3D Solids Research Articles

Augmented Reality for Exploring Solids: A Study on Improving Pre-Service Teachers

Applications of augmented reality are gradually being integrated into teaching at various levels and types of schools. Augmented reality has the potential to transform the training of future teachers in the context of developing their mathematical knowledge, digital skills, and teaching competencies. The paper focuses on researching the impact of augmented reality on the learning of future primary teachers. The aim was to investigate the impact of AR applications on the development of cognitive and psychomotor skills and on students' motivation to learn. The study had a mixed research design. Using a pedagogical experiment, we investigated the effectiveness of an educational intervention based on the use of applications Augmented Reality in combination with hands on activities in the training of future teachers. The educational intervention was a set of activities that were carried out in a mixed reality environment using the 3D solids construction kit, the Polyedres augmentes and GeoGebra applications. The content of the educational intervention was the exploration of significant elements and properties of solids. We tested students' knowledge and abilities in the following areas: identification of simple solids from a picture; identification of significant elements of solids (vertices, edges and faces); identification of the shapes of faces of solids; nets of solids; simple metric tasks with solids. The study was conducted in 2024 with 152 primary education students as part of geometry courses. In line with the results of previous research in this area, we found that AR has the potential to improve understanding of geometric concepts, increase interactivity and student motivation. Augmented reality opens up new possibilities for exploring solids and their properties, as it allows for transfer between planar and spatial representation of solids and helps to develop spatial imagination.

Experimental method for internal deformation measurement of 3D solids with embedded cracks based on 3D printing and digital speckle techniques

Quantification of the internal deformation of fractured solids such as rock masses under external loads, especially the deformation around internal fractures, is crucial for understanding and predicting the failure of fractured solids. However, it is very difficult to achieve the goal using conventional experimental methods. In this study, we proposed a novel internal deformation measurement method based on three-dimensional (3D) printing and digital speckle techniques. The 3D printing technology was applied to fabricate a 3D transparent model with an embedded elliptical crack and to set a speckle pattern on the internal section of the transparent model. The digital image correlation (DIC) method was used to determine the internal deformation field of the 3D fractured model. The measured displacements and strains of the internal sections in the fractured model were compared with the numerical simulation results. The comparison indicates that the proposed experimental method can well determine the deformation inside the 3D model. This built-in speckle method can realize real-time observation of the internal deformation of a 3D solid model in a non-contact and non-destructive manner.

Investigating the pathophysiology and evolution of internal carotid dissection: a fluid-structure interaction simulation study.

Arterial dissection, a condition marked by the tearing of the carotid artery's inner layers, can result in varied clinical outcomes, including progression, stability, or spontaneous regression. Understanding these outcomes' underlying mechanisms is crucial for enhancing patient care, particularly with the increasing use of computer simulations in medical diagnostics and treatment planning. The aim of this study is to utilize computational analysis of blood flow and vascular wall to: (1) understand the pathophysiology of stroke-like episodes in patients with carotid artery dissection; and (2) assess the effectiveness of this method in predicting the evolution of carotid dissection. Utilizing contrast-enhanced magnetic resonance angiography (MRA), we segmented images of the patient's right internal carotid artery. These images were transformed into 3D solids for simulation in Ansys multifisic software, employing a two-way fluid structure interaction (FSI) analysis. Simulations were conducted across two wall conditions (atherosclerotic and normal) and three pressure states (hypotension, normotension, hypertension). The simulations indicated a significant pressure discrepancy between the true and false lumens of the artery. This suggests that flap motion and functional occlusion under hypertensive conditions could be the cause of the clinical episodes. Thrombotic risk and potential for dissection extension were not found to be critical concerns. However, a non-negligible risk of vessel dilation was assessed, aligning with the patient's clinical follow-up data. This study highlights specific hemodynamic parameters that could elucidate carotid artery dissection's mechanisms, offering a potential predictive tool for assessing dissection progression and informing personalized patient care strategies.

Selective Generation of Reactive Oxygen Species in Photocatalytic Oxidation by Tuning Porphyrin-Based COFs' Dimensionality.

