hydrogen bonds may break and reform due to configurational changes of the adjacent collagen molecules, including molecular straightening (below 2 MPa) and molecular twisting together with intermolecular sliding (above 2 MPa).