[en] Lattice systems and discrete networks with dissipative interactions are successfully employed
as meso-scale models of heterogeneous solids. As the application scale generally is much
larger than that of the discrete links, physically relevant simulations are computationally
expensive. The QuasiContinuum (QC) method is a multiscale approach that reduces the
computational cost of direct numerical simulations by fully resolving complex phenomena
only in regions of interest while coarsening elsewhere. In previous work (Beex et al., J. Mech.
Phys. Solids 64, 154-169, 2014), the originally conservative QC methodology was generalized
to a virtual-power-based QC approach that includes local dissipative mechanisms. In this
contribution, the virtual-power-based QC method is reformulated from a variational point of
view, by employing the energy-based variational framework for rate-independent processes
(Mielke and Roub cek, Rate-Independent Systems: Theory and Application, Springer-Verlag,
2015). By construction it is shown that the QC method with dissipative interactions can be
expressed as a minimization problem of a properly built energy potential, providing solutions
equivalent to those of the virtual-power-based QC formulation. The theoretical considerations
are demonstrated on three simple examples. For them we verify energy consistency,
quantify relative errors in energies, and discuss errors in internal variables obtained for different
meshes and two summation rules.
