Hexahedral Finite Element Mesh Research Articles

The Effects of Hind Limb Suspension and Cast Mediated Immobilization on Bone Strength Properties.

Astronauts and patients on bedrest are subject to a combination of bone strength losses and muscle atrophy due to microgravity and unloading. In this study, mice were subject to both hind limb suspension and cast mediated immobilization. Pre-treatment and post-treatment microCT scans were utilized to create finite element models. Both pre-treatment and posttreatment scans were then cropped, rotated and threedimensional image registration was performed to eliminate inconsistency in alignment. A hexahedral finite element mesh was then generated from this 3D data. Finite element analysis was conducted to perform simulated physiological loading of the femoral neck to assess bone strength through bone structural morphology. Hind limb suspension combined with Cast Mediated Immobilization caused a 7.9% decrease in bone FEA stiffness compared to the in-vivo pre-treatment control. No differences were found in bone volume or structural efficiency.

Subject specific hexahedral Finite Element mesh generation of the pelvis from bi-Planar X-ray images

Several Finite Element (FE) models of the pelvis have been developed to comprehensively assess the onset of pathologies and for clinical and industrial applications. However, because of the difficulties associated with the creation of subject-specific FE mesh from CT scan and MR images, most of the existing models rely on the data of one given individual. Moreover, although several fast and robust methods have been developed for automatically generating tetrahedral meshes of arbitrary geometries, hexahedral meshes are still preferred today because of their distinct advantages but their generation remains an open challenge. Recently, approaches have been proposed for fast 3D reconstruction of bones based on X-ray imaging. In this study, we adapted such an approach for the fast and automatic generation of all-hexahedral subject-specific FE models of the pelvis based on the elastic registration of a generic mesh to the subject-specific target in conjunction with element regularity and quality correction. A full hexahedral subject-specific FE mesh was generated with an accurate surface representation.

Construction of hexahedral finite element mesh capturing realistic geometries of a petroleum reserve

The three-dimensional finite element mesh capturing realistic geometries of the Bayou Choctaw site has been constructed using the sonar and seismic survey data obtained from the field. The mesh consists of hexahedral elements because the salt constitutive model is coded using hexahedral elements. Various ideas and techniques to construct finite element mesh capturing artificially and naturally formed geometries are provided. The techniques to reduce the number of elements as much as possible to save on computer run time while maintaining the computational accuracy is also introduced. The steps and methodologies could be applied to construct the meshes of Big Hill, Bryan Mound, and West Hackberry strategic petroleum reserve sites. The methodology could be applied to the complicated shape masses for various civil and geological structures.

Numerical Integration Over A Linear Convex Polyhedron Using An All Hexahedral Discretisation And Gauss Legendre Formulas

Numerical integration is an important ingradient within many techniques of applied mathematics,engineering and scinietific applications, this is due to the need for accurate and efficient integration schemes over complex integration domains and the arbitrary functions as their corresponding integrands. In this paper,we propose a method to discretise the physical domain in the shape of a linear polyhedron into an assemblage of all hexahedral finite elements. The idea is to generate a coarse mesh of all tetrahedrons for the given domain,Then divide each of these tetrahedron further into a refined mesh of all tetrahedrons, if necessary. Then finally, we divide each of these tetrahedron into four hexahedra.We have further demonstrated that each of these hexahedra can be divided into and hexahedra. This generates an all hexahedral finite element mesh which can be used for various applications In order to achieve this we first establish a relation between the arbitrary linear tetrahedron and the standard tetrahedron.We then decompose the standard tetrahedron into four hexahedra. We transform each of these hexahedra into a 2-cube and discover an interesting fact that the Jacobian of these transformations is same and the transformations are also the same but in different order for all the four hexahedra.This fact can be used with great advantage to generate the numerical integration scheme for the standard tetrahedron and hence for the arbitrary linear tetrahedron. We have proposed three numerical schemes which decompose a arbitrary linear tetrahedron into 4, 4( hexahedra.These numerical schemes are applied to solve typical integrals over a unit cube and irregular heptahedron using Gauss Legendre Quadrature Rules. Matlab codes are developed and appended to this paper.

