A multiscale viscoelastic fiber dispersion model for strain rate-dependent behavior of planar fibrous tissues

Recently, we introduced an efficient discrete fiber dispersion model for characterizing the mechanical behavior of soft fibrous tissues, and we also extended that model to consider microscale collagen fiber recruitment, softening, and damage. However, the viscous behavior of collagen fibers was not considered in that study. The goal of this study is to further extend the discrete fiber dispersion model to consider both elastic and viscous behavior of collagen fibers and ground substance such that the strain rate-dependent behavior of soft fibrous tissues can be characterized. We first reformulated the 3D discrete fiber dispersion model to a 2D version for tissues with planar fiber dispersion. Then, we introduced viscous parts to the model by adding Maxwell elements to the elastic parts of the strain–energy function. We implemented the proposed model in a finite element program and illustrated it with three numerical examples. The computational solutions of the first two examples agree well with our previous published results. In the last example, we characterized the rate-dependent behavior of aortic valve tissue with the proposed model. In conclusion, the proposed model is capable of characterizing the viscoelastic behavior of collagen fibers and ground substance. Future studies with patient-specific boundary conditions are necessary to verify this method.