Bi-material topology optimization for energy dissipation with inertia and material rate effects under finite deformations

In this study, a bi-material topology optimization framework is developed for maximizing plastic energy dissipation under a combination of material rate effects, inertia effects, and large deformations. In the developed framework, rate effects are considered by employing a finite deformation viscoplastic model and finite element analysis is carried out using F-bar elements for spatial discretization and the Hilber-Hughes-Taylor algorithm for time integration. A bi-material interpolation strategy is proposed within the density-based design parameterization and used to combine material phases with different phenomenological behavior. Consistent design sensitivities are obtained using a time-dependent adjoint method. Design examples reveal that a much higher percentage of the total energy can be dissipated as plastic work when a soft energy dissipating elasto-viscoplastic phase is combined in an optimized way with a stiffness providing hyperelastic phase than when the energy dissipating phase is considered alone. Moreover, isolating the influence of material rate effects from inertia effects provides insight into how optimized designs can exploit these phenomena.