Biomechanics simulations using cubic Hermite meshes with extraordinary nodes for isogeometric cardiac modeling

Cubic Hermite hexahedral finite element meshes have some well-known advantages over linear tetrahedral finite element meshes in biomechanical and anatomic modeling using isogeometric analysis. These include faster convergence rates as well as the ability to easily model rule-based anatomic features such as cardiac fiber directions. However, it is not possible to create closed complex objects with only regular nodes; these objects require the presence of extraordinary nodes (nodes with 3 or >=5 adjacent elements in 2D) in the mesh. The presence of extraordinary nodes requires new constraints on the derivatives of adjacent elements to maintain continuity. We have developed a new method that uses an ensemble coordinate frame at the nodes and a local-to-global mapping to maintain continuity. In this paper, we make use of this mapping to create cubic Hermite models of the human ventricles and a four-chamber heart. We also extend the methods to the finite element equations to perform biomechanics simulations using these meshes. The new methods are validated using simple test models and applied to anatomically accurate ventricular meshes with valve annuli to simulate complete cardiac cycle simulations.

Hexahedral Mesh Generation Method for Complex Mechanical Structure

An all hexahedral finite element mesh(FEM) generation method is proposed for complex mechanical structure, with the purpose to guarantee finite element simulation efficiency and precision in complex mechanical structure. The error characteristics and its cause in focus local mesh are analyzed by the finite element mesh error estimation. Based on the geometrical features and physical properties of the complex mechanical structure, the recognition criteria of critical region are established. Hexahedral mesh generation algorithm and implementation steps are presented based on the virtual planning model of structure calculation domain and the mesh quality evaluation criterion is also build. Numerical examples show that this method has the ability to generate all hexahedral finite element mesh for complex mechanical structure and critical regions are expressed accurately, and global mesh is distribution with rationality and high quality.

Trimming of 3D solid finite element meshes: sheet metal forming tests and applications

Over the last years, the numerical simulation of integrated processes has become the major challenge in virtual try-out of sheet metal components, including trimming operations that may occur between forming steps. Detailed simulation of trimming processes is a challenging task, particularly when integrated with other forming operations such as deep drawing or hemming. A simplified approach can be adopted in which elements outside the trim surface are deleted from the finite element (FE) model adjusting the remaining to the surface. Following this approach, the state variables are mapped from the old FE mesh to the new trimmed mesh to continue the simulation. This paper addresses this simplified approach to the trimming process exploring a previously presented algorithm (Finite Elem Anal Des 42: 1053---1060, Baptista et al. 2006), which allows the treatment of hexahedral finite element meshes. Particularly, it focuses on the performance evaluation of the implemented strategies for correcting the FE mesh to the trimming surface, including the treatment of pentahedral-shaped elements. Different correction and treatment strategies are evaluated on different types of meshes, based on numerical simulation results of simple mechanical tests: uniaxial tensile test and simple bending test. Finally, two practical applications are given where the local effect of the trimming algorithm is highlighted.

Feature-based multiblock finite element mesh generation

Hexahedral finite element mesh development for anatomic structures and biomedical implants can be cumbersome. Moreover, using traditional meshing techniques, detailed features may be inadequately captured. In this paper, we describe methodologies to handle multi-feature datasets (i.e., feature edges and surfaces). Coupling multi-feature information with multiblock meshing techniques has enabled anatomic structures, as well as orthopaedic implants, to be readily meshed. Moreover, the projection process, node and element set creation are automated, thus reducing the user interaction during model development. To improve the mesh quality, Laplacian- and optimization-based mesh improvement algorithms have been adapted to the multi-feature datasets.

The impact of model assumptions on results of computational mechanics in abdominal aortic aneurysm

