Spatial Gradation Research Articles

3D printing with a 3D printed digital material filament for programming functional gradients

Additive manufacturing, or 3D printing attracts growing attention as a promising method for creating functionally graded materials. Fused deposition modeling (FDM) is widely available, but due to its simple process, creating spatial gradation of diverse properties using FDM is challenging. Here, we present a 3D printed digital material filament that is structured towards 3D printing of functional gradients, utilizing only a readily available FDM printer and filaments. The DM filament consists of multiple base materials combined with specific concentrations and distributions, which are FDM printed. When the DM filament is supplied to the same printer, its constituent materials are homogeneously blended during extrusion, resulting in the desired properties in the final structure. This enables spatial programming of material properties in extreme variations, including mechanical strength, electrical conductivity, and color, which are otherwise impossible to achieve with traditional FDMs. Our approach can be readily adopted to any standard FDM printer, enabling low-cost production of functional gradients.

Implicitly Represented Architected Materials for Multi‐Scale Design and High‐Resolution Additive Manufacturing

AbstractBio‐inspired structured materials have achieved unprecedented progress in realizing exceptional, effective properties. However, a rational design paradigm that enables both tailoring complex 3D architectures and manufacturing the engineered hierarchical structured materials is still missing. To bridge this gap, this study presents a holistic design‐through‐printing framework with implicitly represents cellular materials for high‐resolution structured materials design and manufacturing. Attributed to the parameterized implicit function‐based representation (FRep), the material's microstructures can be effectively controlled to tune the material properties (e.g., isotropic, orthotropic, and anisotropic) while enabling functional gradation in the multi‐scale hierarchical design. Given prescribed material properties in different applications, the proposed framework finds the optimal layout of microstructures with an adaptive cluster‐based topology optimization algorithm. The geometry frustration problem brought by the mixture of distinct microstructures is simultaneously addressed with a spatial gradation scheme in the optimization loop. Lastly, the FRep‐based architected material enables efficient geometry processing (e.g., slicing) for modern AM processes, thus facilitating the manufacturing of high‐resolution delicate designed materials. The proposed framework is scalable and adaptable to accomplish a broad spectrum of design demands in various applications.

Embracing Anisotropy – Opportunities and Challenges to the Functional Application of Advanced Manufacturing of Energetic Materials

Embracing Anisotropy – Opportunities and Challenges to the Functional Application of Advanced Manufacturing of Energetic Materials

Influence of Cu and Al interfacing foil on Al7075/A360 FGMs fabricated by gravity casting

Functionally graded materials (FGMs) are innovative and manipulated modern engineering materials with customized performance or function due to the spatial gradation in morphology. The present research work attempts to fabricate the FGMs with and without interfacing layers by adopting the gravity casting methodology. The fabricated FGM samples were investigated for microstructural and mechanical characteristics, namely, with Cu and Al foils and without an interfacing layer. The FGM samples with Cu, Al foils, and without interfacing foils exhibited microhardness values of 85Hv, 88Hv, and 92Hv, respectively. The microhardness of the fabricated FGM sample without interfacing foil, compared to the FGM sample made with interfacing foil, namely, Cu and Al, is observed as high. The said result may be due to the presence of the intermetallic compounds in the absence of interfacing foil which is confirmed by Scanning Electron Microscope (SEM) and Energy-dispersive X-ray spectroscopy (EDS)analysis.

Doors, privacy and the public sphere: a conceptual discussion on the spatial structure of early modern Istanbul

Abstract The aim of this article is to offer a new conceptual framework for the study of various spaces in Istanbul during the seventeenth and the eighteenth centuries. I contend that rather than the sharp distinction manifested with the public–private dichotomy, we need to focus on gradations of privacy. I offer qāpū and bāb as two new concepts borrowed from the period's own repertoire for representing the macro and micro ends of the spatial gradation. Theoretically, I draw on George Simmel's definition of doors as the interfaces of spatial formation.

