Range Of Relative Densities Research Articles

Fracture behavior of 3D-printed thermoplastics—A dilemma of fracture toughness versus fracture energy

The Material Extrusion (ME) technique in 3D printing facilitates the production of thermoplastic materials with diverse cellular or lattice-like infill geometries, enabling the creation of lightweight, high-performance materials. This study investigates the influence of infill geometry and relative density on the fracture behavior of 3D-printed thermoplastics produced through ME. Polylactic acid (PLA) is used as the model material, with unit cell geometries-square, triangle, and Kagome-and relative densities ranging from 0.4 to 0.8 explored. Tensile tests are first conducted to determine in-plane elastic moduli in two orthogonal directions, accounting for unit cell anisotropy. These results are employed in effective fracture energy calculations. Compact tension fracture tests follow, quantitatively characterize crack growth characteristics in both directions. In both tests, digital image correlation method is used to measure full field strain distributions. Three significant findings emerge. First, there is a power scaling relationship between Elastic Modulus and relative density across all unit cells, with Kagome exhibiting the highest correlation constant. Triangle and Kagome unit cells show negligible orthotropic responses in perpendicular directions for varying relative densities. Second, the relationship between nondimensional fracture toughness and relative density follows a similar scaling law, with minor variations depending on unit cell type. The correlation factor slightly dependens on unit cell geometry but remains around 3 across the the examined relative density range. Third, considering the dissipation of inelastic fracture energy, both triangle and Kagome unit cell geometries demonstrate an order of magnitude higher effective fracture energy (i.e., crack growth resistance) compared to the square unit cell. This is associated with toughening mechanisms such as crack deflection and bifurcation. These findings highlight the disparity between fracture toughness and effective fracture energy in assessing the fracture resistance of 3D-printed thermoplastics, clearly demonstrating that fracture toughness alone is insufficient for a comprehensive assessment. The proposed scaling laws provide predictive insights into the fracture toughness of polymeric materials produced via the ME method.

Imperfection-Enabled Strengthening of Ultra-Lightweight Lattice Materials.

Lattice materials are an emerging family of advanced engineering materials with unique advantages for lightweight applications. However, the mechanical behaviors of lattice materials at ultra-low relative densities are still not well understood, and this severely limits their lightweighting potential. Here, a high-precision micro-laser powder bed fusion technique is dveloped that enables the fabrication of metallic lattices with a relative density range much wider than existing studies. This technique allows to confirm that cubic lattices in compression undergo a yielding-to-buckling failure mode transition at low relative densities, and this transition fundamentally changes the usual strength ranking from plate > shell > truss at high relative densities to shell > plate > truss or shell > truss > plate at low relative densities. More importantly, it is shown that increasing bending energy ratio in the lattice through imperfections such as slightly-corrugated geometries can significantly enhance the stability and strength of lattice materials at ultra-low relative densities. This counterintuitive result suggests a new way for designing ultra-lightweight lattice materials at ultra-low relative densities.

Rational Function-Based Approach for Integrating Tableting Reduced-Order Models with Upstream Unit Operations: Dry Granulation Case Study.

We present a systematic and automatic approach for integrating tableting reduced-order models with upstream unit operations. The approach not only identifies the upstream critical material attributes and process parameters that describe the coupling to the first order and, possibly, the second order, but it also selects the mathematical form of such coupling and estimates its parameters. Specifically, we propose that the coupling can be generally described by normalized bivariate rational functions. We demonstrate this approach for dry granulation, a unit operation commonly used to enhance the flowability of pharmaceutical powders by increasing granule size distribution, which, inevitably, negatively impacts tabletability by reducing the particle porosity and imparting plastic work. Granules of different densities and size distributions are made with a 10% w/w acetaminophen and 90% w/w microcrystalline cellulose formulation, and tablets with a wide range of relative densities are fabricated. This approach is based on product and process understanding, and, in turn, it is not only essential to enabling the end-to-end integration, control, and optimization of dry granulation and tableting processes, but it also offers insight into the granule properties that have a dominant effect on each of the four stages of powder compaction, namely die filling, compaction, unloading, and ejection.

