Anisotropic Finite Element Model Research Articles

Internal Short Circuit and Dynamic Response of Large-Format Prismatic Lithium-Ion Battery Under Mechanical Abuse

Abstract Prismatic lithium-ion batteries (LIBs) are becoming the most prevalent battery type in electric vehicles, and their mechanical safety is garnering increased attention. Understanding the mechanical response and internal short circuit (ISC) of prismatic LIBs during dynamic impact is important for enhancing the safety and reliability of electric vehicles. Thanks to the pioneer's works on the cylindrical and pouch LIB, prismatic LIB can draw on relevant experimental and numerical modeling methods. However, there is still a lack of research on the dynamic effects of prismatic LIB in various loading directions. To address this disparity, the current research utilizes quasi-static and dynamic impact experiments on prismatic LIBs as a foundation. First, the mechanical response of a sizable prismatic LIB under quasi-static conditions and the dynamic effects are examined when subjected to mechanical abuse from various loading directions. Second, an anisotropic finite element model that considers dynamic strain rates are developed, enabling it to accurately represent the mechanical response to both quasi-static and dynamic impact loads. At last, we performed an analysis of ISC occurring under dynamic loading conditions combining the experimental and simulated results. The experimental results as well as the established model can provide reference for the safe design, application, and analysis of prismatic LIBs.

Is All-on-four effective in case of partial mandibular resection? A 3D finite element study

IntroductionThe aim of the work is to analyze stress distribution on 3D Finite Element (FE) models at bone, implant, and framework level of different designs for fixed implant-supported prostheses in completely edentulous patients, comparing results on whole and partially resected mandibles. Materials and methods3D anisotropic FE models of a whole and of a partially resected mandible were created using a TC scan of a cadaver's totally edentulous mandible. Two types of totally implant-supported rehabilitation were simulated, with four implants: parallel fixtures on whole mandible and on resected mandible, All-on-four-configured fixtures on whole mandible and on partially resected mandible. A superstructure comprising only metal components of a prosthetic framework were added, while stress distribution and its maximum values were analyzed at bone, implant, and superstructure level. ResultsThe results highlight that:(1) implant stresses are greater on the whole mandible than on the resected one;(2) framework and cancellous-bone stresses are comparable in all cases;(3) on the resected mandible, maximum stress levels at the cortical-bone/implant interface are higher than in whole-mandible rehabilitation. The opposite applies for maximum stresses on external cortical bone, measured radially with respect to the implant from the point of maximum stress at the interface. DiscussionOn the resected mandible, All-on-four configuration proved biomechanically superior to parallel implants considering radial stresses on implants and cortical bone. Still, maximum stresses increase at the bone/implant interface. A design with four parallel implants minimizes the stress on a resected mandible while, on the whole mandible, the All-on-four rehabilitation proves superior at all levels (bone, implant, and framework).

Homogenized characterization of cylindrical Li‐ion battery cells using elliptical approximation

Homogenization and finding the constitutive model of jellyroll in cylindrical lithium-ion batteries can be challenging because of their form factor. Taking samples out of the original jellyroll wounding or compressing cell assembly in its cylindrical coordinates are two possibilities for measuring the homogenized lateral strength of the cell. However, the former causes loss of accuracy due to changing constraints and electrolyte environment, and the latter requires complex fixtures that are not readily available or even practical to manufacture. Various approaches have been suggested by researchers to circumvent the above difficulties and allow the extraction of hardening curves. However, the precision of those approaches diminishes when the cells are under global compression vs local punch deformations. In this study, an updated homogenization method is established, using a lateral compression test on the jellyroll. The homogenization method is based on the assumption that the circular cross-section of the jellyroll under compression is deformed in an elliptical shape. Then the principle of virtual work is used to extract the hardening curve. To validate the above characterization model, isotropic and anisotropic finite element models were developed using crushable foam and modified honeycomb material models from the LS-DYNA library. Four sets of cell-level experiments were performed on cylindrical batteries using custom-designed fixtures, including flat lateral compression, rod indentation, hemispherical punch, and three-point bending. The voltage and surface temperature of the batteries were measured to capture the onset of short circuit during the tests. Comparison of the simulation results confirmed that the proposed homogenization method and the FE models can predict the behavior of cylindrical lithium-ion batteries with much higher accuracy compared to the currently available methods presented in the literature.

