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1. Tiling Patterns and the Mechanical Properties of Topologically Interlocked Materials

   A. Williams, T. Siegmund ( October 2019 , Proceedings of the 56th Annual Technical Meeting of the Society of Engineering Science)

   Topologically interlocked materials (TIMs) are material systems consisting of one or more repeating unit blocks assembled in a planar configuration such that each block is fully constrained geometrically by its neighbours. The assembly is terminated by a frame that constrains the outermost blocks. The resulting plate-like structure does not use any type of adhesive or fastener between blocks but is capable of carrying transverse loads. These material systems are advantageous due to their potential attractive combination of strength, toughness, and damage tolerance as compared to monolithic plates, especially when using lower strength materials. TIMs are damage tolerant due to the fact that cracks in any single block cannot propagate to neighbouring blocks. Many configurations of TIMs have been conceptualized in the past, particularly in architecture, but less work has been done to understand the mechanics of such varied assembly architectures. This work seeks to expand our knowledge of how TIM architecture is related to TIM mechanics. The present study considers TIMs created from the Archimedean and Laves tessellations. Each tessellation is configured as a TIM by projecting each edge of a tile at alternating angles from the normal to the tiling plane. For each tiling, multiple symmetries exist depending onmore »where the frame is placed relative to the tiling. Six unique tilings and their multiple symmetries and load directions were considered, resulting in 19 unique TIM configurations. All TIM configurations were realized with identical equivalent overall assembly dimensions. The radius of the inscribed circle of the square and hexagon frames were the same, as well as the thickness of the assemblies. The tilings were scaled to possess the similar same number of building blocks within the frame. Finite element models were created for each configuration and subjected to two load types under quasi-static conditions: a prescribed displacement applied at the center of the assembly, and by a gravity load. The force deflection response of all TIM structures was found to be similar to that of a Mises truss, comprised of an initial positive stiffness followed by a period of negative stiffness until failure of the assembly. This response is indeed related to the internal working of load transfer in TIMs. Owing to the granular type character of the TIM assembly, the stress distribution follows a force-network. The key findings of this study are: • The load transfer in TIMs follows from force networks and the geometry of the force network is associated with the dual tessellation of the respective TIM system. • In TIMs based on Laves tessellations (centered around a vertex of the tiling rather than the center of a tile), displayed chirality and exerted a moment normal to the tile plane as they were loaded. • TIMs resulting from tessellations with more than one unique tile, such as squares and octagons, are asymmetric along the normal to the tile plane causing a dependence of the load response to the direction of the transverse load. Work is underway to transform these findings into general rules allowing for a predictive relationship between material architecture and mechanical response of TIM systems. This material is based upon work supported by the National Science Foundation under Grant No. 1662177.« less
2. Behavior of polyhedral built-up glass compression members

   Yost, Joseph Robert ; Akbarzadeh, Masoud ; Bolhassani, Mohammad ; Ryan, Liam ; Schneider, Jens ; Chhadeh, Philipp Amir ( July 2021 , International Conference on Civil Engineering and Architectural Design)

   This research presents an experimental program executed to understand the strength and stiffness properties of hollow built-up glass compression members that are intended for use in the modular construction of all glass, compression-dominant, shell-type structures. The proposed compression-dominant geometric form has been developed using the methods of form finding and three-dimensional graphical statics. This research takes the first steps towards a new construction methodology for glass structures where individual hollow glass units (HGU) are assembled using an interlocking system to form large, compression-dominant, shell-type structures, thereby exploiting the high compression strength of glass. In this study, an individual HGU has an elongated hexagonal prism shape and consists of two deck plates, two long side plates, and four short side plates, as is shown in Figure 1. Connections between glass plates are made using a two-sided transparent structural adhesive tape. The test matrix includes four HGUs, two each fabricated with 1 mm and 2 mm thick adhesive tape. All samples are dimensioned 64 cm on the long axis of symmetry, 51 cm on the short axis of symmetry, and are 10 cm in width. Glass plates are all 10 mm thick annealed float glass with geometric fabrication done using 5-axis abrasivemore »water jet cutting. HGU assembly is accomplished using 3D printed truing clips and results in a rigid three-dimensional glass frame. Testing was done with the HGU oriented such that load was introduced on the short side edges of the two deck plates, resulting in an asymmetric load-support condition. A soft interface material was used between the HGU and steel plates of the hydraulic actuator and support for the purpose of avoiding premature cracking from local stress concentrations on the glass edges at the load and support locations. Force was applied in displacement control at 0.25 mm/minute with a full array of displacement and strain sensors. Test results for load vs. center deck plate transverse deflection are shown in Figure 2. All samples failed explosively by flexural buckling with no premature cracking on the load and support edges of the deck plates. Strain and deformation data clearly show the presence of second-order behavior resulting from bending deformation perpendicular to the plane of the deck plates. In general, linear axial behavior transitions to nonlinear second-order behavior, with increasing rates in deflection and strain growth, ultimately ending in glass fracture on the tension surfaces of the buckled deck plates. The failure resulted in near-complete disintegration of the deck plates, but with no observable cracking in any side plates and a secure connection on all adhesive tape. Results of the experimental program clearly demonstrate the feasibility of using HGUs for modular construction of compression dominant all-glass shell-type structures. This method of construction can significantly reduce the self-weight of the structure, and it will inspire the use of sustainable materials in the construction of efficient structures.« less
3. Application of Digital Image Correlation (DIC) to the Measurement of Strain Concentration of a PVA Dual-Crosslink Hydrogel Under Large Deformation

   https://doi.org/10.1007/s11340-019-00520-4  

   Liu, M. ; Guo, J. ; Hui, C.-Y. ; Zehnder, A. T. ( January 2019 , Experimental Mechanics)