Regulating the selective generation of reactive oxygen species (ROS) is a significant challenge in the field of photocatalytic oxidation, with successful approaches still being limited. Herein, we present a strategy to selectively generate singlet oxygen (1O2) and superoxide radicals (O2•-) by tuning the dimensionality of porphyrin-based covalent organic frameworks (COFs). The transformation of COFs from three-dimensional (3D) solids to two-dimensional (2D) sheets was achieved through the reversible protonation of the imine bond. Upon irradiation, both bulk and thin-layer COF-367 can transfer energy to O2 to generate 1O2. However, thin-layer COF-367 exhibited a superior performance compared to its bulk counterpart in activating O2 to form the O2•- radicals via electron transfer. After excluding the influences of the band structure, O2 adsorption energy, and frontier orbital composition attributed to the dimensionality of the COFs, it is reasonably speculated that the variance in ROS generation arises from the differential exposure ratios of the active surfaces, leading to distinct reaction pathways between the carrier and O2. This study is the first to explore the modulation mechanism of COF dimensionality on the activation of the O2 pathway, underscoring the importance of considering COF dimensionality in photocatalytic reactions.

(Keynote) Macroscopic Materials Synthesized from Nanoparticle Superlattices

One of the promises of nanotechnology in its early developmental stages was the ability to make designer materials with precise control over individual building block composition and organization in 3D space. In recent years, material synthesis methods have advanced to be able to create a multitude of nanoparticles of varying sizes, shapes, and compositions, providing a vast array of building blocks to use as materials fabrication components. Additionally, processing methods have been developed to arrange these nanoparticles into ordered arrays, to dry them into thin films, and even to sinter them into more complex bulk solids. However, the fundamental promise of being able to build a material with controlled hierarchical structure across all length scales (atomic crystal structure, molecular composition; nanoscale feature size, shape, and organization; microstructure; macroscopic form) has been challenging to realize. A materials synthesis and processing route that could create free-standing, macroscopic materials or arbitrary three-dimensional shapes with precisely controlled nanoparticle positions across the entirety of the material composition would therefore be a major advancement. Here, we demonstrate a nanoparticle-based building block called a “Nanocomposite Tecton (NCT)” that enables a self-assembly route to fabricating free-standing 3D solids of arbitrary macroscopic shapes that can utilize a multitude of different nanoparticle compositions, and also possess specifically programmed nanoscale particle arrangements and controlled microstructure. This talk will outline the key synthesis and processing steps that enable this method of making materials with programmed material structure across ~7 orders of magnitude in length scale, thereby realizing a long-standing goal of nanomaterials fabrication.

Integrating Computer Vision and CAD for Precise Dimension Extraction and 3D Solid Model Regeneration for Enhanced Quality Assurance

This paper focuses on the development of an integrated system that can rapidly and accurately extract the geometrical dimensions of a physical object assisted by a robotic hand and generate a 3D model of an object in a popular commercial Computer-Aided Design (CAD) software using computer vision. Two sets of experiments were performed: one with a simple cubical object and the other with a more complex geometry that needed photogrammetry to redraw it in the CAD system. For the accurate positioning of the object, a robotic hand was used. An Internet of Things (IoT) based camera unit was used for capturing the image and wirelessly transmitting it over the network. Computer vision algorithms such as GrabCut, Canny edge detector, and morphological operations were used for extracting border points of the input. The coordinates of the vertices of the solids were then transferred to the Computer-Aided Design (CAD) software via a macro to clean and generate the border curve. Finally, a 3D solid model is generated by linear extrusion based on the curve generated in CATIA. The results showed excellent regeneration of an object. This research makes two significant contributions. Firstly, it introduces an integrated system designed to achieve precise dimension extraction from solid objects. Secondly, it presents a method for regenerating intricate 3D solids with consistent cross-sections. The proposed system holds promise for a wide range of applications, including automatic 3D object reconstruction and quality assurance of 3D-printed objects, addressing potential defects arising from factors such as shrinkage and calibration, all with minimal user intervention.

Free vibration analysis of three-dimensional solids with arbitrary geometries using discrete Ritz method

A numerical method, discrete Ritz method (DRM), is proposed for the free vibration analysis of three-dimensional (3D) solids with arbitrary geometries. The problem is formulated within a cuboidal domain, and arbitrarily shaped 3D solid can be simulated by assigning cutouts within the cuboidal domain. Geometries of 3D solids are characterized by using level set functions. DRM transforms the problem into a variable stiffness system in which Chebyshev polynomials are used to approximate vibrational behavior and Gauss points are used to discretize the cuboidal domain. The vibration behaviors of arbitrarily shaped solids can be numerically simulated by setting the stiffness and thickness of Gauss points within the cutouts to zero. New formulations in DRM have resulted in completely standard energy functionals and computation procedures for arbitrarily shaped 3D solids. Free vibration behaviors of 3D solids, including polygonal cross-section cylinders, circular cylinders, rectangular plates with cutouts, perforated super-elliptical plates, ellipsoids, and pyramids, are investigated, and results are compared with those reported in the literature. DRM is shown to be capable of solving free vibration problems of complex-shaped 3D solids with high precision and stability.

