Graph-Based View of an Equilibrium Model for Nonwoven Tensile Strength Simulations

Focus of this work is the graph-based analytical treatment of the equilibrium model introduced in [4], which allows to determine the tensile behavior of nonwovens over the interaction of the individual fiber connections in the material. We use the representation of fiber structures as arbitrarily directed graphs to derive a compact nonlinear system of equations with characteristic divergence structure and to investigate its solvability and the uniqueness of solution. Further, we discuss the identification of subgraphs for which trivial solutions can be found.