Microstructure-based numerical computational method for the insertion torque of dental implant

The bone quality has a significant effect on the insertion torque of dental implant. In most clinical studies, bone density is used as a gold standard in predicting insertion torque. By contrast, trabecular microstructure is ignored. In this study, a microstructure-based numerical computational method with high accuracy and efficiency for the insertion torque of dental implant was proposed by introducing two microscopic variables, namely, volume fraction and fabric tensor. First, two kinds of 3D microstructural solid models with same volume fraction and fabric tensor were established on the basis of the microstructural topology of six reference specimens. Second, a new numerical simulation method based on homogenous theory was used to explore the material models of these 3D microstructural solid models at the microscopic scale. Then, the anisotropic material models of specimens were developed on the basis of the mixture rule. Thereafter, a numerical simulation based on the anisotropic finite element (FE) model was carried out to acquire the insertion torque. To demonstrate the efficiency and accuracy of the simulation based on the anisotropic FE model, numerical simulations based on isotropic FE model and micro-computer tomography (micro-CT) FE models were also implemented as comparisons. Comparison of the simulated peak insertion torques of the anisotropic, isotropic, and micro-CT FE models with insertion experiments demonstrated the feasibility and potential of the proposed method. The anisotropic FE model reduced the time consumption by 91.85% and enhanced the accuracy by 11.82% compared with the micro-CT and isotropic FE models, respectively.

Accounting for spatial variation of trabecular anisotropy with subject-specific finite element modeling moderately improves predictions of local subchondral bone stiffness at the proximal tibia

IntroductionPreviously, a finite element (FE) model of the proximal tibia was developed and validated against experimentally measured local subchondral stiffness. This model indicated modest predictions of stiffness (R2=0.77, normalized root mean squared error (RMSE%)=16.6%). Trabecular bone though was modeled with isotropic material properties despite its orthotropic anisotropy. The objective of this study was to identify the anisotropic FE modeling approach which best predicted (with largest explained variance and least amount of error) local subchondral bone stiffness at the proximal tibia. MethodsLocal stiffness was measured at the subchondral surface of 13 medial/lateral tibial compartments using in situ macro indentation testing. An FE model of each specimen was generated assuming uniform anisotropy with 14 different combinations of cortical- and tibial-specific density-modulus relationships taken from the literature. Two FE models of each specimen were also generated which accounted for the spatial variation of trabecular bone anisotropy directly from clinical CT images using grey-level structure tensor and Cowin’s fabric-elasticity equations. Stiffness was calculated using FE and compared to measured stiffness in terms of R2 and RMSE%. ResultsThe uniform anisotropic FE model explained 53–74% of the measured stiffness variance, with RMSE% ranging from 12.4 to 245.3%. The models which accounted for spatial variation of trabecular bone anisotropy predicted 76–79% of the variance in stiffness with RMSE% being 11.2–11.5%. ConclusionsOf the 16 evaluated finite element models in this study, the combination of Synder and Schneider (for cortical bone) and Cowin’s fabric-elasticity equations (for trabecular bone) best predicted local subchondral bone stiffness.