Targeted mechanical and energy absorption properties of 3D printed aluminium metamaterials

The potential of 3D-printed AlSi10Mg auxetic structures for diverse mechanical and energy-absorbing needs remains untapped. This article reveals a multi-criteria framework for the laser powder bed fused (L-PBF) −υ architecture considering elastic modulus (E), yield strength (σy), specific energy absorption (SEA), peak crush force (PCF) and crush force efficiency (CFE). The framework seamlessly combines trial data, multi-criteria decision-making, and performance indicators. Five auxetic structures were 3D-printed, characterised for mechanical and energy absorption traits within a 0.17–0.26 relative density range. The outcomes revealed a range of values for various parameters, including the Poisson’s ratio (−0.03 to −0.22), porosity (80.87–87.60 %), CFE (33–83 %), elastic modulus (100–632 MPa), yield strength (1.8–10 MPa), and SEA (0.5–6.8 kJ/kg). The reliability of these structures was ensured through a meticulous selection process based on an extensive literature review and empirical validation. To address the limitations of theoretical models, our work goes beyond theoretical predictions by experimentally validating these properties and integrating advanced methodologies such as the ‘analytic hierarchy process’ (AHP) and the ‘technique for order of preference by similarity to ideal solution’ (TOPSIS). This allows us to determine the best-performing auxetic architecture. The decision-making process was informed by five user-defined parameters prioritised in the order of CFE>−υ> E>σy> SEA based on their relative closeness identifying AUX5 as the best performing auxetic architecture. This study introduces an innovative method for crafting scenario-based auxetic architectures with varying performance levels based on their relative importance.

Ti–6Al–4V hybrid-strut lattice metamaterials: A design strategy for improved performance

Metal hollow-strut lattices manipulate the strut and node sections to achieve higher strength. Although these metamaterials have recently surpassed the structural efficiency of conventional solid-strut lattices of comparable density and topology, they often observe localised yielding and fragmentation through the nodes that limit their structural efficiency. To quantify the effect of this localised failure and to develop mitigating strategies, we have integrated solid and hollow strut and node sections in singular Ti–6Al–4V simple cubic hybrid-strut lattices for a deployable relative density range of 15–30%. Fabricated through laser powder bed fusion these hybrid-strut lattices are stronger (32%), stiffer (15%), and tougher (65%) than solid-strut lattices of equivalent density. Interestingly, the metamaterials with hollow beams can transition from a bending-dominated to a stretch-dominated deformation response with increasing density, while the lattices with solid beams only observed a uniformly stretch-dominated deformation response. The combination of solid and hollow strut and node sections in the hybrid-strut lattice establishes a simple yet effective strategy to enhance structural efficiency and control of failure response without increasing density or manipulating unit cell topology.

Evaluation of Lattice Structures for Medical Implants: A Study on the Mechanical Properties of Various Unit Cell Types

Lattice structures are a prime candidate for applications in the medical implant industry due to their versatile mechanical behaviour, which can be tailored to meet specific patient needs and reduce stress shielding, while enabling the natural flow of body fluids. In this work, the mechanical properties of metallic lattices made of five different unit cell types, Cubic (C), Truncated Octahedron (TO), Truncated Cubic (TC), Rhombicuboctahedron (RCO), and Rhombitruncated Cuboctahedron (RTCO), were evaluated under uniaxial compression at three different relative densities, 5%, 15%, and 45%. The evaluation was experimental, and it was compared with previous and new finite element simulations. Specimens for the experimental tests were fabricated in stainless steel 316L by laser powder bed fusion, and stress–strain curves were obtained for the different lattices. The combination of the test results with a critical interpretation of the deformation mechanisms allowed us to confirm that two unit cell types, TO and RTCO, are stable for the whole range of relative densities evaluated. The other three unit cells exhibit more unpredictable behaviour, either due to manufacturing defects or limitations, or because their unstable compression behaviour leads to bucking. For these reasons, TO and RTCO unit cell types are mechanically more adequate for applications in the medical implant industry.