In-Plane mechanical and failure responses of honeycombs with syntactic foam cell walls

This work investigates the load-bearing and energy absorption capacities of hexagonal honeycombs with syntactic cell walls and spatial gradation of cell densities. Structures are processed and property-tuned by varying the volume fraction of hollow microspheres (microballoons), cell wall thickness, and spatial gradation of cell densities. The mechanical behavior of the structures is characterized by subjecting them to in-plane compression. Full-field deformation and failure responses of these structures at meso- and macro-scales are characterized by digital image correlation (DIC) and postmortem fracture analyses, respectively. Mesoscale analyses reveal heterogeneous strain accumulation at the cell hinges, which leads to a fracture in the vicinity of the hinge. Failure is characterized by a brittle mode in all samples. It is shown that the energy absorption capacity of the structures can be improved with the spatially-controlled incorporation of microballoons into the cell struts, at the penalty of reduced overall strength. In addition, cell-density gradation offers a notable improvement to the energy absorption performance over uniform density structures and a mechanism to lower structural density while achieving high mechanical performance.

Spatially resolved isotope tracing reveals tissue metabolic activity.

Isotope tracing has helped to determine the metabolic activities of organs. Methods to probe metabolic heterogeneity within organs are less developed. We couple stable-isotope-labeled nutrient infusion to matrix-assisted laser desorption ionization imaging mass spectrometry (iso-imaging) to quantitate metabolic activity in mammalian tissues in a spatially resolved manner. In the kidney, we visualize gluconeogenic flux and glycolytic flux in the cortex and medulla, respectively. Tricarboxylic acid cycle substrate usage differs across kidney regions; glutamine and citrate are used preferentially in the cortex and fatty acids are used in the medulla. In the brain, we observe spatial gradations in carbon inputs to the tricarboxylic acid cycle and glutamate under a ketogenic diet. In a carbohydrate-rich diet, glucose predominates throughout but in a ketogenic diet, 3-hydroxybutyrate contributes most strongly in the hippocampus and least in the midbrain. Brain nitrogen sources also vary spatially; branched-chain amino acids contribute most in the midbrain, whereas ammonia contributes in the thalamus. Thus, iso-imaging can reveal the spatial organization of metabolic activity.

3D Periodic Cellular Materials with Tailored Symmetry and Implicit Grading

Periodic cellular materials allow triggering complex elastic behaviors within the volume of a part. In this work, we study a novel type of 3D periodic cellular materials that emerge from a growth process in a lattice. The growth is parameterized by a 3D star-shaped set at each lattice point, defining the geometry that will appear around it. Individual tiles may be computed and used in a periodic lattice, or a global structure may be produced under spatial gradations, changing the parametric star-shaped set at each lattice location.Beyond free spatial gradation, an important advantage of our approach is that elastic symmetries can easily be enforced. We show how shared symmetries between the lattice and the star-shaped set directly translate into symmetries of the periodic structures’ elastic response. Thus, our approach enables restricting the symmetry of the elastic responses – monoclinic, orthorhombic, trigonal, and so on – while freely exploring a wide space of possible geometries and topologies. We make a comprehensive study of the space of symmetries and broad combinations that our method spans and demonstrate through numerical and experimental results the elastic responses triggered by our structures.

Landscape Development Types in Central Lika 1980−2012 − Applying Spatial and Process-Oriented GIS Model

This paper presents an analysis and definition of development types and subtypes in the landscape of Central Lika, based on processes of change in the period 1980−2012 CORINE Land Cover database data for 1980 and 2012 were used to establish the landscape types in Central Lika in those years. The landscape types in Central Lika were determined according to land cover/land use. Based on the mutual relations between the established landscape types in the two observed years, we established six landscape development types and three subtypes in Central Lika. The spatial distribution of landscape development types and subtypes in Central Lika was determined using the Standard Deviational Ellipse (Directional Distribution) spatial analysis method. The results obtained showed that in the observation period (1980−2012), most of the area of Central Lika (89.46%) belonged to the Stagnation landscape type. Other development types were present to a much lesser extent (about 5.5%) and were found to be Vegetation succession, Agrarisation, Vegetation degradation and Built-up land. We established a spatial gradation of three phases in the process of vegetation succession, that is, development subtypes from the centre to the margins of the research area. At the same time, in the observation period, the process and trend of extensification of land use in Central Lika was twice as present as intensification.

