Homogeneous Material Properties Research Articles

TRIGON: A Monte-Carlo graded composition scheme for multiphysics reactor calculations

Typically, Monte-Carlo neutronic calculations of nuclear reactors use a coarse mesh of discrete zones, each with homogeneous material properties. Computation resources limit the spatial resolution, along with the safety parameters’ estimates’ accuracy. As a result, the chosen safety margins for values such as the point power peaking factor need to be larger, resulting in a restricted reactor performance.We present here the TRIGON method that allows neutronic analysis for problems with graded material characteristics, increasing the overall accuracy with little computational penalty, and by using standard Monte-Carlo tools. We use a non-rectangular mesh, along with a specialized tallying scheme to effectively model piecewise-linearly varying materials. We demonstrate the method’s applicability in multiphysics problem solutions by calculating a reactor with a coolant temperature gradient, as well as in a continuous fuel burnup problem. We focus on MTR type research reactor fuel, but the method may suit power reactors just as well.

Finite element modeling with subject-specific mechanical properties to assess knee osteoarthritis initiation and progression.

Finite element models of the knee can be used to identify regions at risk of mechanical failure in studies of osteoarthritis. Models of the knee often implement joint geometry obtained from magnetic resonance imaging (MRI) or gait kinematics from motion capture to increase model specificity for a given subject. However, differences exist in cartilage material properties regionally as well as between subjects. This paper presents a method to create subject-specific finite element models of the knee that assigns cartilage material properties from T2 relaxometry. We compared our T2 -refined model to identical models with homogeneous material properties. When tested on three subjects from the Osteoarthritis Initiative data set, we found the T2 -refined models estimated higher principal stresses and shear strains in most cartilage regions and corresponded better to increases in KL grade in follow-ups compared to their corresponding homogeneous material models. Measures of cumulative stress within regions of a T2 -refined model also correlated better with the region's cartilage morphology MRI Osteoarthritis Knee Score as compared with the homogeneous model. We conclude that spatially heterogeneous T2 -refined material properties improve the subject-specificity of finite element models compared to homogeneous material properties in osteoarthritis progression studies. Statement of Clinical Significance: T2 -refined material properties can improve subject-specific finite element model assessments of cartilage degeneration.

Ph-Net: Parallelepiped Microstructure Homogenization Via 3d Convolutional Neural Networks

Microstructures are attracting academic and industrial interests with the rapid development of additive manufacturing. The numerical homogenization method has been well studied for analyzing mechanical behaviors of microstructures; however, it is too time-consuming to be applied to online computing or applications requiring high-frequency calling, e.g., topology optimization. Data-driven homogenization methods emerge as a more efficient choice but limit the microstructures into a cubic shape, which are infeasible to the periodic microstructures with a more general shape, e.g., parallelepiped. This paper introduces a fine-designed 3D convolutional neural network (CNN) for fast homogenization of parallel-shaped microstructures, named PH-Net. Superior to existing data-driven methods, PH-Net predicts the local displacements of microstructures under specified macroscope strains instead of direct homogeneous material, motivating us to present a label-free loss function based on minimal potential energy. For dataset construction, we introduce a shape-material transformation and voxel-material tensor to encode microstructure type,base material and boundary shape together as the input of PH-Net, such that it is CNN-friendly and enhances PH-Net on generalization in terms of microstructure type, base material, and boundary shape. PH-Net predicts homogenized properties with hundreds of acceleration compared to the numerical homogenization method and even supports online computing. Moreover, it does not require a labeled dataset and thus is much faster than current deep learning methods in training processing. Benefiting from predicting local displacement, PH-Net provides both homogeneous material properties and microscopic mechanical properties, e.g., strain and stress distribution, yield strength, etc. We design a group of physical experiments and verify the prediction accuracy of PH-Net.