Field-assisted sintering of barium titanate and 45S5 bioactive glass for biomedical applications

The development of electrically active biomaterials, which create electrical cues on demand to foster cellular stimulation, remains a challenge. Here, we utilized a Field-assisted sintering approach to densify barium titanate and 45S5 bioactive glass to create a piezoelectric and potentially bioactive composite. By using Field-assisted sintering, we aimed to fabricate dense piezoelectric specimens, preserving a low degree of crystallization of the bioactive glass to keep bioactivity as high as possible. Therefore, we have varied the compositions of the materials and processed them at different sintering temperatures. This enabled us to produce dense test specimens in the 94 %–98 % relative density range. The samples were successfully polarized, and piezoelectric charge constants d33 were determined for the composites. The content of bioactive glass and the sintering temperature influence the charge constant d33. It is in the range of 0.8–3.4 pC/N for the composites, approximately in the order of magnitude assigned to natural tissues such as bone. X-ray diffraction was used to analyze the composition of the processed samples and to investigate the influence of an additional thermal post-treatment. Altogether, we established a process window for field-assisted sintering, allowing the fabrication of a piezoelectric and potentially bioactive biomaterial for tissue engineering.

Stiffness, strength, anisotropy, and buckling of lattices derived from TPMS and Platonic and Archimedean solids

Lattice metamaterials have gained considerable attention due to their distinctive topological structures and multifunctional properties. In this work, the effect of topology, loading conditions, and relative density on the effective mechanical properties of various novel lattice architectures is investigated numerically and experimentally. Thirteen strut-based lattices derived from triply periodic minimal surfaces (five lattices) as well as Platonic (three lattices) and Archimedean (five lattices) solids are considered for the first time, and their anisotropic mechanical properties, including uniaxial, shear, and bulk moduli and strengths as well as their total stiffness, buckling strengths, Poisson’s ratio, and anisotropy are investigated as a function of a wide range of relative densities (0.1% to 37%). Finite element analysis is employed to capture the full effective behavior of these lattices using periodic boundary conditions. Bifurcation analysis is performed to predict the threshold relative density governing their buckling vs yielding deformation behavior. Selected lattice structures of various relative densities are 3D printed using polymer selective laser sintering additive manufacturing technique and tested under quasi-static uniaxial compression where the experimental and numerical results are compared. The numerical results indicate that the deformation behavior can be altered between stretching and bending dominated mode of deformation as function of loading. Archimedean lattices are shown to outperform a wide range of strut-based lattices. This work opens the doors for more investigations of the multifunctional properties of these novel types of lattices and their engineering applications. Furthermore, the generated comprehensive data are useful in optimizing latticed structures using topology optimization techniques.

Compression properties of cellular iron lattice structures used to mimic bone characteristics

Recently, cellular materials made by the repetition of unit cells, that is, iron lattices have become appealing to mimic the structure of bone. The aim of the study is to choose the most adequate lattice structures, which have the compressive mechanical properties closer to the ones of bone, in the perspective of their use as temporary implants. Five types of unit cells were selected, such as, cubic (C), truncated octahedron (TO), truncated cubic (TC), rhombicuboctahedron (RCO), and rhombitrucated cuboctahedron (RTCO). The mechanical properties were assessed by numerical simulations with a finite-element analysis. The size effect was studied with the comparison of results among samples with different numbers of unit cells. Simulations covered a wide range of relative densities. Graded dense-in and dense-out configurations were constructed with lattices of types RTCO and TO, being the unit cells, themselves graded. Lattice structures RTCO and TO were found to be stable at every relative density studied, while C, TC and RCO lattices are unstable at low densities. The evaluation of size effects was not conclusive, which could be biased by other factors. The Young's modulus of RTCO and TO lattices enable to reproduce the properties of both trabecular and cortical bone, with an appropriate choice of the relative density. To mimic trabecular bone, only RTCO and TO structures with low relative densities, can be used, while arrangements of C, TC and RCO cells can only replicate the properties of cortical bone. Graded cells may have the same properties as non-graded with lower density.

