Strength and stiffness of network materials with preferentially oriented fibers

Materials made from fibers, referred to here as Network materials, are ubiquitous in biology and engineering. In most practical situations, fibers have preferential orientation in one spatial direction or in a plane. Here we use discrete network models to derive the relationship between the stiffness and strength of networks with pre-aligned fibers and network parameters, including the degree of alignment. Both stiffness and strength can be represented by the product of two functions, one accounting for the effect of alignment and the other representing the effect of network parameters, such as the network density and fiber properties. Failure under multiaxial loading is also considered and it is concluded that failure surfaces in stress space can be collapsed by normalizing the axes with the respective (pre-alignment-dependent) uniaxial strength. This generalizes the structure-properties relation established based on uniaxial tests to the multiaxial case. The inferred scaling laws are compared with a collection of experimental data from the literature obtained with diverse network materials.