Multiscale quasicontinuum methods for fibrous materials

The QC method was originally proposed for (conservative) atomistic lattice models and
is based on energy-minimization. Lattice models for fibrous materials however, are often
non-conservative and energy-based QC methods can thus not straightforwardly be
used. Examples presented here are a lattice model proposed for woven fabrics and a lattice model to describe interfiber bond failure and subsequent frictional fiber slidings. A QC framework is proposed that is based on the virtual-power statement of a non-conservative lattice model. Using the virtual-power statement, dissipative mechanisms can be included in the QC framework while the same summation rules suffice. Its validity is shown for a lattice model with elastoplastic trusses. The virtual-power-based QC method is also adopted to deal with the lattice model for bond failure and subsequent fiber sliding presented. In contrast to elastoplastic interactions that are intrinsically local dissipative mechanisms, bond failure and subsequent fiber sliding entail nonlocal dissipative mechanisms. Therefore, the virtual-power-based QC method is also equipped with a mixed formulation in which not only the displacements are interpolated, but also the internal variables associated with dissipation.