DLP printed 3D gyroid structure: Mechanical response at meso and macro scale

Rapid prototyping (RP) technology enables the fabrication of complex geometries, making lattice structures increasingly popular. Lattice structures, known as cellular materials, have garnered significant attention over the past two decades due to their ability to optimise mass distribution in components. These structures excel in mechanical properties, catering to energy absorption (bending-dominated structures) and structural performance (stretch-dominated structures). In this paper, we investigate the behaviour of stretch-dominated lattice structures using periodic surface models, specifically focusing on sheet-based Gyroid cells, to allow for a more efficient macroscale modelling. We study cells and scaffolds of different sizes, considering various triply periodic minimal surface thicknesses and relative densities ranging from approximately 0.2 to 0.65. We explore load applications in directions different from the unit cell's principal axes and analyse the strain rate effect on both bulk and cellular material. The lattice structures are manufactured using epoxy resin and digital light processing (DLP) technology. In the range of relative density investigated, both in quasi-static and dynamic conditions, a linear trend is observed for Young's modulus and compression yield strength. To extend the quasi-static results to the dynamic regime, we employ a more generalized normalization technique. This approach divides Young's modulus and compression yield strength by the behaviour of the base material at a specific strain rate, facilitating the correlation of mechanical properties across the two loading regimes. Based on experimental findings, we implemented and calibrated a bi-linear material model for describing, in macroscale, triply periodic minimal surface (TPMS) Gyroid structures. The model coefficients are parameterized with respect to relative density. In addition, the presented material law was compared with that proposed by Gibson-Ashby. Furthermore, we evaluated the anisotropy of both the base material and the unit cell. The first one is done by testing the 3D printed samples in directions different from the printing one, the latter by using the Zener factor. The anisotropy evaluation confirmed the isotropic behaviour of the unit cell within the range of relative density and test conditions investigated. Finally, we perform linear elastic 3D macroscopic and mesoscopic model simulations for combined shear-compression tests using the implemented bi-linear material model and the anisotropic stiffness matrix (obtained through the homogeneous formulation) for the macroscale, and the base material for the mesoscopic one. The results demonstrate the suitability of the proposed equivalent material model for studying the TPMS Gyroid structure in the elastic regime, both in quasi-static and dynamic states. This allows for an efficient FE modelling process of complex lattice structures.

Novel Design Charts for Anisotropic Effective Elastic Properties of Pyramidal Lattice Materials

Novel design charts for predicting the anisotropic effective elastic properties of pyramidal lattices are proposed for a wide range of relative density and various struts shape through finite element (FE) simulations. Pyramidal lattices are 3D printed using digital light processing (DLP) and are subsequently subjected to uniaxial compression tests to provide a partial experimental validation for the presented design charts. Regarding strut shape, the presented results uncover that using hollow-tapered instead of solid-uniform struts leads significant improvements for effective Young's and shear moduli. In addition, this study has paved the way towards enhancing our understanding of how the anisotropy of pyramidal lattices can be tailored by tuning the relative density and strut architecture. Resorting to an analytical framework, results indicate that controlling the void volume fraction of struts can lead the same effective Young's modulus for all three principal directions of pyramidal lattices with low relative densities.