In principle, superiority of computational wall stress analyses compared with the maximum diameter criterion for rupture risk evaluation of abdominal aortic aneurysm (AAA) has been demonstrated. The results of finite element analyses should be evaluated carefully, however, because computational strains and stresses are highly dependent on the quality and complexity of each step of AAA simulation. Most clinically active vascular specialists are not familiar with the processes of computational mechanics to evaluate the quality of AAA simulations. For better understanding and to provide insights in computational biomechanics of AAA, the effect of different computational model assumptions on the results of simulation are explained and demonstrated. Four patients with asymptomatic (n = 3) and symptomatic (n = 1) infrarenal AAAs with distinctly different aneurysm morphologies were exemplarily studied. For segmentation and 3-dimensional (3D) reconstruction of AAA and thrombus, 3-mm computed tomography (CT) slices were used, and a high-density hexahedral element-dominated finite element mesh was generated. Subsequent AAAs were simulated on seven different levels, culminating in the most realistic ortho-pressure-finite element analyses simulations, including thrombus, wall calcifications, and prestress state of AAA geometry with nonlinear hyperelastic material and geometric model assumptions. Alterations in displacements due to model assumptions are up to 740% for a specific aneurysm. The average maximum discrepancy among the four morphologies between simple and advanced models is 607%. Differences in peak wall stress between simple and realistic models are up to 210% individually and 170% on average. Differences of model assumptions are more important for simulation results than differences between patient-specific morphologies. Because the biomechanical behavior of AAA is nonlinear in many senses, comparisons between individual morphologies and statistics are only valid when detailed information about preconditions and model assumptions is provided.

Hexahedral mesh generation constraints

For finite element analyses within highly elastic and plastic structural domains, hexahedral meshes have historically offered some benefits over tetrahedral finite element meshes in terms of reduced error, smaller element counts, and improved reliability. However, hexahedral finite element mesh generation continues to be difficult to perform and automate, with hexahedral mesh generation taking several orders of magnitude longer than current tetrahedral mesh generators to complete. Thus, developing a better understanding of the underlying constraints that make hexahedral meshing difficult could result in dramatic reductions in the amount of time necessary to prepare a hexahedral finite element model for analysis. In this paper, we present a survey of constraints associated with hexahedral meshes (i.e., the conditions that must be satisfied to produce a hexahedral mesh). In presenting our formulation of these constraints, we will utilize the dual of a hexahedral mesh. We also discuss how incorporation of these constraints into existing hexahedral mesh generation algorithms could be utilized to extend the class of geometries to which these algorithms apply. We also describe a list of open problems in hexahedral mesh generation and give some context for future efforts in addressing these problems.

Adaptive generation of hexahedral element mesh using an improved grid-based method

An improved grid-based algorithm for the adaptive generation of hexahedral finite element mesh is presented in this paper. It is named as the inside-out grid-based method and involves the following four steps. The first step is the generation of an initial grid structure which envelopes the analyzed solid model completely. And the elements size and density maps are constructed based on the surface curvature and local thickness of the solid model. Secondly, the core mesh is generated through removing all the undesired elements using even and odd parity rules. The third step is to magnify the core mesh in an inside-out manner through a surface node projection process using the closest position approach. To match the mesh to the characteristic boundary of the solid model, a minimal Scaled Jacobian criterion is employed. Finally, in order to handle the degenerated elements and improve the quality of the resulting mesh, two comprehensive techniques are employed: the insertion technique and collapsing technique. The present method was applied in the mesh construction of different engineering problems. Scaled Jacobian and Skew metrics are used to evaluate the hexahedral element mesh quality. The application results show that all-hexahedral element meshes which are well-shaped and capture all the geometric features of the original solid models can be generated using the inside-out grid-based method presented in this paper.

A biomechanical study of the modified intertrochanteric valgus osteotomy:a three-dimensional finite element analysis

Objective To evaluate the differences in biomechanical performance between the traditional Bombelli-type and modified Z-type valgus osteotomies through finite element analysis. Methods The CT images obtained from a standardized composite femur were used to create 4 solid femoral models and hexahedral finite element meshes of intertrochanteric valgus with the preoperative neck-shaft angle at 120°, 110°, 100° and 90° respectively. Four finite element models with the postoperative neck-shaft angle corrected at 150° for each type of osteotomy were then created. Single leg stance was applied in simulated loading on each finite element model, and the material properties were assumed linear, isotropic and homogeneous. The stress distribution in the postoperative femora and fixation plate as well as the normal contact force of the osteotomized plane were analyzed and compared between the 2 types of osteotomy through the 4 models. Results Serious deformity and high local stress near the osteotomized plane were found in Bombel- li-osteotomized femur with preoperative femoral shaft-neck angle at 90° However, no obvious difference in the stress distribution was found among the 4 Z-osteotomy models. The deformity in Z-osteotomy models was less than that in the Bombelli-osteotomy models. Besides, the stress distributed on osteotomized plane in Z-osteotomy was higher than that in the traditional Bombelli-osteotomy when the preoperative femoral shaft-neck angle was 90°. Conclusion The Z-osteotomy may be a better alternative for large range correction of intertrochanteric varus of femur. Key words: Femur; Osteotomy; Biomechanics

