Abstract
Topology optimization for damping design of lattice structures is proposed in this work. Compared to metal lattice or viscoelastic materials, lattice structures made of soft materials composed of bi-stable elements show exceptional energy dissipation properties with fully recoverable capacity. Theoretical energy absorption capacity is a key concept to describe damping properties of architectured metamaterials, which reflects the maximum energy absorption per element if a bi-stable chain contains infinite buckling elements. To achieve extreme damping design, topology optimization algorithm is formulated to achieve extreme theoretical energy absorption capacity within a prescribed design domain. An approximate mathematical expression for the energy absorption capacity is formulated with rigorous derivation of sensitivities. Element strain energy in P-norm formulation is constrained at limit points to alleviate material softening failure under large strain. Four design cases are presented and discussed in detail. Results demonstrate that the optimal bi-stable elements achieved by topology optimization algorithm show programmable properties with desired energy dissipation capacity.
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