Corrosion study on chill casting effect on aluminium A356 reinforced with Hematite metal matrix composites

In this article, an attempt have been made through investigate the effect of copper chill on Aluminium Metal Matrix Composites (AMMCs), and also to explore the corrosion resistance of the prepared Al A356-Hematite particulate metal matrix composites, which is cast through sand casting practice without and with copper chills at ends to get isotropic and homogeneous material properties under liquid metallurgical manner, by varying weight fractions of Hematite particulates assortments from 0 wt% −12 wt% in segments about 3 wt%. The test samples were prepared as per ASTM criteria. The prepared specimens were subjected to corrosion test and Micrographic analysis. The experiments were conducted to study the corrosion rate by weight-loss method, the specimens were soaked in 3.5% NaCl solution with a time intervals of 24 h to 96 h in steps of 24 h. Result shows that, the copper chill A356-Hematite composites shows lesser corrosion rate compare to without copper chill. Micrographic investigation has been executed using XRD (X-Ray Diffraction) patterns and SEM (Scanning Electron Microscope) photos. The presence of Hematite elements was conformed by XRD pattern and also revealed that the even distribution of Hematite elements in the A356 matrix alloy of composite casted with copper chills. It was also pragmatic that fine-grained structure is obtained due to rapid cooling which influences in enlightening the corrosion resistance of the composites with copper chills. And also due to an increased content of reinforcement in both without and with copper chill composites results in significant enhancement in corrosion resistance. The Copper chill specimens shows higher corrosion resistance than As-cast specimens.

Modeling of the mechanical properties of fused deposition modeling (FDM) printed fiber reinforced thermoplastic composites by asymptotic homogenization

Fused deposition modeling (FDM) is a low-cost additive manufacturing method with moderate tolerances and high design flexibility. Ample studies are being undertaken for modeling the mechanical properties of FDM by using the Finite Element Method (FEM). The process technique of FDM results in anisotropic inner structures that are affected by the chosen manufacturing parameters. Moreover, composite filaments, such as fiber-reinforced polymers, have anisotropy even in filament form before FDM printing. These anisotropic effects are needed to be examined and incorporated for an adequate model. In order to speed up the design stage, we aim to prepare a practical method for simulating the mechanical properties of FDM-printed fiber-reinforced polymer composites. In this work, we computed the homogenized material properties for various fiber lengths, fiber volume percentages, and fiber orientations by asymptotic homogenization at the microscale. Then, mesoscale simulations are carried out through FEM simulations by incorporating the influences of process parameters. In this way, we demonstrate the effect of various micro- and mesostructural features on the homogenized properties step by step.

Static, free vibration, and buckling analyses of laminated composite plates via an isogeometric meshfree collocation approach

An isogeometric meshfree collocation (IMC) approach is developed for the static, free vibration, and buckling analyses of laminated composite plates. As a promising alternative to the Galerkin method, the collocation method is introduced into the isogeometric analysis framework to reduce the computational cost and improve the convergence rate. An adaptive refinement strategy based on the gradient of strain energy is further implemented to generate more accurate results with higher computational efficiency. By adopting the first-order shear deformation plate theory, only one element is required to be modeled through the thickness of the laminated composite plate with homogenized material properties. The robustness and efficacy of the proposed method are demonstrated through a series of benchmark problems. It is found that the proposed approach can yield more accurate results at a similar convergence rate than its isogeometric analysis collocation counterpart. The effects of changing parameters such as the Young’s modulus ratio, thickness-to-span ratio, and orthotropy angle on the structural analysis of composite plates are subsequently investigated in detail under different boundary and loading conditions. The simulation results are in good agreement with reference solutions.

T2 Mapping Refined Finite Element Modeling to Predict Knee Osteoarthritis Progression.