Mapping-based 3D hexahedral finite element mesh generation method

Mapping mesh generation is widely applied in pre-processes of Finite Element Method (FEM). In this study, the basic 3D mapping equations by Lagrange interpolating function are founded. Based these equations, a mapping pattern library, which maps essential configurations e.g. line, circle, rotary body, sphere etc. to hexahedral FEM mesh, has been built. Then available FEM mesh will be generated by clipping and assembling the mapped essential objects. Study case illustrates that the proposed method is simple and efficient to generate valid FEM mesh for complex 3D engineering structure.

Tetrahedral versus hexahedral finite elements in numerical modelling of the proximal femur

The objective of this study was to evaluate and compare tetrahedral and hexahedral finite element meshes of simplified and realistic proximal intact femur geometries. Theoretical expressions of stresses and strains were derived for the simplified model of the femur. For the analysis of the realistic geometry of the proximal femur, a CAD model of the third generation composite femur (Pacific Research Labs, Vashion Island, WA) was used and simulations were performed with Hyperworks ® (Altair Engineering, Inc., Troy, MI) finite element analysis software. Convergence tests with hexahedral (8- and 20-node brick-elements) and tetrahedral (4- and 10-node tetrahedrons) elements were analysed by comparing the periosteal von Mises stresses and principal strains at a selected point of the femur. The numerical periosteal strains were also compared with experimental ones to determine the accuracy of the finite elements. Overall, we concluded, for the simplified femur, that tetrahedral linear element allowed results more closely to theoretical ones, but hexahedral quadratic elements seem to be more stable and less influenced to the degree of refinement (NDOF) of the mesh. It was not possible to correlate these findings with those observed for the realistic proximal femur simulations where no significant differences were seen using refined meshes, with more than NDOF = 20 000 for hexahedral elements.

A patient-specific computational model of fluid–structure interaction in abdominal aortic aneurysms

It is generally believed that knowledge of the wall stress distribution could help to find better rupture risk predictors of abdominal aortic aneurysms (AAAs). Although AAA wall stress results from combined action between blood, wall and intraluminal thrombus, previously published models for patient-specific assessment of the wall stress predominantly did not include fluid-dynamic effects. In order to facilitate the incorporation of fluid–structure interaction in the assessment of AAA wall stress, in this paper, a method for generating patient-specific hexahedral finite element meshes of the AAA lumen and wall is presented. The applicability of the meshes is illustrated by simulations of the wall stress, blood velocity distribution and wall shear stress in a characteristic AAA. The presented method yields a flexible, semi-automated approach for generating patient-specific hexahedral meshes of the AAA lumen and wall with predefined element distributions. The combined fluid/solid mesh allows for simulations of AAA blood dynamics and AAA wall mechanics and the interaction between the two. The mechanical quantities computed in these simulations need to be validated in a clinical setting, after which they could be included in clinical trials in search of risk factors for AAA rupture.

Subject specific Modeling to Estimate Patellofemoral Joint Contact Stress

0012 PURPOSE: Patellofemoral (PF) pain is one of the most common causes of visits to sports medicine clinics, yet its etiology remains elusive. Elevated stress in the PF joint cartilage and subchondral bone is a plausible mechanism for pain. Cartilage Vol. stress cannot be measured directly in-vivo, so we must combine medical imaging data with numerical modelling techniques to estimate subject-specific joint loads and tissue stresses. The purpose of this research is to estimate cartilage stress in a group of patients who currently have PF pain and compare these stresses with a group of healthy, active, age-matched controls. METHODS: Accurate bone and cartilage models of the femur and patella were created for each subject using static highresolution MR images and manual segmentation. Bone models were used to resolve 3D PF joint kinematics from 2D real-time MR images, whilst the cartilage models were used to generate 3D hexahedral finite element meshes. Real-time MR images were taken using an open configuration magnet, which permits subjects to stand or squat in an upright posture during scanning. Gait analysis was also performed to obtain lower limb kinematic and kinetic data during walking, running, squatting, and stair climbing using standard inverse dynamics. Muscle activation data collected from lower limb EMG during these tasks were used as input into a musculoskeletal model to estimate in vivo muscle forces and resultant PF joint contact forces. These contact forces were used in conjunction with PF joint kinematics from the real-time MRI and the femur and patella cartilage meshes to estimate cartilage stress using a finite element approach. RESULTS: Preliminary from a subset of patients will be presented to illustrate the modelling techniques outlined above. CONCLUSIONS: The methods presented in this paper offer a unique insight into the mechanism of the PF joint and can be used to further our knowledge of PF pain and potential rehabilitation strategies. Supported by the Department of Veterans Affairs, Rehabilitation R&D Service (grant #A2592R) and the National Science Foundation.