Anisotropic finite element models for brain injury prediction: the sensitivity of axonal strain to white matter tract inter-subject variability

Computational models incorporating anisotropic features of brain tissue have become a valuable tool for studying the occurrence of traumatic brain injury. The tissue deformation in the direction of white matter tracts (axonal strain) was repeatedly shown to be an appropriate mechanical parameter to predict injury. However, when assessing the reliability of axonal strain to predict injury in a population, it is important to consider the predictor sensitivity to the biological inter-subject variability of the human brain. The present study investigated the axonal strain response of 485 white matter subject-specific anisotropic finite element models of the head subjected to the same loading conditions. It was observed that the biological variability affected the orientation of the preferential directions (coefficient of variation of 39.41% for the elevation angle—coefficient of variation of 29.31% for the azimuth angle) and the determination of the mechanical fiber alignment parameter in the model (gray matter volume 55.55–70.75%). The magnitude of the maximum axonal strain showed coefficients of variation of 11.91%. On the contrary, the localization of the maximum axonal strain was consistent: the peak of strain was typically located in a 2 cm3 volume of the brain. For a sport concussive event, the predictor was capable of discerning between non-injurious and concussed populations in several areas of the brain. It was concluded that, despite its sensitivity to biological variability, axonal strain is an appropriate mechanical parameter to predict traumatic brain injury.

Morphology based anisotropic finite element models of the proximal femur validated with experimental data

Finite element analysis (FEA) of bones scanned with Quantitative Computed Tomography (QCT) can improve early detection of osteoporosis. The accuracy of these models partially depends on the assigned material properties, but anisotropy of the trabecular bone cannot be fully captured due to insufficient resolution of QCT. The inclusion of anisotropy measured from high resolution peripheral QCT (HR-pQCT) could potentially improve QCT-based FEA of the femur, although no improvements have yet been demonstrated in previous experimental studies.This study analyzed the effects of adding anisotropy to clinical resolution femur models by constructing six sets of FE models (two isotropic and four anisotropic) for each specimen from a set of sixteen femurs that were experimentally tested in sideways fall loading with a strain gauge on the superior femoral neck. Two different modulus–density relationships were tested, both with and without anisotropy derived from mean intercept length analysis of HR-pQCT scans.Comparing iso- and anisotropic models to the experimental data resulted in nearly identical correlation and highly similar linear regressions for both whole bone stiffness and strain gauge measurements. Anisotropic models contained consistently greater principal compressive strains, approximately 14% in magnitude, in certain internal elements located in the femoral neck, greater trochanter, and femoral head.In summary, anisotropy had minimal impact on macroscopic measurements, but did alter internal strain behavior. This suggests that organ level QCT-based FE models measuring femoral stiffness have little to gain from the addition of anisotropy, but studies considering failure of internal structures should consider including anisotropy to their models.

Are two-dimensional images sufficient to assess the atherosclerotic plaque vulnerability: a viscoelastic and anisotropic finite element model

Introduction Although plenty of studies have been performed on the detection and therapy of instable plaques, thrombus mediated ischemic cardiovascular disease still remains the leading cause of death in developed countries [1]. The rupture of unstable atherosclerotic plaque in coronary artery regularly leads to a significant

Evaluation of Axonal Strain as a Predictor for Mild Traumatic Brain Injuries Using Finite Element Modeling.

Finite element (FE) models are often used to study the biomechanical effects of traumatic brain injury (TBI). Measures based on mechanical responses, such as principal strain or invariants of the strain tensor, are used as a metric to predict the risk of injury. However, the reliability of inferences drawn from these models depends on the correspondence between the mechanical measures and injury data, as well as the establishment of accurate thresholds of tissue injury. In the current study, a validated anisotropic FE model of the human head is used to evaluate the hypothesis that strain in the direction of fibers (axonal strain) is a better predictor of TBI than maximum principal strain (MPS), anisotropic equivalent strain (AESM) and cumulative strain damage measure (CSDM). An analysis of head kinematics-based metrics, such as head injury criterion (HIC) and brain injury criterion (BrIC), is also provided. Logistic regression analysis is employed to compare binary injury data (concussion/no concussion) with continuous strain/kinematics data. The threshold corresponding to 50% of injury probability is determined for each parameter. The predictive power (area under the ROC curve, AUC) is calculated from receiver operating characteristic (ROC) curve analysis. The measure with the highest AUC is considered to be the best predictor of mTBI. Logistic regression shows a statistical correlation between all the mechanical predictors and injury data for different regions of the brain. Peaks of axonal strain have the highest AUC and determine a strain threshold of 0.07 for corpus callosum and 0.15 for the brainstem, in agreement with previously experimentally derived injury thresholds for reversible axonal injury. For a data set of mild TBI from the national football league, the strain in the axonal direction is found to be a better injury predictor than MPS, AESM, CSDM, BrIC and HIC.