Effect of Sintering Temperature on Phase Formation and Mechanical Properties of Al–Cu–Li Alloy Prepared from Secondary Aluminum Powders

Aluminum and its alloys are very versatile materials used in a wide range of applications due to the initial characteristics of pure aluminum and the combination of properties obtained from its blend with other elements. Considering that aluminum is the second-most-produced metal after steel, and that its production will increase over time based on the demand to produce products through conventional and additive methodologies, this will lead to an increase in the energy consumed as well as the footprint of carbon generated. It is for this reason that the generation of competitive aluminum alloys must be approached from secondary sources (recycling). To address these environmental issues, in this work, 2070 aluminum alloy (AA2070) samples were manufactured using secondary aluminum powder and compared with the primary aluminum source. The samples were compacted at 700 MPa and sintered at a different range of temperatures between 525 °C and 575 °C. The study includes thermodynamic modeling, microstructure, and mechanical characterization. Microstructure and phases characterization were carried out via scanning electron microscopy (SEM) and X-ray diffraction (XRD) analysis, respectively, whereas the mechanical characterization comprised relative density evaluation, hardness, and flexion tests. Results were compared with the calculation of phase stability using Thermo-Calc software 2020a. Based on the results obtained, it can be concluded that the secondary AA2070 optimal sintered temperature, where the components raised the highest mechanical properties and effective relative density range, is 575 °C. Furthermore, the recycled alloys have similar relative densities and flexural strengths than the corresponding alloys made from primary aluminum powder.

Assessing the compressive and tensile properties of TPMS-Gyroid and stochastic Ti64 lattice structures: A study on laser powder bed fusion manufacturing for biomedical implants

In the field of additive manufacturing, the design and fabrication of lattice structures have garnered substantial attention, particularly for their potential in advanced material applications. This study focuses on the mechanical properties of titanium alloy Ti64 lattice structures fabricated by Laser Powder Bed Fusion. It examines the mechanical features of two structure types, TPMS Gyroid and Stochastic Voronoi, analyzing their design and fabrication interplay. To evaluate mechanical properties, two methodologies to compute stress were employed: Method A, nominal diameter calculations of the cross-sectional area as a bulk material, and Method B, averaged cross-sectional area measurements along the open-cell porous structures. Method A generally showed lower Elastic Modulus and Yield Stress than Method B, highlighting the importance of geometric accuracy in lattice design mechanics. Both TPMS gyroid and stochastic lattices, within a 0.1–0.5 relative density range, displayed mechanical properties similar to human bone, suggesting their potential in orthopedic use. This could help reduce stress shielding and improve implant lifespan. The findings were further complemented by Scanning Electron Microscopy and Digital Image Correlation evaluations, highlighting the intricate relationship between fabrication parameters, lattice morphology, and the emergent microstructural characteristics.

Bayesian areal disaggregation regression to predict wildlife distribution and relative density with low-resolution data.

For species of conservation concern and human-wildlife conflict, it is imperative that spatial population data be available to design adaptive-management strategies and be prepared to meet challenges such as land use and climate change, disease outbreaks, and invasive species spread. This can be difficult, perhaps impossible, if spatially explicit wildlife data are not available. Low-resolution areal counts, however, are common in wildlife monitoring, that is, the number of animals reported for a region, usually corresponding to administrative subdivisions, for example, region, province, county, departments, or cantons. Bayesian areal disaggregation regression is a solution to exploit areal counts and provide conservation biologists with high-resolution species distribution predictive models. This method originated in epidemiology but lacks experimentation in ecology. It provides a plethora of applications to change the way we collect and analyze data for wildlife populations. Based on high-resolution environmental rasters, the disaggregation method disaggregates the number of individuals observed in a region and distributes them at the pixel level (e.g., 5 × 5 km or finer resolution), thereby converting low-resolution data into a high-resolution distribution and indices of relative density. In our demonstrative study, we disaggregated areal count data from hunting bag returns to disentangle the changing distribution and population dynamics of three deer species (red, sika, and fallow) in Ireland from 2000 to 2018. We show an application of the Bayesian areal disaggregation regression method and document marked increases in relative population density and extensive range expansion for each of the three deer species across Ireland. We challenged our disaggregated model predictions by correlating them with independent deer surveys carried out in field sites and alternative deer distribution models built using presence-only and presence-absence data. Finding a high correlation with both independent data sets, we highlighted the ability of Bayesian areal disaggregation regression to accurately capture fine-scale spatial patterns of animal distribution. This study uncovers new scenarios for wildlife managers and conservation biologists to reliably use regional count data disregarded so far in species distribution modeling. Thus, it represents a step forward in our ability to monitor wildlife population and meet challenges in our changing world.

