Scaling of the Elastic Behavior of Two-Dimensional Topologically Interlocked Materials Under Transverse Loading

Abstract

Topologically interlocked materials (TIMs) are a class of 2D mechanical crystals made by a structured assembly of an array of polyhedral elements. The monolayer assembly can resist transverse forces in the absence of adhesive interaction between the unit elements. The mechanical properties of the system emerge as a combination of deformation of the individual unit elements and their contact interaction. The present study presents scaling laws relating the mechanical stiffness of monolayered TIMs to the system characteristic dimensions. The concept of thrust line analysis is employed to obtain the scaling laws, and model predictions are validated using finite element simulations as virtual experiments. Scaling law powers were found to closely resemble those of classical plate theory despite the distinctly different underlying mechanics and theory of TIM deformation.

Short review on architectured materials with topological interlocking mechanisms

“…One of the advantages of TIM is the highly tunable stiffness by simply changing the shape and size of the building blocks. The scaling law of the effective stiffness of a planar assembly of tetrahedral building blocks is given as a function of the number of the blocks and their size . Moreover, the effective stiffness of TIM with cubic building blocks can also exhibit negative values during unloading .…”

“…The scaling law of the effective stiffness of a planar assembly of tetrahedral building blocks is given as a function of the number of the blocks and their size. 20 Moreover, the effective stiffness of TIM with cubic building blocks can also exhibit negative values during unloading. 12,14,15,21 The major advantage of TIM is probably their behavior in fracture and their high tolerance for failure of individual building blocks.…”

Manufacture and Mechanics of Topologically Interlocked Material Assemblies

“…Finite element simulations are computationally more costly than simulations with the respective DEM approach but also provide information on the stress and strain fields in the unit elements, as well as enable one to include failure criteria for the unit elements into the simulation [11,26,28,46,48,49]. An example of such simulation and comparison to the experimental findings is shown in Fig.…”

Stiffness Percolation in Stochastically Fragmented Continua

“…Interlocking was recently used to produce such a class of metamaterials whose behavior is controlled by the contacts between components and depends less on the constitutive behavior of individual components. These studies considered assemblies of identical and periodically arranged interlocking objects held together either by their shape or by a confining pressure [18][19][20][21]. Such assemblies are damage tolerant, as any load-induced crack is trapped at the interfaces between components [22,23].…”