Exploring the Fracture Toughness of Tessellated Materials With the Discrete-Element Method

Abstract

Architectured materials contain highly controlled structures and morphological features at length scales intermediate between the microscale and the size of the component. In dense architectured materials, stiff building blocks of well-defined size and shape are periodically arranged and bonded by weak but deformable interfaces. The interplay between the architecture of the materials and the interfaces between the blocks can be tailored to control the propagation of cracks while maintaining high stiffness. Interestingly, natural materials such as seashells, bones, or teeth make extensive use of this strategy. While their architecture can serve as inspiration for the design of new synthetic materials, a systematic exploration of architecture-property relationships in architectured materials is still lacking. In this study, we used the discrete element method (DEM) to explore the fracture mechanics of several hundreds of 2D tessellations composed of rigid “tiles” bonded by weaker interfaces. We explored crack propagation and fracture toughness in Voronoi-based tessellations (to represent intergranular cracking in polycrystalline materials), tessellations based on regular polygons, and tessellations based on brick-and-mortar. We identified several toughening mechanisms including crack deflection, crack tortuosity, crack pinning, and process zone toughening. These models show that periodic architectures can achieve higher toughness when compared with random microstructures, the toughest architectures are also the most anisotropic, and tessellations based on brick and mortar are the toughest. These findings are size independent and can serve as initial guidelines in the development of new architectured materials for toughness.

Modeling of 3D Brick‐and‐Mortar Structures Using Cohesive Zone Finite Elements

“…An alternative method that has been used in analytical models [10,14,22] and in discrete element method (DEM) [15,24,25,38] of 2D brick-and-mortar structures is to use a cohesive zone model (CZM) to describe the deformation and failure response of the soft layers. The CZM is defined by a traction-separation law which inherently incorporates damage.…”

“…[2] Another advantage of the structure is its large range of design parameters, which results in a highly tunable response.Many studies have explored the effect of different design parameters on the response of the structure under uniaxial tension, including the aspect ratio of the bricks, [3][4][5][6][7][8][9][10] the relative stiffness between the material of the bricks and the material of the layers, [5,7,[11][12][13] the relative material properties of the layers perpendicular and parallel to the loading direction, [7,10] the volume fraction of each phase, [4,5,7,9] the overlap ratio of the bricks, [4,6,9] and the shape of the tiles. [5,8,[14][15][16][17][18][19][20][21] These parameters have been shown to significantly affect the elastic modulus, yield stress, toughness, and failure regime of the structure. The efficient exploration of these design parameters has been enhanced by the development of models, including analytical models [7,8,10,14,22,23] and computational models, such as lattice spring models, [2,11,12,…”

“…[5,8,[14][15][16][17][18][19][20][21] These parameters have been shown to significantly affect the elastic modulus, yield stress, toughness, and failure regime of the structure. The efficient exploration of these design parameters has been enhanced by the development of models, including analytical models [7,8,10,14,22,23] and computational models, such as lattice spring models, [2,11,12,21] discrete element models, [15,24,25] and finite-element (FE) models. [8,9,16,[26][27][28][29][30][31] Notably, these models have predominantly been limited to 2D structures (i.e., structures with bricks that are extruded in the third dimension and can therefore be modeled in 2D).Another design parameter of brick-and-mortar structures is the introduction of a third dimension to the bricks to form non-planar brick shapes, such as the osteomorphic brick.…”

Controlling failure regimes in Brick-and-Mortar structures

“…Further investigation into these structures has shown that they not only have exceptional combinations of strength and toughness, but that they also exhibit a highly tunable mechanical response. This is due to the large number of design parameters associated with the structure, including their geometric [11,12,15,[22][23][24][25][26][27][28][29][30] and material [18,23,28,31] parameters, and the control of design over multiple length scales [11,17,20,32]. Their tunable response extends the existing design parameter space, broadening the possible applications for this type of structure.…”