An isotropic zero Poisson's ratio metamaterial based on the aperiodic ‘hat’ monotile

Metamaterials are synthetic materials, engineered to have desirable mechanical properties. This paper is concerned with a class of cellular metamaterials that minimise the Poisson's ratio, a metric that characterises the deformation behaviour of materials according to their orthogonal response to applied force. This secondary deformation is usually visually apparent as a sideways “bulge”, and can limit the longevity of multi-material components, from aircraft parts to medical implants, because of the interference shear stresses that arise between different materials due to deformations in different directions by different amounts. As a result, low Poisson's ratio can be a desirable mechanical property and the challenge of producing cellular metamaterials that have reduced Poisson's ratio has received significant research attention. However, solutions that have been proposed tend to be limited in their applicability, either because they are anisotropic, so behaviour varies greatly according to direction of the applied force, or because they are very low in relative density, so have low stiffness. Here we introduce a new cellular metamaterial, a honeycomb based on the recently discovered aperiodic ‘hat’ monotile, which offers nominally zero Poisson's ratio. Results from compression testing and computational modelling show that the behaviour of this metamaterial is isotropic, and is consistent across a range of relative densities, leading to the exciting conclusion that zero Poisson's ratio is possible for different stiffnesses. We envisage that this metamaterial will facilitate otherwise unfeasible technologies, such as morphing wing structures and medical devices that better mimic the behaviour of tissues such as cartilage.

Comparative performance evaluation of microarchitected lattices processed via SLS, MJ, and DLP 3D printing methods: Experimental investigation and modelling

Additively manufactured mechanical metamaterials are gaining prominence in lightweight energy-absorption applications due to their exceptional mass-specific properties. Herein, we examine the energy absorption characteristics of micro-architected truss-, shell- and plate-lattice structures, namely, Octet, Kelvin, Gyroid, SC, BCC and FCC over a range of relative densities under quasi-static compression via both experiments and finite element analysis (FEA). Employing different 3D printing methods, namely, Digital Light Processing, Selective Laser Sintering and Material Jetting, the lattices were fabricated using PlasGray™ (photo-resin based plastic), PA12 (Nylon) and VeroWhite (photo-resin based rigid plastic) respectively. Our results indicate that the SC lattice structure outperforms in terms of stiffness and strength, while the Gyroid lattice outperforms in terms of energy absorption efficiency (η). At lower relative densities (<0.3), η reaches up to 61% for the Gyroid lattices made of PlasGray, while only at high relative densities the Octet truss lattices compete with the Gyroid lattices. For Gyroid lattices made of PA12 with a relative density of 0.23, an energy absorption efficiency of 68% was observed. Design maps are presented for all lattice structures processed and tested herein, to demonstrate their relative merits. Moreover, a two-step FEA was executed on a chosen array of lattices to thoroughly investigate the extensive design possibilities, utilising the elastic-plastic, Drucker-Prager, and concrete damage plasticity material models for PlasGray, PA12, and VeroWhite, respectively, with calibration based on experimental results. The results highlight that the tailored design of Gyroid lattices enabled by AM positions them as promising candidates for lightweight energy-absorbing applications.

Experimental study on permeability and strength characteristics of MICP-treated calcareous sand

