Design principles for energy dissipation in viscoelastic network metamaterials

Abstract

Mechanical energy dissipation in networked materials is relevant for applications from vibration isolation to impact protection, yet identifying optimal dissipative architectures in large disordered truss networks is computationally prohibitive with conventional finite element methods. We develop an efficient graph Laplacian-based spectral framework for viscoelastic truss networks, in which the full continuum dynamics of each rod are retained exactly and the problem size scales with the number of joints rather than element-level discretization points. Using this framework, we investigate how redistributing cross-sectional areas within a network (without changing material composition) controls energy dissipation. We find that random redistribution typically reduces dissipation relative to a uniform baseline, while gradient-based optimization yields nontrivial architectures whose form is governed by the intrinsic attenuation length of the base material. Focusing on driving frequencies near a global resonant mode of the network, we show that the optimal mass distribution decays from the source (driven joint) with the attenuation length scale, and at small attenuation lengths the optimal architecture is independent of the boundary conditions. These results motivate future studies of dissipation length scale based design principles on more complex disordered architectures and provide an efficient computational framework for exploring such structures at scale.