Development of finite element models for studying the electrical excitation of myocardium

The propagation of the electrical excitation wave in the isotropic and anisotropic finite element models of the myocardium is studied. The geometrical image of the heart is constructed on the basis of magnetic resonance tomography (MRT) data by the region growing method. A filtering algorithm is proposed for elimination of excess details. The propagation of the myocardium excitation impulse is described in the framework of the monodomain model of conductivity. The Aliev–Panfilov and Beeler–Reuter equations are used to relate the transmembrane current to transmembrane potential. The model equations are solved by the splitting method. The influence of the degree of approximation on the performance of the finite element model is investigated. The interaction between the additional excitation source and the propagating excitation wave is considered. The proposed model allowed us to trace the propagation of the excitation impulse through the curvilinear isotropic media and in the 3D image of the heart obtained on the basis of MRT data.

Constructing anisotropic finite element model of bone from computed tomography (CT).

Image-based finite element (FE) modeling of human bones has been increasingly applied as a useful tool in biomedical engineering. However, most existing image-based FE models assume isotropic mechanical properties for bones, although bones are typically anisotropic material. In this study, we attempted to construct anisotropic FE models from medical computed tomography (CT) scans by modifying the existing empirical relations of bone elasticity-density. The hypothesis adopted in the study is that bone anisotropy is generated by the variations of bone density and the proposed anisotropic relations should degenerate to the isotropic ones if bone density variation is taken zero. The effect of considering bone anisotropy in FE models was investigated by numerical studies. The obtained numerical results showed that the relative error in the finite element solutions produced respectively by the isotropic and anisotropic FE models can be as large as 50%. We concluded from this preliminary study that the consideration of anisotropy in bone FE models has a significant effect on the accuracy of bone behavior predicted by the FE models. However, well-designed bone tests have to be conducted to validate the anisotropic bone elasticity-density relation proposed in this study.

Finite-element simulation of myocardial electrical excitation

Based on a single-domain model of myocardial conduction, isotropic and anisotropic finite element models of the myocardium are developed allowing excitation wave propagation to be studied. The Aliev-Panfilov phenomenological equations were used as the relations between the transmembrane current and the transmembrane potential. Interaction of an additional source of initial excitation with an excitation wave that passed and the spread of the excitation wave are studied using heart tomograms. A numerical solution is obtained using a splitting algorithm that allows the nonlinear boundary-value problem to be reduced to a sequence of simpler problems: ordinary differential equations and linear boundary-value problems in partial derivatives.

Computer-aided simulation of the AMg6 alloy rolling process with allowance for its anisotropy

Some data obtained in the course of computer-aided simulation of a process of plane AMg6 alloy specimen rolling in the CAE-system MSC.SuperForm are presented. The influence of a real material structure upon the stress-strain state and the flow pattern of layers throughout the specimen height is taken into account. Also determined are the values of total pressure of metal on the rolls and a moment of rolling with the use of the isotropic and anisotropic finite element models (FEM) of specimens.

Use of anisotropic modelling in electrical impedance tomography; Description of method and preliminary assessment of utility in imaging brain function in the adult human head