This paper presents a novel method for informing cartilage material properties in finite element models from T2 relaxometry. In the developed pipeline, T2 relaxation values are mapped to elements in subject-specific finite element models of the cartilage and menisci. The Young's modulus for each element within the cartilage is directly calculated from its corresponding T2 relaxation voxel value. Our model was tested on a single subject (Subject ID 9932809, Kellgren-Lawrence grade 2) from the Osteoarthritis Initiative dataset at baseline imaging. For comparison, an identical finite element model was built with homogeneous material properties. Kinematics of the stance phase of a standard gait cycle were used as model constraints. Simulation results were compared qualitatively to the MRI Osteoarthritis Knee Score (MOAKS) from the same baseline timepoint. Our T2-refined material model showed higher maximum shear strain in regions with moderate cartilage loss as compared to the homogeneous material model, and the homogeneous model showed higher maximum principal stress and maximum shear strain in regions with no cartilage loss. These results show that a homogeneous material model likely underestimates tissue strains in regions with cartilage damage while overestimating strains in regions with healthy cartilage. This preliminary study demonstrates that T2-refined material properties are more appropriate than assumptions of homogeneity in predictive models of cartilage damage.Clinical relevance- The proposed pipeline demonstrates a computationally efficient way to improve the subject-specificity of finite element models used for evaluation of osteoarthritis.

A numerical anatomy-based modelling of bamboo microstructure

Bamboo has attracted considerable recent interest in sustainable buildings as the fastest-growing natural material retaining mechanical properties similar to structural wood while being an effective CO2 absorber during its growth. Previous efforts to estimate bamboo material properties and their behaviour using homogenisation techniques used simplified assumptions on the geometry of the inhomogeneous microstructure, hence these methods failed to account for the different homogenised material properties in the directions lateral to the bamboo culm. This study presents a novel anatomy-based numerical bamboo microstructure analysis that accurately represents the geometrical features of the material, leading to a transversely anisotropic effective material model. We compare the resulting effective elastic properties to those obtained with state-of-the-art numerical and analytical approaches found in the literature. It is concluded that our anatomy-based representative volume element provides a better understanding of the material microstructure and its corresponding effective stiffness properties in the longitudinal and lateral directions.

Numerical wave speed sensitivity study for assessment of myocardial elasticity in a simplified linear elastic and isotropic left ventricle model

Since tissue elasticity can change with pathology, noninvasive assessment of elasticity has received increasing attention. Emerging methods for assessing cardiac elasticity utilize either an external source to induce propagating shear waves or intrinsic longitudinal waves created by natural cardiac events such as left ventricle stretching that occurs due to atrial kick during late diastole. However, the effect of morphological variations that occur in diseased hearts on this longitudinal stretch wave and the corresponding estimate of elasticity is not well understood and is an active area of research. This study investigated the sensitivity of longitudinal wave speed to material properties and chamber geometry parameters through numerical simulations using a finite element model of a bullet-shaped chamber with homogeneous isotropic linear elastic material properties. A longitudinal impulse displacement was applied to the base edge of the model to investigate wave propagation from this boundary. Parametric studies were performed for variables of interest related to geometry and material properties. The wave speeds estimated from simulation results were used to determine wave speed sensitivity to each variable. Wave speed was found to be a strong function of material elasticity and a weak function of chamber geometry and viscous damping. Simulated wave speed as a function of elasticity was in good agreement with wave speeds determined from an analytical expression for longitudinal wave speed in elastic thin plates. These promising preliminary results increase our understanding of how these parameters affect intrinsic longitudinal wave speed and warrant future studies addressing the impact of patient-specific model geometry, material anisotropy and hyperelasticity, and boundary conditions on wave speed.

Integration of Design for Additive Manufacturing Constraints With Multimaterial Topology Optimization of Lattice Structures for Optimized Thermal and Mechanical Properties

Abstract The design of multimaterial lattice structures with optimized elasticity tensor, coefficient of thermal expansion (CTE), and thermal conductivity is the main objective of the research presented in this article. In addition, the additive manufacturability of the lattice structure is addressed using a prismatic density filter to eliminate support structures, and an octant symmetry filter is used to design symmetric lattices. A density-based topology optimization model is formulated with a homogenization method and solved using a sequential linear programming method to obtain the desired unit cell geometry of the lattice structure. The optimized unit cell obtained has high mechanical stiffness, a low CTE, and low thermal conductivity. A finite element analysis is carried out on the optimized lattice structure and an equivalent cube of computed effective properties (with the same loading and boundary conditions) to validate the computed homogenized material properties. The results from the finite element analysis show that the methodology followed to generate the lattice structure is accurate. Such lattice structures with tailored material properties can be used in aerospace parts that are subjected to mechanical and thermal loads. The complex multimaterial geometry produced from the topology optimization routine presented here is intended explicitly for the manufacture of parts using the directed energy deposition process with multiple material deposition nozzles.

