A Finite Element Analysis of Viscoelastic Behavior in Spinodoid Metamaterials

Abstract

Recent advancements in additive manufacturing have led to significant progress in the field of metamaterials, wherein the introduction of microscopic features affects the material properties on a macroscale. Common examples of these materials are truss-based and plate-based structures. However, these lattices bear inherent susceptibility to stress concentration points, which undermine their overall performance. Incorporating smooth surfaces in the material design can be a promising strategy for solving that issue. One noteworthy class of smooth metamaterials originates from the topologies formed in the process of spinodal decomposition. For small fluctuations, these structures can be described mathematically using Gaussian random fields (GRF) stemming from the superposition of standing waves. Recent research work has led to the development of a subtype of these structures, termed spinodoids. Spinodoids are anisotropic structures formed through a biased sampling of wave direction vectors encompassing the underlying GRF.
The development of spinodoid topologies has allowed for extensive design exploration and property-structure investigations, important in the context of many potential future applications, such as bone biomaterials design. Until now, the majority of studies performed on spinodoid metamaterials were limited to the elastic regime. However, many materials, especially biological tissues such as bone, rarely exhibit purely elastic behaviour. Thus, exploring other material regimes is of great interest. This work attempts a finite element analysis of three different types of spinodoid structures: lamellar, cubic, and columnar. These structures' properties are based on a generalized Maxwell model for cortical bone. The study explores how tuning the design parameters influences their mechanical behaviour in a viscoelastic regime.