Electrical Impedance Tomography (EIT) is an imaging method which enables a volume conductivity map of a subject to be produced from multiple impedance measurements. It has the potential to become a portable non-invasive imaging technique of particular use in imaging brain function. Accurate numerical forward models may be used to improve image reconstruction but, until now, have employed an assumption of isotropic tissue conductivity. This may be expected to introduce inaccuracy, as body tissues, especially those such as white matter and the skull in head imaging, are highly anisotropic. The purpose of this study was, for the first time, to develop a method for incorporating anisotropy in a forward numerical model for EIT of the head and assess the resulting improvement in image quality in the case of linear reconstruction of one example of the human head. A realistic Finite Element Model (FEM) of an adult human head with segments for the scalp, skull, CSF, and brain was produced from a structural MRI. Anisotropy of the brain was estimated from a diffusion tensor-MRI of the same subject and anisotropy of the skull was approximated from the structural information. A method for incorporation of anisotropy in the forward model and its use in image reconstruction was produced. The improvement in reconstructed image quality was assessed in computer simulation by producing forward data, and then linear reconstruction using a sensitivity matrix approach. The mean boundary data difference between anisotropic and isotropic forward models for a reference conductivity was 50%. Use of the correct anisotropic FEM in image reconstruction, as opposed to an isotropic one, corrected an error of 24 mm in imaging a 10% conductivity decrease located in the hippocampus, improved localisation for conductivity changes deep in the brain and due to epilepsy by 4–17 mm, and, overall, led to a substantial improvement on image quality. This suggests that incorporation of anisotropy in numerical models used for image reconstruction is likely to improve EIT image quality.

Influence of anisotropy on peri-implant stress and strain in complete mandible model from CT

This paper reveals the influence of elastic anisotropy for the peri-implant stress and strain in personalized mandible. First, from CT data, the individual geometry of the complete range of mandible was well reproduced, also the separation between cortical and cancellous bone. Then, by an ad hoc automatic mesh generator integrated with anisotropic material assignment function, high quality anisotropic finite element model of the complete mandible was created, with two standard threaded implants embedded in posterior zone. The values of principal stress and strain in surrounding bone were evaluated under buccolingual oblique loading, and compared to that of the same FE model with equivalent isotropic material. Results of the analyses demonstrated that the percentage increase of stress and strain in anisotropic case reached up to 70%. It is concluded that anisotropy has significant effects on peri-implant stress and strain and careful consideration should be given to its use in biomechanical FE studies.

Flow and electrical anisotropy in the upper mantle: Finite-element models constraints on the effects of olivine crystal preferred orientation and microstructure

Long-period magnetotelluric (MT) data shows that electrical conductivity in the upper mantle is highly anisotropic. Agreement between high electrical conductivity directions and seismic anisotropy fast directions suggests that anisotropic diffusion of hydrogen along oriented olivine crystals controls the anisotropy of electrical conductivity in the upper mantle, since both seismic waves and hydrogen diffusion are faster along the [1 0 0] axis of olivine. Thus, MT electrical anisotropy data, like seismic anisotropy, may be used to map flow patterns in the upper mantle. However, observed electrical anisotropies are significantly higher than seismic ones. To quantify the influence of strain-induced crystal preferred orientations of olivine on upper mantle bulk electrical conductivities, we calculate the macroscopic electrical conductivity anisotropy of a series of naturally and experimentally deformed peridotites using an anisotropic finite-element model. These models, which fully take into account the microstructure: crystal and shape preferred orientations, based on orientation maps obtained by indexation of electron back-scattered diffraction (EBSD) patterns, show macroscopic electrical anisotropy factors ranging from 3 to 16. The intensity of electrical anisotropy depends to first order on the intensity of the olivine crystal preferred orientations, but the relation saturates for strong crystal preferred orientations. In addition, the spatial distribution of the various crystal orientations may significantly enhance influence the anisotropy in strongly textured mantle rocks. The strongest anisotropy factors (>10) occur in mantle rocks in which deformation by dislocation creep has produced not only crystal but also strong shape preferred orientations, even if the latter is masked by recrystallization. Higher anisotropy factors (>100) observed in a few MT experiments imply however an additional, as yet unknown, mechanism controlling electrical conduction at asthenospheric depths in these regions.