3-Dimensional Bond-Based Peridynamic Representative Volume Element Homogenization

In this study, a 3-dimensional (3D) implementation of representative volume element homogenization using bond-based peridynamic formulation is presented. Periodic boundary condition is established by coupling the displacements of periodic point pairs. Homogenized (effective) material properties are obtained based on peridynamic displacement gradient tensor. The current approach is validated by considering a composite material without defects and comparing homogenized properties with results obtained from another homogenization approach. Next, the capability of the current approach is demonstrated by considering randomly generated cracks with arbitrary orientation and location. It can be concluded that the current approach can be an alternative approach to obtain 3-dimensional homogenized material properties for heterogeneous materials with defects.

A homogenization method for nonlinear inhomogeneous elastic materials

BackgroundFast simulation techniques are strongly favored in computer graphics, especially for the nonlinear inhomogeneous elastic materials. The homogenization theory is a perfect match to simulate inhomogeneous deformable objects with its coarse discretization, as it reveals how to extract information at a fine scale and to perform efficient computation with much less DOF. The existing homogenization method is not applicable for ubiquitous nonlinear materials with the limited input deformation displacements. MethodsIn this paper, we have proposed a homogenization method for the efficient simulation of nonlinear inhomogeneous elastic materials. Our approach allows for a faithful approximation of fine, heterogeneous nonlinear materials with very coarse discretization. Modal analysis provides the basis of a linear deformation space and modal derivatives extend the space to a nonlinear regime; based on this, we exploited modal derivatives as the input characteristic deformations for homogenization. We also present a simple elastic material model that is nonlinear and anisotropic to represent the homogenized materials. The nonlinearity of material deformations can be represented properly with this model. The material properties for the coarsened model were solved via a constrained optimization that minimizes the weighted sum of the strain energy deviations for all input deformation modes. An arbitrary number of bases can be used as inputs for homogenization, and greater weights are placed on the more important low-frequency modes. ResultsBased on the experimental results, this study illustrates that the homogenized material properties obtained from our method approximate the original nonlinear material behavior much better than the existing homogenization method with linear displacements, and saves orders of magnitude of computational time. ConclusionsThe proposed homogenization method for nonlinear inhomogeneous elastic materials is capable of capturing the nonlinear dynamics of the original dynamical system well.

Monitoring of Torque Induced Strain in Composite Shafts with Embedded and Surface-Mounted Optical Fiber Bragg Gratings.

In this study, silica glass, optical fiber Bragg gratings (FBGs) are used for torque-induced strain monitoring in carbon fiber reinforced polymer (CFRP) hollow shafts toward the development of a methodology for structural load monitoring. Optical fibers with gratings are embedded during shaft manufacturing, by an industrial filament winding process, along different orientations with respect to its central axis and surface mounted after production. Experimental results are supported by numerical modeling of the shaft with appropriate boundary conditions and homogenized material properties. For an applied torque up to 800 Nm, the strain sensitivity of an embedded grating positioned along the reinforcing fibers’ direction winded under 55° is in the order of 3.6 pm/Nm, while this value is more than 4× times higher than the other examined orientations. The study also shows that surface-mounted optical fiber Bragg gratings along the reinforcing carbon fibers’ direction perform equally well in monitoring strains in composite shafts under torque.