The creation of a high‐fidelity finite element model of the kidney for use in trauma research

AbstractA detailed finite element model of the human kidney for trauma research has been created directly from the National Library of Medicine Visible Human Female (VHF) Project data set. An image segmentation and organ reconstruction software package has been developed and employed to transform the 2D VHF images into a 3D polygonal representation. Non‐uniform rational B‐spline (NURBS) surfaces were then mapped to the polygonal surfaces, and were finally utilized to create a robust 3D hexahedral finite element mesh within a commercially available meshing software. The model employs a combined viscoelastic and hyperelastic material model to successfully simulate the behaviour of biological soft tissues. The finite element model was then validated for use in biomechanical research. Copyright © 2002 John Wiley & Sons, Ltd.

Achieving finite element mesh quality via optimization of the Jacobian matrix norm and associated quantities. Part II?A framework for volume mesh optimization and the condition number of the Jacobian matrix

Three-dimensional unstructured tetrahedral and hexahedral finite element mesh optimization is studied from a theoretical perspective and by computer experiments to determine what objective functions are most effective in attaining valid, high-quality meshes. The approach uses matrices and matrix norms to extend the work in Part I to build suitable 3D objective functions. Because certain matrix norm identities which hold for 2×2 matrices do not hold for 3×3 matrices, significant differences arise between surface and volume mesh optimization objective functions. It is shown, for example, that the equality in two dimensions of the smoothness and condition number of the Jacobian matrix objective functions does not extend to three dimensions and further, that the equality of the Oddy and condition number of the metric tensor objective functions in two dimensions also fails to extend to three dimensions. Matrix norm identities are used to systematically construct dimensionally homogeneous groups of objective functions. The concept of an ideal minimizing matrix is introduced for both hexahedral and tetrahedral elements. Non-dimensional objective functions having barriers are emphasized as the most logical choice for mesh optimization. The performance of a number of objective functions in improving mesh quality was assessed on a suite of realistic test problems, focusing particularly on all-hexahedral ‘whisker-weaved’ meshes. Performance is investigated on both structured and unstructured meshes and on both hexahedral and tetrahedral meshes. Although several objective functions are competitive, the condition number objective function is particularly attractive. The objective functions are closely related to mesh quality measures. To illustrate, it is shown that the condition number metric can be viewed as a new tetrahedral element quality measure. Published in 2000 by John Wiley & Sons, Ltd.

A dual geometry—topology constraint approach for determination of pseudo-swept shapes as applied to hexahedral mesh generation

The current paper presents a pseudo-sweep algorithm to determine whether a given volume constitutes an approximately swept shape for the purpose of hexahedral finite element mesh generation. The pseudo-swept shape determination approach consists of three steps. Step 1: Determining the source surface, target surface, and lateral surface of a given solid object B. Two requirements: topological and geometric requirements, are used to determine these three surfaces. Step 2: Creating a submappable lateral surface. A submappable surface is one that allows the sweeping of a two dimensional quadrilateral mesh from the source surface to target surface. Step 3: Modifying the topology of the source surface. If the topologies of the source and target surfaces are different, an approach called Topology Mapping is applied. The Topology Mapping approach maps the target surface to the source surface so that sweeping of quadrilateral mesh from the source surface to the target surface is possible. Once the above three steps are applied, a hexahedral mesh is generated by sweeping a quadrilateral mesh from the source surface, along the lateral surface, to the target surface.

Automatic generation of hexahedral finite element meshes

FE-simulation of complex metal forming processes is often hampered by mesh distortion. In this case a new mesh of quadrilateral or hexahedral elements must be generated (remeshing). This cannot be done effectively by using currently available methods. This paper presents a new algorithm for the generation of hexahedral element meshes. The quality of the algorithm is demonstrated by the simulation of a complex forging process.