Quasi-Continuum Analysis of Networked Materials

The skeleton of many natural and artificial structures may be abstracted as networks of elements interacting in a non-linear fashion. Examples include rubber, gels, soft tissues, and lattice materials. Understanding the multiscale nature of deformation and failure of networked structure holds key for uncovering origins of fragility in many complex systems including biological tissues and enables designing novel materials. However, these processes are intrinsically multiscale and for large scale structures it is computationally prohibitive to adopt a full discrete approach.
Here, we introduce a new adaptive numerical algorithm for solving polymer networks using an extended version of the Quasi-Continuum (QC) method. In regions of high interest, for example near defects or cracks, each polymer chain is idealized using the worm like chain model. Away from these imperfections, the network structure is computationally homogenized, using Hill-Mandell’s principle, to yield an anisotropic material tensor consistent with the underlying network structure. Overall, only a fraction of the network nodes is solved at each time step. We illustrate the accuracy and efficiency of the method by applying it to study the fracture of large scale polymer network problems.