Non-invasive prediction of the mouse tibia mechanical properties from microCT images: comparison between different finite element models

New treatments for bone diseases require testing in animal models before clinical translation, and the mouse tibia is among the most common models. In vivo micro-Computed Tomography (microCT)-based micro-Finite Element (microFE) models can be used for predicting the bone strength non-invasively, after proper validation against experimental data. Different modelling techniques can be used to estimate the bone properties, and the accuracy associated with each is unclear. The aim of this study was to evaluate the ability of different microCT-based microFE models to predict the mechanical properties of the mouse tibia under compressive load. Twenty tibiae were microCT scanned at 10.4 µm voxel size and subsequently compressed at 0.03 mm/s until failure. Stiffness and failure load were measured from the load–displacement curves. Different microFE models were generated from each microCT image, with hexahedral or tetrahedral mesh, and homogeneous or heterogeneous material properties. Prediction accuracy was comparable among models. The best correlations between experimental and predicted mechanical properties, as well as lower errors, were obtained for hexahedral models with homogeneous material properties. Experimental stiffness and predicted stiffness were reasonably well correlated (R2 = 0.53–0.65, average error of 13–17%). A lower correlation was found for failure load (R2 = 0.21–0.48, average error of 9–15%). Experimental and predicted mechanical properties normalized by the total bone mass were strongly correlated (R2 = 0.75–0.80 for stiffness, R2 = 0.55–0.81 for failure load). In conclusion, hexahedral models with homogeneous material properties based on in vivo microCT images were shown to best predict the mechanical properties of the mouse tibia.

Effective properties and eddy current losses of soft magnetic composites

This paper presents a semi-analytical homogenization model for Soft Magnetic Composites (SMCs), providing the effective magnetic behavior and the level of Eddy Current (EC) losses. Both linear and nonlinear magnetic behavior are considered. A magnetic circuit made of SMC is then modeled with a Finite Element Model (FEM). The size of heterogeneities of SMC being much smaller than the device size, the proposed approach relieves the burden of a very fine mesh in the FEM, by using the effective properties of an equivalent homogeneous material. The approach is validated by comparing the results on the homogenized magnetic circuit with the ones obtained from a computationally heavy FEM describing the heterogeneities with a very fine mesh. The results show that the homogenized model provides a very accurate description of the magnetic behavior and EC losses of SMC for both linear and nonlinear cases.

Time fractional thermoelastic problem of a thick cylinder with non homogeneous material properties

In this article, we assume a two dimensional thermoelastic problem of nonhomogeneous thick hollow cylinder within the context of fractional order derivative of order 0 < α ≤ 2. Convective heat exchange boundary conditions are applied at the curved surface, whereas the lower surface and the upper surface of the cylinder are considered at zero temperature. Furthermore cylinder is subjected to a sectional heating at the outer curved surface of cylinder. Let the material properties of the cylinder except Poisson’s ratio and density are considered to be expresses by a simple power law in axial direction. The solution of the thermoelastic problem is obtained in terms of trigonometric and Bessel’s functions. Both the thermal and mechanical behavior is analyzed by the influence of inhomogeneity. Numerical computations are carried out for a mixture of copper and tin metals for both homogeneous and nonhomogeneous cases. Results of numerical solutions are illustrated graphically for temperature distribution and thermal stresses for all the different values of the fractional-order parameter α with the help of Mathematica software.

Dynamic modelling, simulation and experiments of a micro-cutter with applications to cell perforation

The nonlinear three-dimensional dynamic equations of motion of a micro-cutter driven longitudinally at ultrasonic operating frequencies are derived using Kane's method. The micro-cutter is assumed to be immersed in a fluid, and in contact with an oocyte, which is to be perforated by the micro-cutter. The micro-cutter is modelled as an Euler-Bernoulli cantilever beam attached to a moving base. The shear and rotary inertia effects are neglected by considering a slender-shaped beam with homogeneous and isotropic material properties. It is assumed that there is no slip between the micro-cutter tip and the embryo membrane. The model presented demonstrates that the longitudinal excitation input of a micropipette results in excitation of out-of-plane, lateral motion due to the nonlinear dynamic coupling of the dynamics. Experimental results of membrane perforation are presented in the work supporting oocyte micro-cutter observations regarding suitable frequencies of excitation for effective oocyte membrane perforation.