Biomimetic Scaffolds with a Mineral Gradient and Funnel-Shaped Channels for Spatially Controllable Osteogenesis.

A facile method is described herein for generating a mineral gradient in a biodegradable polymer scaffold. The gradient is achieved by swelling a composite film made of polycaprolactone (PCL) and hydroxyapatite (HAp) nanoparticles with a PCL solution. During the swelling process, the solvent and PCL polymer chains diffuse into the composite film, generating a gradient in HAp density at their interface. The thickness of the mineral gradient can be tuned by varying the extent of swelling to match the length scale of the natural tendon-to-bone attachment (20-60 µm). When patterned with an array of funnel-shaped channels, the mineral gradient presents stem cells with spatial gradations in both biochemical cues (e.g., osteoinductivity and conductivity associated with the HAp nanoparticles) and mechanical cues (e.g., substrate stiffness) to stimulate their differentiation into a graded distribution of cell phenotypes. This new class of biomimetic scaffolds holds great promise for facilitating the regeneration of the injured tendon-to-bone attachment by stimulating the formation of a functionally graded interface.

Spatial optimization of watershed best management practice scenarios based on boundary-adaptive configuration units

Spatial optimization of watershed best management practice (BMP) scenarios based on watershed modeling is an effective decision support tool for watershed management. During such optimization, existing types of BMP configuration units for configuring BMPs (or BMP configuration units, e.g. subbasins, hydrologic response units, farms) remain fixed boundaries once they have been created through spatial discretization prior to BMP scenario optimization. This sort of “boundary-fixed” method does not allow for adjustments to the spatial characteristics of BMP configuration units. Hence, it runs the risk of missing superior BMP scenarios that could have been obtained by adjusting unit boundaries and may produce less effective spatial optimization. In this article, we propose a new approach to the spatial optimization of BMP scenarios based on boundary-adaptive configuration units. The proposed optimization approach adopts slope positions (basic landform units along hillslopes inherently related to physical hillslope processes) as BMP configuration units and dynamically adjusts their boundaries by using quantitative information about their spatial gradation (i.e. fuzzy slope positions) during the optimization. A case study conducted in the Youwuzhen watershed in Fujian, China, showed that the proposed optimization approach can significantly enlarge the search space and obtain optimal BMP scenarios with better cost-effectiveness and higher optimization efficiency than with boundary-fixed units. The proposed optimization approach provides a new alternative framework for spatial optimization of BMP scenarios, in which other watershed models, intelligent optimization algorithms, and BMP configuration units available for boundary adjustment can be applied to BMP scenario optimization in a boundary-adaptive manner. This study also exemplifies the potential for transforming qualitative, vague, and empirical geographical knowledge about slope position units related to physical hillslope processes and BMPs into quantitative, explicit, and automated geospatial algorithms for effectively resolving environmental management problems in a more geographically meaningful way.

Characterization of Spatially Graded Biomechanical Scaffolds.

Advances in fabrication have allowed tissue engineers to better mimic complex structures and tissue interfaces by designing nanofibrous scaffolds with spatially graded material properties. However, the nonuniform properties that grant the desired biomechanical function also make these constructs difficult to characterize. In light of this, we developed a novel procedure to create graded nanofibrous scaffolds and determine the spatial distribution of their material properties. Multilayered nanofiber constructs were synthesized, controlling spatial gradation of the stiffness to mimic the soft tissue gradients found in tendon or ligament tissue. Constructs were characterized using uniaxial tension testing with digital image correlation (DIC) to measure the displacements throughout the sample, in a noncontacting fashion, as it deformed. Noise was removed from the displacement data using principal component analysis (PCA), and the final denoised field served as the input to an inverse elasticity problem whose solution determines the spatial distribution of the Young's modulus throughout the material, up to a multiplicative factor. Our approach was able to construct, characterize, and determine the spatially varying moduli, in four electrospun scaffolds, highlighting its great promise for analyzing tissues and engineered constructs with spatial gradations in modulus, such as those at the interfaces between two disparate tissues (e.g., myotendinous junction, tendon- and ligament-to-bone entheses).