3D solid of SARS-CoV-2 viral particles applying Legendre polynomials from tomography Fourier analysis.

We show the construction of 3D solids (volumetric 3D models) of SARS-CoV-2 viral particles from the tomographic studies (videos) of SARS-CoV-2-infected tissues. To this aim, we propose a video analysis (tomographic images) by frames (medical images of the virus), which we set as our metadata. We optimize the frames by means of Fourier analysis, which induces a periodicity with simple structure patterns to minimize noise filtering and to obtain an optimal phase of the objects in the image, focusing on the SARS-CoV-2 cells to obtain a medical image under study phase (MIS) (process repeated over all frames). We build a Python algorithm based on Legendre polynomials called "2DLegendre_Fit," which generates (using multilinear interpolation) intermediate images between neighboring MIS phases. We used this code to generate m images of size M×M, resulting in a matrix with size M×M×M (3D solid). Finally, we show the 3D solid of the SARS-CoV-2 viral particle as part of our results in several videos, subsequently rotated and filtered to identify the glicoprotein spike protein, membrane protein, envelope, and the hemagglutinin esterase. We show the algorithms in our proposal along with the main MATLAB functions such as FourierM and Results as well as the data required for the program execution in order to reproduce our results.

The effect of visuo-haptic exploration on the development of the geometric cross-sectioning ability

Cross-sectioning is a shape understanding task where the participants must infer and interpret the spatial features of three-dimensional (3D) solids by depicting their internal two-dimensional (2D) arrangement. An increasing body of research provides evidence of the crucial role of sensorimotor experience in acquiring these complex geometrical concepts. Here, we focused on how cross-sectioning ability emerges in young children and the influence of multisensory visuo-haptic experience in geometrical learning through two experiments. In Experiment 1, we compared the 3D printed version of the Santa Barbara Solids Test (SBST) with its classical paper version; in Experiment 2, we contrasted the children’s performance in the SBST before and after the visual or visuo-haptic experience. In Experiment 1, we did not identify an advantage in visualizing 3D shapes over the classical 2D paper test. In contrast, in Experiment 2, we found that children who had the experience of a combination of visual and tactile information during the exploration phase improved their performance in the SBST compared with children who were limited to visual exploration. Our study demonstrates how practicing novel multisensory strategies improves children’s understanding of complex geometrical concepts. This outcome highlights the importance of introducing multisensory experience in educational training and the need to make way for developing new technologies that could improve learning abilities in children.

Computational Parametric Analysis of Cellular Solids with the Miura‐Ori Metamaterial Geometry under Quasistatic Compressive Loads

Origami‐based metamaterials have widespread application prospects in various industries including aerospace, automotive, flexible electronics, and civil engineering structures. Among the wide range of origami patterns, the fourfold tessellation known as Miura‐ori is of particular attraction to engineers and designers. More specifically, researchers have proposed different 3D structures and metamaterials based on the geometric characteristics of this classic origami pattern. Herein, a computational modeling approach for the design and evaluation of 3D cellular solids with the Miura‐ori metamaterial geometry which can be of zero or nonzero thicknesses is presented. To this end, first, a range of design alternatives generated based on a numerical parametric model is designed. Next, their mechanical properties and failure behavior under quasistatic axial compressive loads along three perpendicular directions are analyzed. Then, the effects of various geometric parameters on their energy absorption behavior under compression in the most appropriate direction are investigated. The findings of this study provide a basis for future experimental investigations and the potential application of such cellular solids for energy‐absorbing purposes.

Application of a microplane damage model for concrete to an isogeometric scaled boundary formulation for 3D solids

AbstractMicroplane models have the advantage of describing damage‐induced anisotropy, which is common in quasi‐brittle materials such as concrete, in a simple and straightforward way. Over the past decades, various microplane models have been formulated to describe different loading cases and phenomena in concrete structures. They include pure damage and pure plasticity based microplane models or a combination of these two approaches. In this work, as a first step, a microplane damage model, which is derived from the principle of energy equivalence, is applied in the framework of an isogeometric 3D solid in boundary representation. Isogeometric analysis has the advantage that it can represent exactly complex geometries, which can influence the correct description of damage evolution. In addition, the use of a boundary representation in combination with NURBS and B‐splines is in accordance with the modeling technique common in CAD and allows for a straightforward application of the design model to the analysis process. The boundary is described using bi‐variate NURBS while the interior of the solid is approximated using uni‐variate B‐splines. The combination of isogeometric analysis with a model that can capture the finely distributed cracking of the concrete matrix represents a modeling strategy that can effectively support the development of thin‐walled shell structures made of textile‐reinforced concrete. Several examples are studied in order to investigate the ability of the microplane damage model to correctly describe quasi‐brittle fracture in this kind of non‐standard discretization formulation. Furthermore, a comparison to the standard finite element method is conducted.