Calcareous sand is the main fill material for island reclamation projects, but untreated calcareous sand might not be used as a reclamation fill due to its poor mechanical properties. Microbial induced calcite precipitation (MICP) was directly used to consolidate calcareous sands. One-dimensional sand column tests were conducted to identify the optimized solutions and to investigate the effects of cement solution concentration, relative density, and consolidation frequencies on the permeability and mechanical properties of MICP-treated calcareous sands. Finally, three-dimensional model tests were carried out to investigate the effective consolidation range of microbially treated calcareous sands. The results show that the MICP-treated calcareous sand shows a reduction in the permeability of the sample, while the calcium carbonate cementation and its filling effect improves the mechanical properties of the soil. The one-dimentional test results show that the effective values for cement solution concentration, relative density, and consolidation frequencies range from 0.5 mol/L to 1.5 mol/L, 30%–70%, and 5–15 times. The consolidation frequencies have the greatest influence on the permeability and strength properties of the treated calcareous sand. A quadratic polynomial regression model for permeability and strength was established through response surface analysis, and the regression model proved to be highly accurate and reliable through testing. In three-dimentional tests, the consolidation range tends to move downwards in a trapezoidal shape, showing a "big bottom and small top" pattern, with a consolidation range of approximately 34 times the diameter of the pipe. This study serves as a reference for selecting consolidation parameters for subsequent tests and applications of MICP-treated calcareous sands.

Experimental investigation on in-plane compressive behaviour of 2D chiral ceramics

Five kinds of 2D chiral ceramics of 3 mol% yttria-stabilized tetragonal ZrO2 (3Y-TZP) material with an extensive relative density range was fabricated by an additive manufacturing technique based on the digital light processing (DLP) system. The in-plane compressive behaviours of the chiral structures were investigated with a uniaxial compression test. The effects of geometric parameters, including the ligament length-radius ratio and the wall thickness-radius ratio, were studied carefully through experiments. Furthermore, the relationships between Poisson's ratios and relative densities of the five chiral structures were obtained by finite element analysis. The results illustrated that increasing the relative density, like decreasing L/r or increasing t/r, is an excellent way to increase the mechanical properties of chiral ceramics, while decreasing L/r is a better way to increase the energy absorption capacity for chiral ceramics from an engineering perspective. Anti-tetrachiral ceramics own the best energy absorption capacity due to their strong deformation abilities brought by the deformation mode. The Poisson's ratio of 2D chiral structures also varies with the relative density.

Design and analysis of a lightweight beam-type topologically interlocked material system

Topologically interlocked material systems are assemblies of interlocking building blocks which exhibit advantageous combinations of strength and toughness under transverse load. In general, the structural efficiency of structural members carrying a transverse load can be modulated by shaping the cross-section. This study provides novel insights into the effectiveness of material removal on the mechanical behavior of a beam-type topologically interlocked material system. A reference configuration with solid building blocks is established and its response is investigated by experiments and finite element analysis (FEA) models. A parametric investigation combining several approaches for material removal with a range of relative material densities is conducted, and the response of resulting assemblies is reported. The force–displacement behavior and the load transfer of the reduced weight systems are compared to the solid reference system and to that of an extruded box beam. Results show that lintels made with material-removed blocks retain the general load–deflection response characteristics of lintels made from solid building blocks, despite significant changes to the load transfer pattern internally. Material removal approaches exist such that the lintel retains the mass-specific mechanical properties of the solid structure.

Dilatancy Effects on Surface Foundations on Dry Sand

This paper presents the results of finite-element analyses of rigid-surface strip foundations on dry cohesionless soil subjected to displacement-controlled vertical loading. A two-surface constitutive model with a non-associated flow rule, representing the full range of pressure-dependent drained shear strength and volume change behavior of dry sand, is employed to model the soil. A range of foundation widths and sand initial relative densities is covered. The results show that, for narrow, rigid-strip foundations, the conventional bearing-capacity calculation provides a reasonable indication of the load-carrying capacity of the foundation. However, there is no peak in the load-carrying capacity for wide foundations, and the load–deformation curve exhibits stiffening behavior, even at large settlements; this is particularly apparent at larger values of the initial relative density. Based on the results, it is observed that with the increase in vertical foundation loading, the vertical stiffness of the foundation increases with each loading increment, due to the tendency of the dense sand to become more dilatant with the increase in confining pressure. At large settlements, the state of the sand beneath the foundation approaches the critical state. Settlement vectors beneath the foundations on dense sand reveal that the displacements approximate one-dimensional compression.