   Hydrogels are a class of soft, highly deformable materials formed by swelling a network of polymer chains in water. With mechanical properties that mimic biological materials, hydrogels are often proposed for load bearing biomedical or other applications in which their deformation and failure properties will be important. To study the failure of such materials a means for the measurement of deformation fields beyond simple uniaxial tension tests is required. As a non-contact, full-field deformation measurement method, Digital Image Correlation (DIC) is a good candidate for such studies. The application of DIC to hydrogels is studied here with the goal of establishing the accuracy of DIC when applied to hydrogels in the presence of large strains and large strain gradients. Experimental details such as how to form a durable speckle pattern on a material that is 90% water are discussed. DIC is used to measure the strain field in tension loaded samples containing a central hole, a circular edge notch and a sharp crack. Using a nonlinear, large deformation constitutive model, these experiments are modeled using the finite element method (FEM). Excellent agreement between FEM and DIC results for all three geometries shows that the DIC measurements are accurate up tomore »strains of over 10, even in the presence of very high strain gradients near a crack tip. The method is then applied to verify a theoretical prediction that the deformation field in a cracked sample under relaxation loading, i.e. constant applied boundary displacement, is stationary in time even as the stress relaxes by a factor of three.« less
4. Incorporating tissue anisotropy and heterogeneity in finite element models of trabecular bone altered predicted local stress distributions

   https://doi.org/10.1007/s10237-017-0981-8  

   Hammond, Max A. ; Wallace, Joseph M. ; Allen, Matthew R. ; Siegmund, Thomas ( November 2017 , Biomechanics and Modeling in Mechanobiology)

   Trabecular bone is composed of organized mineralized collagen fibrils, which results in heterogeneous and anisotropic mechanical properties at the tissue level. Recently, biomechanical models computing stresses and strains in trabecular bone have indicated a significant effect of tissue heterogeneity on predicted stresses and strains. How-ever, the effect of the tissue-level mechanical anisotropy on the trabecular bone biomechanical response is unknown. Here, a computational method was established to automatically impose physiologically relevant orientation inherent in trabecular bone tissue on a trabecular bone microscale finite element model. Spatially varying tissue-level anisotropic elastic properties were then applied according to the bone mineral density and the local tissue orientation. The model was used to test the hypothesis that anisotropy in both homogeneous and heterogeneous models alters the predicted distribution of stress invariants. Linear elastic finite element computations were performed on a 3 mm cube model isolated from a microcomputed tomography scan of human trabecular bone from the distal femur. Hydrostatic stress and von Mises equivalent stress were recorded at every element, and the distributions of these values were analyzed. Anisotropy reduced the range of hydrostatic stress in both tension and compression more strongly than the associated increase in von Mises equivalent stress. The effectmore »of anisotropy was independent of the spatial redistribution high compressive stresses due to tissue elastic heterogeneity. Tissue anisotropy and heterogeneity are likely important mechanisms to protect bone from failure and should be included for stress analyses in trabecular bone.« less
5. Hemivariational continuum approach for granular solids with damage-induced anisotropy evolution

   https://doi.org/10.1177/1081286520968149  

   Timofeev, Dmitry ; Barchiesi, Emilio ; Misra, Anil ; Placidi, Luca ( May 2021 , Mathematics and Mechanics of Solids)

   Mechanical behavior of materials with granular microstructures is confounded by unique features of their grain-scale mechano-morphology, such as the tension–compression asymmetry of grain interactions and irregular grain structure. Continuum models, necessary for the macro-scale description of these materials, must link to the grain-scale behavior to describe the consequences of this mechano-morphology. Here, we consider the damage behavior of these materials based upon purely mechanical concepts utilizing energy and variational approach. Granular micromechanics is accounted for through Piola’s ansatz and objective kinematic descriptors obtained for grain-pair relative displacement in granular materials undergoing finite deformations. Karush–Kuhn–Tucker (KKT)-type conditions that provide the evolution equations for grain-pair damage and Euler–Lagrange equations for evolution of grain-pair relative displacement are derived based upon a non-standard (hemivariational) variational approach. The model applicability is illustrated for particular form of grain-pair elastic energy and dissipation functionals through numerical examples. Results show interesting damage-induced anisotropy evolution including the emergence of a type of chiral behavior and formation of finite localization zones.