MANAGEMENT ASPECTS OF ENVIRONMENTAL AND ECONOMIC CONSEQUENCES WATER-EROSION DESTRUCTION OF SOILS IN THE STEPS OF UKRAINE

Using GIS technologies, spatial raster models for the distribution of the values of the factors influencing the potential danger of soil erosion were created, the erosion hazard was estimated using the modified RUSLE (Revised Universal Soil Loss Equation) model, the potential of annual soil losses from arable land was calculated, and the spatial gradation of erosion disturbance was presented administratively territorial units in the steppe zone of Ukraine. Allocated about 32.7% of arable land, which have increased erosion hazard. About 48 administrative-territorial units have a specific area of less than 5% of erosion-disturbed lands and are characterized by a stable type of agrolandscapes to water-erosion processes. The predominant number of administrative-territorial units with high erosion-accumulative potential, the proportion of the area is 15% or more, located in the western and southwestern parts of the steppe zone of Ukraine. The specific area of erosion-hazardous lands in separate administrative-territorial units reaches up to 32%. Over the past years, the design and implementation of land conservation activities have declined significantly. Land conservation occurs mainly in a natural way. It should be noted that article 27 of the Law of Ukraine «On Land Protection» provides for economic incentives for measures to protect and use land and increase soil fertility, but there is no procedure for this. Therefore, the results obtained make it possible to determine the managerial aspects of the environmental and economic consequences of water-erosion degradation of soils and the need for spatially discrete-distributive implementation of adaptive-landscape anti-erosion design with elements of soil-protective agriculture.

Cinco tensores de curvatura. Una aproximación a la topología espacio-temporal contemporánea

La cultura contemporánea se identifica con sus propias formas de producción y reproducción del espacio. Un proyecto absolutamente visual de dimensión imaginaria. Lo que aquí se busca exponer es la emergencia de una nueva topología espacio temporal a través del análisis de ciertas estrategias proyectuales cuyas formas y estructuras organizativas se redefinen lógica y tácticamente para comprender las dinámicas complejas del mundo contemporáneo.A través de cinco estrategias proyectuales concretas, “Cinco Tensores de Curvatura Contemporáneos”, se irá trazando una lectura transversal que introduce modelos y discursos provenientes del campo de la sociología y la arquitectura. Los tensores de curvatura denominados así por el sociólogo Luis Castro Nogueira en el libro “La risa del espacio” (1997), hacen referencia a prácticas materiales cuyos códigos visuales pliegan y tensan lo que fue el primer momento espacial moderno. Todo este proceso de gradación espacial concluye en el espacio virtual. Una tipicidad sintética y simulada por dispositivos electrónicos en la que sujeto, objeto y medio devienen en una progresiva condición inmaterial. Lejos de establecer modelos absolutos estos desplazamientos topológicos buscan instaurar una actitud crítica necesaria para proyectarse hacia futuros escenarios.

Tailorable elasticity of cantilever using spatio-angular functionally graded biomimetic scales

Cantilevered beams are of immense importance as structural and sensorial members for a number of applications. Endowing tailorable elasticity can have wide ranging engineering ramification. Such tailorability could be possible using some type of spatial gradation in the beam's material or cross section. However, these often require extensive additive and subtractive material processing or specialized casts. In this letter, we demonstrate an alternative bio inspired mechanical pathway, which is based on exploiting the nonlinearity that would arise from a functionally graded distribution of biomimetic scales on the surface using an analytical approach. This functional gradation is geometrically sourced and could arise from either spatial or angular gradation of scales. We analyze such a functionally graded cantilever beam under uniform loading. In comparison with uniformly distributed scales, we find significant differences in bending stiffness for both spatial and angular gradations. Spatial and angular functional gradation share some universality but also sharp contrasts in their effect on the underlying beam. A combination of both types of gradation in the structure can be used to alternatively increase or decrease stiffness and therefore a pathway to tailor the elasticity of a cantilever beam relatively easily. These results give rise to an architected framework for designing and optimizing the topography of leveraged solids.

