Modelling Fibrous Materials as a Large Deformation, Non-Local and Non-Linear Truss Network

Abstract

Modelling fibrous networks is crucial to understand the mechanics of soft materials like ligaments, connective tissues, alveolus sac and nonwoven fabrics. Simulation of these fibrous networks has been typical restricted to modelling them as a local continuum where the filaments are connected to the nearest neighbors. These methods do not capture the actual microstructure of the fibers, where there are non-local connections. Non-local connection refers to long fibers that connect cross-links that are not near each other. This thesis proposes modelling fibrous networks as a truss system with large deformation. A network of trusses will be able to capture the microstructure of fibrous networks more accurately. The strain energy of the truss system will be assembled and solved by minimizing the total potential energy of the system. Modelling of local and non-local fibrous networks have been done in this work. The random fibrous networks were generated from the probability distribution of cross-links identified in the SEM (Scanning Electron Microscope) images of the fibrous material. The nodes were then connected by truss elements based on the probability distribution of number of nodal connections as a function of distance. Various other methods for developing random fibrous network have also been proposed in this work. A pulmonary alveolus sac of a human lung was modelled as a case of a local system. It was found that there were no significant differences between results obtained if linear response of fibers was used instead of non-linear response. Also, no significant differences were exhibited between approximating the non-local system as a continuum versus modelling it as a network of trusses. A non-local system of type 1 collagen fiber was generated as a random truss network. It was found that there were significant differences between results obtained if linear response of fibers was used instead of non-linear. The deformation mode of non-local fibrous network was different for linear and non-linear. Also, significant differences were exhibited between approximating the non-local system as a continuum versus modelling it as a network of trusses.