An SFEM Abaqus UEL for Nonlinear Analysis of Solids

In this paper, three different smoothed finite element method (SFEM), viz., node-based smoothed finite element method (NS-FEM), face-based smoothed finite element method (FS-FEM) and [Formula: see text]-finite element method ([Formula: see text]-FEM) are adopted for 3D solids undergoing large deformation. The common feature of all these techniques is the introduction of smoothed strain which is written as a weighted average of the compatible strain field over smoothing domains. The choice of smoothing domain is what differentiates them. The spatial discretization can be based on the simplest and automatically genera-table four-node tetrahedral elements and aforementioned techniques have shown to yield accurate results even on a coarser discretization. To take the advantages of the SFEM, it is beneficial to the FEM community to have it implemented in the widely used Abaqus[Formula: see text] software. Such an implementation is challenging because the neighboring SFEM elements are interconnected in the smoothed strain matrices in the elemental level. In this work, the above-mentioned SFEM models are implemented in the commercial software Abaqus using the softwares’ user element (UEL) feature. The challenges during the definition and the assembly of the smoothing domains are effectively addressed in this work. The developed UEL and the associated files can be downloaded from https://github.com/nsundar/3DSFEM. The implementation is validated against benchmark examples and the robustness is demonstrated with complicated real-life problems, viz., tire patch contact with road and simulation of human thumb.

Diatom-inspired stiffness optimization for plates and cellular solids

Diatoms, a class of aquatic autotrophic microorganisms, are characterized by silicified exoskeletons with highly complex architectures. These morphologies have been shaped by the selection pressure that the organisms have been subjected to during their evolutionary history. Two properties which are highly likely to have contributed to the evolutionary success of current diatom species are lightweightness and structural strength. Thousands of diatom species are present in water bodies today, and although each has its unique shell architecture, a strategy that is common across species is the uneven and gradient solid material distribution across their shells. The aim of this study is to present and evaluate two novel structural optimization workflows inspired by material grading strategies in diatoms. The first workflow mimics the Auliscus intermidus diatoms’ surface thickening strategy and generates continuous sheet structures with optimal boundaries and local sheet thickness distributions when applied to plate models subjected to in-plane boundary conditions. The second workflow mimics the Triceratium sp. diatoms’ cellular solid grading strategy, and produces 3D cellular solids with optimal boundaries and local parameter distributions. Both methods are evaluated through sample load cases, and prove to be highly efficient in transforming optimization solutions with non-binary relative density distributions into highly performing 3D models.

Non‐van der Waals 2D Materials for Electrochemical Energy Storage

AbstractThe development of advanced electrode materials for the next generation of electrochemical energy storage (EES) solutions has attracted profound research attention as a key enabling technology toward decarbonization and electrification of transportation. Since the discovery of graphene's remarkable properties, 2D nanomaterials, derivatives, and heterostructures thereof, have emerged as some of the most promising electrode components in batteries and supercapacitors owing to their unique and tunable physical, chemical, and electronic properties, commonly not observed in their 3D counterparts. This review particularly focuses on recent advances in EES technologies related to 2D crystals originating from non‐layered 3D solids (non‐van der Waals; nvdW) and their hallmark features pertaining to this field of application. Emphasis is given to the methods and challenges in top‐down and bottom‐up strategies toward nvdW 2D sheets and their influence on the materials’ features, such as charge transport properties, functionalization, or adsorption dynamics. The exciting advances in nvdW 2D‐based electrode materials of different compositions and mechanisms of operation in EES are discussed. Finally, the opportunities and challenges of nvdW 2D systems are highlighted not only in electrochemical energy storage but also in other applications, including spintronics, magnetism, and catalysis.

Process study of copper preparation by FDM-assisted limited domain electrodeposition

A combination of Fused Deposition Modeling (FDM) and electrochemical deposition was used to prepare copper samples, and the influence of different copper anodes on the composition and microstructure of the prepared samples were investigated. It was shown that under the deposition conditions of constant current, the deposited products were mainly copper with trace impurity elements when brass, leaded brass, phosphor bronze, manganese copper, purple copper, and beryllium copper were used as anodes. The surface morphology of copper films obtained when brass was used as an anode was the flattest, and the thickness was also the largest. Electrodeposition experiments of 20 and 150 layers of copper samples were conducted using brass as the anode and the preliminary validation of FDM-assisted electrochemical additive manufacturing fabricating 3D solids.