Computational contact mechanics analysis of laterally graded orthotropic half-planes

PurposeFrictional sliding contact problems between laterally graded orthotropic half-planes and a flat rigid stamp are investigated. The presented study aims at guiding engineering applications in the prediction of the contact response of orthotropic laterally graded members.Design/methodology/approachThe solution procedure is based on a finite element (FE) approach which is conducted with an efficient FE analysis software ANSYS. The spatial gradations of the orthotropic stiffness constants through the horizontal axis are enabled utilizing the homogeneous FE approach. The Augmented Lagrangian contact algorithm is used as an iterative non-linear solution method in the contact analysis.FindingsThe accuracy of the proposed FE solution method is approved by using the comparisons of the results with those computed using an analytical technique. The prominent results indicate that the surface contact stresses can be mitigated upon increasing the degree of orthotropy and positive lateral gradations.Originality/valueOne can infer from the literature survey that, the contact mechanics analysis of orthotropic laterally graded materials has not been investigated so far. In this study, an FE method-based computational solution procedure for the aforementioned problem is addressed. The presented study aims at guiding engineering applications in the prediction of the contact response of orthotropic laterally graded members. Additionally, this study provides some useful points related to computational contact mechanics analysis of orthotropic structures.

Geo-modeling of water-erosion processes in the Dnieper River basin

The paper presents the internal structure of the geomorphological system and performs geo-modeling of water-erosion processes in the basin of the Dnieper river. As a result of hydrological geo-modeling, the study identifies 776 basins of orders IV–IX and determines the total length of the erosion network of the transborder basin. Based on GIS technology, it creates spatial raster models of the distribution of the values of factors influencing potential hazards of soil erosion; assesses erosion hazards using the modified RUSLE (Revised Universal Soil Loss Equation) model; calculates the potential of annual soil loss of arable land, and presents a spatial gradation of potential erosive violations of sub-basins of various orders in the area of the Dnieper river basin.

A Dynamical Computational Model of Circulating Blood Gases, Hemoglobin Binding, and pH Regulation in the Microcirculation

A new computational model is developed to characterize the dynamical aspects of simultaneous blood‐tissue transport and exchange of O2, CO2, HCO3− and H+ in the coronary microcirculation by accurately simulating the rapidly changing intra‐capillary concentration profiles as the blood gets warmed, acidified, deoxygenated, and carbonated while flowing through the myocardial capillaries. It is based on our 2006 steady‐state, nonlinear, convection‐diffusion‐permeation‐reaction computational model of circulating blood gases, hemoglobin (Hb) binding, and acid‐base buffering in the blood which is available for download from our JSim model repository (http://www.physiome.org/jsim/models/webmodel/NSR/Exchange_O2_CO2_HCO3_and_H+). The kinetics are complicated by: (i) intravascular axial diffusion, (ii) RBC/plasma velocity ratio > 1, (iii) gas and ion permeation through RBC, endothelial and cell membranes, (iv) carbonic anhydrase‐catalyzed CO2 hydration reaction and HCO3‐ buffering in blood and tissue, (v) nonlinear competitive temperature‐dependent binding of Hb, O2, CO2 and H+ inside RBCs, (vi) myoglobin‐facilitated transport of O2 in cardiac cells, and (vii) O2 consumption and CO2 production inside mitochondria, with CO2 production and the respiratory quotient dependent upon the substrates, gas concentrations, cardiac work levels, and the rate of mitochondrial oxidative phosphorylation. These interactions smooth the axial spatial gradations in fluxes of O2 from blood into tissue and of CO2 out into the lung air. The simplest version of this extended model focuses on intracapillary RBC‐plasma interactions and the conditions for alveolar‐arterial differences in oxygen saturation. The cell‐tissue versions incorporate a new kinetic model of cytochrome c oxidase (CcO) that accurately characterizes the kinetics of O2 consumption by CcO as a function of cytochrome c redox fraction, mitochondrial inner membrane electrical and proton gradients (i.e. proton motive force; energy state), O2, and pH. The model serves as the dynamical exchange component of whole body gas exchange and acid‐base regulation. With augmentation to bind 15O2 or 17O2, this model can be used for the analysis of dynamic PET image sequences or NMR studies for estimating the regional tissue O2 consumption.Support or Funding InformationSupported by NIH grant U01‐HL122199

