41. Modeling Deformation and Damage of Random Fiber Network (RFN) Materials

Fiber materials are used in a wide range of products. Fibers can be directly bonded to each other to form 2D and 3D network materials, commonly referred to as random fiber network (RFN) materials. Examples of such materials are paper, textiles, or nonwoven felts. An RFN represents a random structure on the microscale, which governs a complex deformation and fracture behavior. This is due to a size effect in the mechanical behavior of the network because of its heterogeneous nature: the fibers introduce long-range microstructural effects in the material that distribute forces and deformation in a complex manner that is very different compared to more continuous materials. A fiber network material used in a product must meet performance requirements through the entire use cycle including manufacturing and end-use situations. This chapter presents a framework for analyzing deformation, damage, and fracture in network materials using continuum damage mechanics. Material degradation, or damage, is described in a diffuse sense and the influence of damage on the mechanical properties is governed by an internal length variable. To correctly describe gradients in strain and damage, a nonlocal field theory (gradient theory) must be added to the framework. A mathematical framework for such theory is presented.