Abrupt onset of the capillary-wave spectrum at wall-fluid interfaces.

Surfaces between 3D solids and fluids exhibit a wide variety of phenomena both at equilibrium, such as roughening transitions, interfacial fluctuations and wetting, and also out-of-equilibrium, such as the surface growth of driven interfaces. These phenomena are described very successfully using lower dimensional (2D) effective models which focus on the physics associated with emergent mesoscopic lengths scales, parallel to the interface, where the 2D-like behaviour is physically transparent. However, the precise conditions under which this dimensional reduction is justifiable have remained unclear. Here we show that, for a wall-fluid interface, a dimensional reduction from 3D-like to 2D-like behaviour - identified via the decay of density correlations - occurs abruptly at a specific value of the contact angle, and indicates the beginning of interfacial-like 2D behaviour and the spontaneous onset of the capillary-wave spectrum. The reduction from 3D to 2D is characterised by the divergence of a correlation length perpendicular to the interface revealing a morphological change in the nature of density correlations. Counter-intuitive effects occur, including that 3D behaviour can persist up to the wetting temperature and also that 2D behaviour can begin when no wetting layer is present and the adsorption is negative.

Exploring Students’ Geometrical Thinking Through Dynamic Transformations Using 3D Computer-Based Representations

This paper examines Grade 6 students’ thinking about geometrical solids and their properties in the context of a computer-based task. The main focus is to explore how students interact with a number of tasks based on the dynamic transformation of computer-based representations of 3D solids in a geometry classroom with the aid of a Dynamic Geometric Environment. The analysis of two teaching experiments suggests that the dynamic transformations of geometrical solids encourage the students to investigate relationships between the solids and their properties and their 2D representations. Through the tasks, students realize the existence of non-trivial conventions in 2D representations and become aware that angles and edge dimensions may be distorted. The study provides insight into student learning around geometric solids and their properties, and consequently an opportunity to enhance the teaching of 3D geometry.

TOPOLOGICAL RELATIONSHIPS IN R3 FOR 3D CADASTRE

Abstract. 3D cadastre is necessary for accurately representing real-world parcels that not only exist on land but also above and below ground. The ability to cater to the physical and legal attributes of these 3D parcels is important as it affects the Rights, Restrictions and Responsibilities (RRRs). Tasks such as modification and analysis of 3D parcels also require topological information in addition to the geometrical properties of a 3D parcel. Topological properties describe the connectivity information between objects. In terms of the 3D cadastre, the intrinsic topology is used to ensure the spatial objects that make up a 3D solid are valid, while extrinsic topology is used to determine adjacent 3D solids or overlapping parcels. This paper attempted to define topological relationships in 3D space specifically for the use of 3D cadastre. 3D to 3D solid and 2D to 2D surface topological interactions were defined and proved using the Dimensionally Extended Nine Intersection Model (DE-9IM). The “meet (touches)” and “overlaps” topological relationships were found to be the main topological relationship used in the 3D cadastre.

On the dynamics of 3D nonlocal solids

The stress-driven nonlocal continuum theory is a well-established integral elasticity formulation. Modelling the elastic strain via a convolution integral between stress and an averaging kernel, the theory leads to an integro-differential structural problem for arbitrary 3D nonlocal solids. Integral elasticity solutions are mainly available for 1D solids by adopting a bi-exponential kernel and reverting the boundary-value integro-differential problem to an equivalent differential formulation involving both classical and constitutive boundary conditions. A general computational framework to implement the stress-driven theory for 3D nonlocal solids is still missing. This paper tackles this issue, solving the relevant integro-differential problem by a two-field finite-element approach involving displacements and stresses. The approach can handle the dynamics of complex small-size structures of arbitrary shape. Focusing on free vibration responses, two examples are presented: a 2D rectangular plate, serving as benchmark to demonstrate size effects captured by stress-driven nonlocal elasticity, and a 3D solid modelling a typical dual microcantilever resonator with overhang.

3D printed metamaterials for damping enhancement and vibration isolation: Schwarzites

Schwarzites are 3D solids with negative Gaussian curvatures that have unusual and interesting mechanical properties. Energy dissipation is one such property Schwarzites offer due to their high ductility and strength. The energy dissipating mechanism can be exploited to remove energy from dynamic systems that have continuous energy input and reduce the system response. Here, the energy dissipation is characterized for 3D printed specimen with solid and Schwarzite geometry. Further, the usefulness of the property is shown by analyzing the reduction in response quantities by performing dynamical simulations. It is found that having Schwarzites geometry increases the damping ratio by nearly 80% with the same amount of material as a solid support. Further, vibration isolation properties of Schwarzites are also illustrated.