Soil property variation mapping through data mining of soil category maps

AbstractSpatial information on soil properties is an important input to hydrological models. In current hydrological modelling practices, soil property information is often derived from soil category maps by the linking method in which a representative soil property value is linked to each soil polygon. Limited by the area‐class nature of soil category maps, the derived soil property variation is discontinuous and less detailed than high resolution digital terrain or remote sensing data. This research proposed dmSoil, a data‐mining‐based approach to derive continuous and spatially detailed soil property information from soil category maps. First, the soil–environment relationships are extracted through data mining of a soil map. The similarity of the soil at each location to different soil types in the soil map is then estimated using the mined relationships. Prediction of soil property values at each location is made by combining the similarities of the soil at that location to different soil types and the representative soil property values of these soil types. The new approach was applied in the Raffelson Watershed and Pleasant Valley in the Driftless Area of Wisconsin, United States to map soil A horizon texture (in both areas) and depth to soil C horizon (in Pleasant Valley). The property maps from the dmSoil approach capture the spatial gradation and details of soil properties better than those from the linking method. The new approach also shows consistent accuracy improvement at validation points. In addition to the improved performances, the inputs for the dmSoil approach are easy to prepare, and the approach itself is simple to deploy. It provides an effective way to derive better soil property information from soil category maps for hydrological modelling. Copyright © 2014 John Wiley & Sons, Ltd.

The mechanics of PLGA nanofiber scaffolds with biomimetic gradients in mineral for tendon-to-bone repair

Attachment of dissimilar materials is prone to failure due to stress concentrations that can arise their interface. A compositionally or structurally graded transition can dissipate these stress concentrations and thereby toughen an attachment. The interface between compliant tendon and stiff bone utilizes a monotonic change in hydroxylapatite mineral (“mineral”) content to produce a gradient in mechanical properties and mitigate stress concentrations. Previous efforts to mimic the natural tendon-to-bone attachment have included electrospun nanofibrous polymer scaffolds with gradients in mineral. Mineralization of the nanofiber scaffolds has typically been achieved using simulated body fluid (SBF). Depending on the specific formulation of SBF, mineral morphologies ranged from densely packed small crystals to platelike crystal florets. Although this mineralization of scaffolds produced increases in modulus, the peak modulus achieved remained significantly below that of bone. Missing from these prior empirical approaches was insight into the effect of mineral morphology on scaffold mechanics and on the potential for the approach to ultimately achieve moduli approaching that of bone. Here, we applied two mineralization methods to generate scaffolds with spatial gradations in mineral content, and developed methods to quantify the stiffening effects and evaluate them in the context of theoretical bounds. We asked whether either of the mineralization methods we developed holds potential to achieve adequate stiffening of the scaffold, and tested the hypothesis that the smoother, denser mineral coating could attain more potent stiffening effects. Testing this hypothesis required development of and comparison to homogenization bounds, and development of techniques to estimate mineral volume fractions and spatial gradations in modulus. For both mineralization strategies, energy dispersive X-ray analysis demonstrated the formation of linear gradients in mineral concentration along the length of the scaffolds, and Raman spectroscopic analysis revealed that the mineral produced was hydroxylapatite. Mechanical testing showed that the stiffness gradient using the new method was significantly steeper. By analyzing the scaffolds using micromechanical modeling techniques and extrapolating from our experimental results, we present evidence that the new mineralization protocol has the potential to achieve levels of stiffness adequate to contribute to enhanced repair of tendon-to-bone attachments.