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Numerical studies of compression failure in triply periodic minimal surface-based ceramic foams
Get PDFMicrostructures with minimal surfaces can be often found in natural porous architectures, where the surface tension minimizes the area. The triply periodic minimal surfaces (TPMS) [1] are an example of such microstructures. Compared with other porous structures, TPMS have three significant features: firstly, their geometries can be completely expressed via analytical functions; secondly, TPMS are periodic in three independent directions and thirdly, the mean curvature of TPMS is zero [2]. Transforming the TPMS-based unit cell into a lattice structure has particular usage in aerospace, nuclear energy, and biomedical applications where light weight, high stiffness, and temperature resistance are of critical importance. In the presented studies, the failure behavior of four typical TPMS structures (Primitive, Gyroid, Neovius, and IWP) under compression was studied using finite element analysis. Numerical modeling of the damage propagation and strength prediction was performed by removing the finite elements in which the appropriate damage criterion is reached. Utilizing the equations of the generated TPMS structures, the wall thickness of unit cell was considered the main parameter that defined the ceramics volume fraction and should be taken into consideration. Therefore, various unit cell models for different wall thicknesses were generated and used to investigate the impact of the cell geometry on the damage initiation, propagation, and overall compression strength. The results of compression strength and damage development were compared with those of other TPMS structures for the same wall thickness and volume fraction. Finally, the grade TPMS porous structure was provided to verify the effect of wall thickness variation on damage evolution on the macroscale
Projector assembly: bridging Poisson and elasticity formulations
Get PDFVirtual element methods define their shape functions implicitly (tailored to each element’s geometry), foregoing the typical reference element and transformation scheme usually employed by the finite element method. The formulation leverages the use of polynomial projections supplied by heuristic stabilizations when necessary. These projections are represented by projector matrices, which require the solution of a local system. Elasticity formulations usually employ an ð¿ 2 -projection from a displacement multifield onto a strain multifield, requiring the solution of a considerably larger system than a typical Poisson problem would require, with dense matrices and lots of zeroes. This work presents a way to obtain the projections for elasticity formulation by assembling from the ð¿ 2 -projection for each derivative of the one-field a Poisson formulation, resulting in smaller local systems being solved and more efficient storage. This approach is based on the linearity of both projections and derivatives, and is shown in the examples to preserve the convergence rate of the method
Computational interpretation of shape memory epoxy: processing and its operation
Get PDFThe shape forming and restoration mechanisms of shape memory epoxy originate from the molecular-scale dynamics that epoxy molecules undergo during thermomechanical processes. In this study, the microstructural changes that occur at the molecular scale caused by heat and load during the programming and operation of the epoxy network were investigated using molecular dynamics simulations. The mechanical behaviors of each molecule were analyzed by classifying it into translation, rotation, and deformation based on the classical kinematic framework. Specifically, depending on its structural properties, each molecular component was rearranged to different levels, forming local residual stresses. The principle leading to shape recovery as the subsequent thermal load breaks the equilibrium of residual stresses and resulting changes in the mechanical anisotropy of entire epoxy network were also analyzed through a subcontinuum perspective. This study has the potential to be extended to a method for designing epoxy resins that satisfy desired physical properties and shape recovery performanc
Input-output reduced order modeling for public health intervention evaluation
Get PDFIn recent years, mathematical models have become an indispensable tool in the planning, evaluation, and implementation of public health interventions. Models must often provide detailed information for many levels of population stratification. Such detail comes at a price: in addition to the computational costs, the number of considered input parameters can be large, making effective study design difficult. To address these difficulties, we propose a novel technique to reduce the dimension of the model input space to simplify model-informed intervention planning. The method works by first applying a dimension reduction technique on the model output space. We then develop a method which allows us to map each reduced output to a corresponding vector in the input space, thereby reducing its dimension. We apply the method to the HIV Optimization and Prevention Economics (HOPE) model, to validate the approach and establish proof of concept
Effect of particle-size-scaling on particle interactions in DEM-simulations of sand in the context of air pluviation
Get PDFDEM (discrete element method) is a widely used numerical simulation method, which models the behaviour of a bulk substrate based on the individual interactions of many particles. One of its possible applications is the modelling of sand behaviour in different laboratory tests, e.g., cone penetration tests [1] or direct shear tests [2]. Furthermore, DEM is specifically of interest as a modelling method for investigating air pluviation, because it models the individual inter-particle and particle-environment interactions, both friction and collisions, which determine the compaction and homogeneity of the created samples. However, one disadvantage of DEM is the relatively long computational time [3] especially with decreasing particle sizes. This makes larger particle sizes compared to reality more interesting, especially for large scale or repeating simulations. On the other hand, if the size of the chosen particles is too large, certain interactions, such as interactions with other materials and equipment, may not be simulated in a way that properly represents real behaviour. This would lead to preferring smaller sized particles, which again would lead to longer computational times. Therefore, the chosen particle size as an important aspect of DEM simulations will be discussed, as well as the effects on different simulation aspects. This includes necessary parameter calibrations, the resulting inter-particle and particle-environment interactions as well as the achieved simulation results and accuracies. Of specific interest is the largest particle size, at which accurate and realistic results concerning real-world particle interactions can be achieved. Further, the effects of graded particle sizes to better represent the sand during the pluviation process will be discussed
