Microstructural modeling of cross-linked fiber network embedded in continuous matrix

Abstract

A soft tissue's macroscopic behavior is determined by its microstructural components (often a collagen fiber network surrounded by a non-fibrillar matrix (NFM)). In the present study, a coupled fiber-matrix model is developed to quantify the internal stress field within such a tissue and to explore interactions between the collagen fiber network and matrix.

A volume averaging based multiscale model is presented to effectively link the microstructure mechanics of the cross-linked fiber network to the overall tissue mechanics. This development demonstrates that the methodology developed can be applied to real systems and sets the stage for future developments and application to more complicated cases.

To gain additional insight in the mechanics of cross-linked fiber embedded in matrix, a linear material model is also employed to represent both the fibers and matrix and the solution fields are examined for the case of an isotropic network. As the matrix modulus increases, the network is constrained to deform more affinely. This leads to internal forces acting between the network and the matrix, which produce strong stress concentrations at the network cross-links. This interaction increases the apparent modulus of the network and decreases the apparent modulus of the matrix. A model is developed to predict the effective modulus of the composite and its predictions are compared with numerical data for a variety of networks.

Fibers are represented as one-dimensional nonlinear springs and the NFM, meshed via tetrahedra, is modeled as a compressible neo-Hookean solid. Three-dimensional finite element modeling is employed to couple the two tissue components, and the resulting representative volume element (RVE) is subjected to uniaxial tension. The overall coupled RVE response yields results consistent with those obtained using a previously developed parallel model based upon superposition. The detailed stress field in the composite RVE demonstrates the high degree of inhomogeneity in NFM mechanics, which cannot be addressed by a parallel model.

Voronoi tessellations (representing the collagen networks) are embedded in a continuous three-dimensional NFM. To achieve computational efficiency, fibers are represented as one-dimensional wire edges embedded in three-dimensional matrix where conventional two-manifold geometric modeling is not applicable. Therefore non-manifold geometric modeling providing unified representation of general combinations of 1D, 2D and 3D geometric entities is employed in creating the geometry of fiber embedded matrix. After the (parasolid) geometric model is created, conforming mesh is generated by using automatic meshing tools.