Constitutive model for fiber-reinforced materials with deformable matrices

A great number of biological structures are composed of fibers (elastin, collagen, etc.) dispersed on an aqueous matrix in such a complex way that a detailed mechanical analysis based on microconstituents is, for practical purposes, out of reach. Consequently, the preferred approach to the mechanical behavior of these materials is based on setting up of constitutive equations that homogenize the behavior while capturing their main microstructural features. This work presents a simple macroscopic model for fiber-reinforced materials with deformable matrices, especially suited to many biological structural tissues. The constitutive equation is derived by imposing equivalence between the virtual works of both the fiber-reinforced and the equivalent continuum media, showing that it is independent of the control volume used for such equivalence. The model is particularized to incompressible materials, and an extension to orthotropic biological fibers is shown. Numerical simulations of uniaxial tests on silk fibers demonstrate the model's ability to capture the progressive alignment of the microconstituents under large deformations.