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Abstract The present study is concerned with the deformation response of an architectured material system, i.e., a 2D-material system created by the topological interlocking assembly of polyhedra. Following the analogy of granular crystals, the internal load transfer is considered along well-defined force networks, and internal equivalent truss structures are used to describe the deformation response. Closed-form relationships for stiffness, strength, and toughness of the topologically interlocked material system are presented. The model is validated relative to direct numerical simulation results. The topologically interlocked material system characteristics are compared with those of monolithic plates. The architectured material system outperforms equivalent size monolithic plates in terms of toughness for nearly all possible ratios of modulus to the strength of the material used to make the building blocks and plate, respectively. In addition, topologically interlocked material systems are shown to provide better strength characteristics than a monolithic system for low strength solids. 

Topologically interlocked stereotomic material systems are load-carrying assemblies of unit elements interacting by contact and friction. This contribution summarizes research on such material systems in a variety of configurations based on tessellation geometry and percolation, and it considers external rigid confined, external flexible confined, internal flexible confined, as well as considers the unit elements as solids (elastic and elastic-brittle) or shells (elastic), and under consideration of a range of assembly geometries. Siegmund, T. (2018). Topologically Interlocked Material Systems: From a Material Design Concept to Properties. In T. Siegmund & F. Barthelat (Eds.) Proceedings of the IUTAM Symposium Architectured Materials Mechanics, September 17-19, 2018, Chicago, IL: Purdue University Libraries Scholarly Publishing Services, 2018. https://docs.lib.purdue.edu/iutam/presentations/abstracts/70 

Topologically interlocked stereotomic material (TISM) systems are load-carrying assemblies of unit elements interacting by contact and friction. Past research on these material systems has demonstrated attractive mechanical response characteristics, including damage tolerance, impact resistance, adaptive property control, tuneable acoustical characteristics, as well as disassembly and reuse. In this work, we aim to expand the range of topologically interlocked material systems for which such response is found. The theory of tessellations is the underpinning to create new material systems. We present a comparative study on the deflection response to transverse loading for two underlying tessellations and boundary conditions. Williams, A., & Siegmund, T. (2018). Tesselations and Percolations in Topologically Interlocked Stereotomic Material Systems. In T. Siegmund & F. Barthelat (Eds.) Proceedings of the IUTAM Symposium Architectured Materials Mechanics, September 17-19, 2018 , Chicago, IL: Purdue University Libraries Scholarly Publishing Services, 2018. https://docs.lib.purdue.edu/iutam/presentations/abstracts/79 

This publication contains a finite element model for the analysis of bone core under consideration of bone tissue heterogeneity and tissue anisotropy. The model for bone tissue heterogeneity and anisotropy follows: Hammond, M.A., Wallace, J.M., Allen, M.R. and Siegmund, T., 2018. Incorporating tissue anisotropy and heterogeneity in finite element models of trabecular bone altered predicted local stress distributions. Biomechanics and Modeling in Mechanobiology, 17(2), pp.605-614. In this publication the finite element model, material set assignment and local orientations are provided. This dataset contains an inp file in the syntax of Abaqus/Standard software v2017. 

This publication contains a finite element model for the analysis of single bone trabeculae under consideration of bone tissue heterogeneity and tissue anisotropy. The model for bone tissue heterogeneity and anisotropy follows: Hammond, M.A., Wallace, J.M., Allen, M.R. and Siegmund, T., 2018. Incorporating tissue anisotropy and heterogeneity in finite element models of trabecular bone altered predicted local stress distributions. Biomechanics and Modeling in Mechanobiology, 17(2), pp.605-614. In this publication the finite element model, material set assignment and local orientations are provided. This dataset contains an inp file in the syntax of Abaqus/Standard software v2017. 

At the nanoscale bone is composed of aligned heterogeneously mineralized collagen fibrils. While raloxifene (Ral) and bisphosphonate (BP) treatment preserve bone mass, they also affect bone quality through changes in collagen hydration and mineral density/heterogeneity, respectively. It was hypothesized that the effects of pharmacological treatment on the tissue would alter linear microcracking in finite element (FE) models of trabeculae reflecting control (Ctrl), Ral and BP. A FE mesh of a single canine vertebral body trabecula was generated from a micro- CT scan using ScanIP. A custom MATLAB code imposed tissue property heterogeneity and a collagen fibril orientation parallel to the trabecular surface. Ctrl was heterogeneous (based on vBMD) in both modulus and strength, and BP was homogenous (+25% of Ctrl mean modulus and strength). Ctrl and BP models had identical microcracking toughness. Ral had increased microcracking toughness (+25%) and the same modulus and strength heterogeneity as Ctrl. Transverse deflections were applied to simulate bending of the trabeculae, microcrack formation and propagation was simulated with the imposed orientation using the extended FE method in Abaqus/Standard, and the energy dissipated by the microcrack was assessed. 

At the nanoscale bone is composed of aligned mineralized collagen fibrils organized into packets along the surface of trabecular bone creating an anisotropic tissue microstructure. Newer packets at the trabecular surfaces are usually less mineralized than older bone in the interior of the trabeculae, which along with irregular mineral deposition within packets, forms a heterogeneous material across the span of a trabeculae. However, finite element (FE) models of bone typically use homogenous isotropic material properties, because it is challenging to build anisotropy and heterogeneity into a model in a way that is applicable to the complex geometries of trabecular bone. Both the material anisotropy and heterogeneity may influence the stress state of trabecular bone, and it is important to understand the implications of such differences for determining bone biomechanical failure. It was hypothesized that taking into consideration both the tissue anisotropy and heterogeneity of bone’s biomechanical properties would alter the expected failure locations by reducing tensile stress on near surface elements of an FE model of canine trabecular bone. The objective of this study was to test this hypothesis and to develop a method to apply anisotropic and heterogeneous material properties to a model automatically from micro-computed tomography (μCT) data.