Determination of high-order frequency response of nonlinear systems using the arc-length method
Get PDFWhile linear systems have been extensively studied in the past few decades, systems with strong nonlinearities are not as widely investigated. One of the reasons why these are less applied in engineering is due to the fact that solving nonlinear equations usually demands a steep increase in processing capacity and time when compared to their linear counterparts. As computers become more powerful, significantly more advanced nonlinear systems can be studied and analyzed, providing solutions that are more accurate for real-world applications. When it comes to frequency analysis, it is possible that nonlinear frequency response shows the phenomena of hardening or softening. In this case, the resonance peaks of the frequency response are tilted to the right or left, respectively, in comparison with linear frequency response. The consequences of these phenomena might prove essential to safety assessment of real-life structures as the resonance peak might greatly differ from those obtained in a linear analysis. In this study, the high-order frequency response of the Helmholtz-Duffing oscillator is analyzed in order to evaluate its influence on the system. The oscillator exhibits Duffing nonlinearities represented by cubic springs and Helmholtz nonlinearities represented by quadratic springs. The high-order harmonic balance method was used to determine the dynamic equation in the frequency domain. The nonlinearities were numerically integrated based on the coefficients of the Fourier series. Originally used to find the solution path of nonlinear static structural analyses, the arc-length method was adapted to determine the nonlinear frequency respons
Beyond lubrication flow for thin-film manufacturing
Get PDFReynolds’ hydrodynamic lubrication theory has been used extensively to analyze and quantify thin film manufacturing1 . Applications span liquid flows in bearings, coatings, and molds, and gas flows between rigid or elastic surfaces. To enable further applications of efficient, reduced-order modelling, we pursue streamlined algorithms for non-Newtonian liquids in marginally “thin” geometries with multiple phases and capillarity. The goal is expanded use of “modified”, non-traditional lubrication methods to bring physics-based knowledge to bear in process design, optimization, and control methods
Design of in-mold decoration mold for complex thin-walled parts
Get PDFIn order to address the issues of warping deformation and long-term production of complex thin-walled parts during In-Mold Decoration (IMD) production, the structure design of the IMD mold was carried out with the humidifier top cover as the production object. To ensure the flow characteristics of molten plastic in the mold during the injection molding process, based on the technical contradiction analysis of TRIZ theory, the hot runner mold is improved to mix cold and hot runner, that is, the sprue is set as a hot runner, the branch runner is set as a cold runner, and use a multi-point injection cold gate solution. And construct a complex structure numbering method to arrange and design various complex structure undercut-forming side insert mechanism, design of special structure lifters along the same direction of motion the two inverted buckle at the same time undercut-forming. The lifter mechanisms are used to complete the molding, parting, demolding and ejection of plastic parts, multiple uses for one mechanism. In order to optimize product quality and improve production efficiency, providing theoretical and empirical support for the production of complex thin walled parts with IMD molds. Then design the cooling system and demolding mechanism separately. Finally, based on Moldflow software, the final flow of plastic part warpage analyzed. The maximum warping deformation of the product is 0.7055mm, while the maximum warping deformation of the traditional cold runner mold is 0.8519mm, reducing the warping deformation of the humidifier top cover
Pratt truss characteristics for optimal weight
Get PDFThis paper presents a study on the characteristics of Pratt trusses under conditions of optimal or near-optimal weight. Trusses with varying numbers of panels, spans, and heights are selected for analysis. Several characteristics describing truss geometry and internal forces are examined. Four dimensioning approaches are developed to perform calculations and obtain data for analysis. A parametric model of truss geometry is developed and integrated with a finite element calculation algorithm in the Rhino8/Grasshopper software. The data are processed and analyzed using the machine learning software Weka and the statistical analysis software RStudio. Results show correlations between various truss characteristics. This study focuses on truss weight and height-span ratio to find the optimal weight. Based on truss height at optimal weight for each span, other characteristics are analyzed. It is observed that a larger number of panels increases the truss weight but also makes the results more consistent and predictable. The objective of this work is to better understand Pratt truss performance, which can be used to reduce the size of optimization tasks
Three-field model for wave propagation in porous media based on mixture theories
Get PDFSimulations of wave propagation in porous media are important to the understanding of various phenomena, such as seismic effects and non-destructive testing. The derivation and implementation of finite element analysis for a fully dynamic three-field deformable porous media model based on the de la Cruz and Spanos (dCS) theory [1] is presented. The dCS theory accounts for the fluid viscous dissipation mechanism and nonreciprocal solid-fluid interactions, which are neglected in Biot theory [2]. While the Biot theory is based on experimental data, the dCS theory is derived from mixture theories associated with the volume fraction concept and representing the connection between micro and macro pore scales. dCS results presented build upon recent FE model for quasi-static analysis [3]. Here, for the fully dynamic case incorporating both fluid and solid inertia, the accuracy and robustness of the FEA model is verified by wave propagation examples in one and two dimensions. Time integration scheme utilized and the changes in convergence rates according to how strongly coupled is the system will be discussed. The required element approximation order for all variables to ensure numerical stability will be demonstrated. The presented model is compared with the results from Biot theory, allowing one to observe the differences between the two theories and their relevance. The solutions in the time and frequency domain are also discussed, where the analysis of the correspondent eigenproblem leads to important information regarding wave velocity and attenuation