L.A.A. Beex, R.H.J. Peerlings and M.G.D. Geers
Computer Methods in Applied Mechanics and Engineering, 269, 108–122 (2014).
Structural lattice models incorporating trusses and beams are frequently used to mechan- ically model fibrous materials, because they can capture (local) mesoscale phenomena. Physically relevant lattice computations are however computationally expensive. A suit- able multiscale approach to reduce the computational cost of large-scale lattice computa- tions is the quasicontinuum (QC) method. This method resolves local mesoscale phenomena in regions of interest and coarse grains elsewhere, using only the lattice model. In previous work, a virtual-power-based QC framework is proposed for lattice models that include local dissipative mechanisms. In this paper, the virtual-power-based QC method is adopted for lattice models in which bond failure and subsequent frictional fiber sliding are incorporated – which are of significant importance for fibrous materials such as paper, cardboard, textile and electronic textile. Bond failure and fiber sliding are nonlocal dissipa- tive mechanisms and to deal with this nonlocality, the virtual-power-based QC method is equipped with a mixed formulation in which the kinematic variables as well as the internal history variables are interpolated. Previously defined summation rules can still be used to sample the governing equations in this QC framework. Illustrative examples are presented.