Multiscale optimisation of resonant frequencies for lattice-based additive manufactured structures

This paper introduces a novel methodology for the optimisation of resonant frequencies in three-dimensional lattice structures. The method uses a multiscale approach in which the homogenised material properties of the lattice unit cell are defined by the spatially varying lattice parameters. Material properties derived from precomputed simulations of the small scale lattice are projected onto response surfaces, thereby describing the large-scale metamaterial properties as polynomial functions of the small-scale parameters. Resonant frequencies and mode shapes are obtained through the eigenvalue analysis of the large-scale finite element model which provides the basis for deriving the frequency sensitivities. Frequency tailoring is achieved by imposing constraints on the resonant frequency for a compliance minimisation optimisation. A sorting method based on the Modal Assurance Criterion allows for specific mode shapes to be optimised whilst simultaneously reducing the impact of localised modes on the optimisation. Three cases of frequency constraints are investigated and compared with an unconstrained optimisation to demonstrate the algorithms applicability. The results show that the optimisation is capable of handling strict frequency constraints and with the use of the modal tracking can even alter the original ordering of the resonant mode shapes. Frequency tailoring allows for improved functionality of compliance-minimised aerospace components by avoiding resonant frequencies and hence dynamic stresses.

Finite element analysis of eyeball with its microstructure by use of homogenization method

An effective simulation of the eyeball containing microstructures which are optic nerves and lamina cribrosa, through homogenization method, was studied. Entire domain of the eyeball is divided into a fine-scale zone and a coarse-scale zone to reduce the number of degrees of freedom accompanied by modeling the microstructures. In the coarse-scale zone, homogenized material properties of the lamina cribrosa combined with the optic nerves are employed to compute overall behavior, while the optic nerves are directly modeled to obtain their local behavior in the fine-scale zone. Numerical tests with models having different size of the fine-scale zone showed that this homogenization scheme did not severely deteriorate solution accuracy and makes it possible to reflect the microstructures with reduced computational cost. Then, this multiscale method was employed to confirm a clinical result that a greater susceptibility to development of glaucoma corresponds to a larger curvature of the lamina cribrosa.

Optimization of the failure criterion in micro-Finite Element models of the mouse tibia for the non-invasive prediction of its failure load in preclinical applications

New treatments against osteoporosis require testing in animal models and the mouse tibia is among the most common studied anatomical sites. In vivo micro-Computed Tomography (microCT) based micro-Finite Element (microFE) models can be used for predicting the bone strength non-invasively, after proper validation against experiments. The aim of this study was to evaluate the ability of different microCT-based bone parameters and microFE models to predict tibial structural mechanical properties in compression. Twenty tibiae were scanned at 10.4 μm voxel size and subsequently tested in uniaxial compression at 0.03 mm/s until failure. Stiffness and failure load were measured from the load-displacement curves. Standard morphometric parameters were measured from the microCT images. The spatial distribution of bone mineral content (BMC) was evaluated by dividing the tibia into 40 regions. MicroFE models were generated by converting each microCT image into a voxel-based mesh with homogeneous isotropic material properties. Failure load was estimated by using different failure criteria, and the optimized parameters were selected by minimising the errors with respect to experimental measurements. Experimental and predicted stiffness were moderately correlated (R2 = 0.65, error = 14% ± 8%). Normalized failure load was best predicted by microFE models (R2 = 0.81, error = 9% ± 6%). Failure load was not correlated to the morphometric parameters and weakly correlated with some geometrical parameters (R2 < 0.37). In conclusion, microFE models can improve the current estimation of the mouse tibia structural properties and in this study an optimal failure criterion has been defined. Since it is a non-invasive method, this approach can be applied longitudinally for evaluating temporal changes in the bone strength.