Stress analysis of implant‐supported partial prostheses in anisotropic mandibular bone: in‐line versus offset placements of implants

Three-dimensional, anisotropic finite element models were executed to investigate the biomechanical effects of in-line and offset placements of implants on implant-supported partial prostheses. Three implant placements of finite element models were created: in-line, buccal offset and lingual offset placements. The mesh models of a cadaver mandibular segment and a three-united crown containing the 2nd premolar, the 1st molar and the 2nd molar were constructed by computer tomography images. The material properties of mandible were applied as transversely isotropic and linearly elastic. Two loading modes (100N), vertical and oblique, were evaluated in all models. Insignificant difference was observed in implant stresses between the in-line and offset placements under the vertical loading mode. Under the oblique loading, however, the offset placement decreased the implant stress by a maximum of 17%. The maximum stress at cortical bone and trabecular bone around each implant did not show conspicuous difference between the in-line and offset placements. This study demonstrated the mechanisms of how stresses were distributed between the in-line and offset placements. Even though the offset placements showed the benefit of decreasing implant stresses, justified from the bone stress the offset placements provided no advantage for the stress decreasing over the in-line placement.

Pulsatile movement of the zenith aortic stent-graft

The anisotropic property of porcine aortic valve leaflet has potentially significant effects on its mechanical behaviour and the failure mechanisms. However, due to its complex nature, testing and modelling the anisotropic porcine aortic valves remains a continuing challenge to date. This study has developed a nonlinear anisotropic finite element model for porcine heart valves. The model is based on the uniaxial experimental data of porcine aortic heart valve leaflet and the properties of nonlinear composite material. A finite element code is developed to solve this problem using the 8-node super-parameter nonlinear shells and the update Lagrangian method. The stress distribution and deformation of the porcine aortic valves with either uniform and non-uniform thicknesses in closed phase and loaded condition are calculated. The results showed significant changes in the stress distributions due to the anisotropic property of the leaflets. Compared with the isotropic valve at the same loading condition, it is found that the site of the peak stress of the anisotropic leaflet is different; the maximum longitudinal normal stress is increased, but the maximum transversal normal stress and in-plane shear stress are reduced. We conclude that it is very important to consider the anisotropic property of the porcine heart valves in order to understand the failure mechanism of such valves in vivo.

A fully 3-D anisotropic numerical model of the DI-B in situ diffusion experiment in the Opalinus clay formation

In situ diffusion experiments have been performed at underground research laboratories in clay formations to overcome the limitations of laboratory diffusion experiments and investigate possible scale effects. The DI-B experiment is a long-term, natural-scale, in situ diffusion experiment performed in a packed section in a borehole drilled vertically into the anisotropic Opalinus clay formation at Mont Terri in Switzerland. A cocktail of non-radioactive tracers was used. Tracers were monitored for one year at the test interval and measured at samples taken from an overcored interval. Contrary to the methods used so far for the interpretation of in situ experiments which rely on 2-D models and disregard diffusion across bedding, here we present a fully 3-D anisotropic finite element model of the DI-B experiment. The numerical model has been calibrated with iodide and deuterium data. The fully anisotropic 3-D model provides reliable estimates of effective diffusion coefficients and accessible porosities for deuterium and iodide which are within the range of published values. We show that a simple 2-D model can be safely used to interpret data along central profiles although it may lead to biased estimates when applied to profiles located near the edges of the test interval. Computed concentrations in the borehole are much less sensitive to changes in model parameters than concentrations along profiles. Computed concentrations close to the borehole are most sensitive to the accessible porosity while concentrations at distances greater than 0.085 m are most sensitive to the diffusion coefficient parallel to the bedding. Computed concentrations along some profiles are sensitive to the effective diffusion perpendicular to bedding.

Comparison of regularization techniques for the reconstruction of transmembrane potentials in the heart.

Computer simulations to reconstruct the transmembrane potential distribution were performed for an anisotropic finite element model of the heart. Transmembrane potential was reconstructed in the form of 3D patches. Test patterns generated with a cellular automaton were used. Tikhonov 0-order and 2-order reconstruction techniques were compared. Tikhonov 2-order regularization was shown to deliver better solutions; this is demonstrated by the inspection of the source space of the inverse problem and by the comparison of the correlation coefficients between the reconstructed and original distributions. Time information was incorporated into the regularization.