ANCF Modeling of the Contact Geometry and Deformation in Biomechanics Applications

2012 ◽  
Author(s):  
F. Marina Gantoi ◽  
Michael A. Brown ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Contact Surface ◽  
Spline Function ◽  
Geometric Description ◽  
Surface Geometry ◽  
B Splines ◽  
Contact Points ◽  
Contact Formulation ◽  
Parametric Relationship

The purpose of this investigation is to demonstrate the use of the finite element (FE) absolute nodal coordinate formulation (ANCF) and multibody system (MBS) algorithms in modeling both the contact geometry and ligaments deformations in biomechanics applications. Two ANCF approaches can be used to model the rigid contact surface geometry. In the first approach, fully parameterized ANCF volume elements are converted to surface geometry using parametric relationship that reduces the number of independent coordinate lines. This parametric relationship can be defined analytically or using a spline function representation. In the second approach, an ANCF surface that defines a gradient deficient thin plate element is used. This second approach does not require the use of parametric relations or spline function representations. These two geometric approaches shed light on the generality of and the flexibility offered by the ANCF geometry as compared to computational geometry (CG) methods such as B-splines and NURBS (Non-Uniform Rational B-Splines). Furthermore, because B-spline and NURBS representations employ a rigid recurrence structure, they are not suited as general analysis tools that capture different types of joint discontinuities. ANCF finite elements, on the other hand, lend themselves easily to geometric description and can additionally be used effectively in the analysis of ligaments, muscles, and soft tissues (LMST), as demonstrated in this paper using the knee joint as an example. In this study, ANCF finite elements are used to define the femur/tibia rigid body contact surface geometry. The same ANCF finite elements are also used to model the MCL and LCL ligament deformations. Two different contact formulations are used in this investigation to predict the femur/tibia contact forces; the elastic contact formulation where penetrations and separations at the contact points are allowed, and the constraint contact formulation where the non-conformal contact conditions are imposed as constraint equations, and as a consequence, no separations or penetrations at the contact points are allowed. For both formulations, the contact surfaces are described in a parametric form using surface parameters that enter into the ANCF finite element geometric description. A set of nonlinear algebraic equations that depend on the surface parameters is developed and used to determine the location of the contact points. These two contact formulations are implemented in a general MBS algorithm that allows for modeling rigid and flexible body dynamics.

Finite Element Modeling of the Contact Geometry and Deformation in Biomechanics Applications1

2013 ◽  
Vol 8 (4) ◽  
Author(s):  
F. Marina Gantoi ◽  
Michael A. Brown ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Contact Surface ◽  
Spline Function ◽  
Geometric Description ◽  
Surface Geometry ◽  
B Splines ◽  
Contact Points ◽  
Contact Formulation ◽  
Parametric Relationship

The main contribution of this paper is to demonstrate the feasibility of using one computational environment for developing accurate geometry as well as performing the analysis of detailed biomechanics models. To this end, the finite element (FE) absolute nodal coordinate formulation (ANCF) and multibody system (MBS) algorithms are used in modeling both the contact geometry and ligaments deformations in biomechanics applications. Two ANCF approaches can be used to model the rigid contact surface geometry. In the first approach, fully parameterized ANCF volume elements are converted to surface geometry using parametric relationship that reduces the number of independent coordinate lines. This parametric relationship can be defined analytically or using a spline function representation. In the second approach, an ANCF surface that defines a gradient deficient thin plate element is used. This second approach does not require the use of parametric relations or spline function representations. These two geometric approaches shed light on the generality of and the flexibility offered by the ANCF geometry as compared to computational geometry (CG) methods such as B-splines and NURBS (Non-Uniform Rational B-Splines). Furthermore, because B-spline and NURBS representations employ a rigid recurrence structure, they are not suited as general analysis tools that capture different types of joint discontinuities. ANCF finite elements, on the other hand, lend themselves easily to geometric description and can additionally be used effectively in the analysis of ligaments, muscles, and soft tissues (LMST), as demonstrated in this paper using the knee joint as an example. In this study, ANCF finite elements are used to define the femur/tibia rigid body contact surface geometry. The same ANCF finite elements are also used to model the MCL and LCL ligament deformations. Two different contact formulations are used in this investigation to predict the femur/tibia contact forces; the elastic contact formulation which allows for penetrations and separations at the contact points, and the constraint contact formulation in which the nonconformal contact conditions are imposed as constraint equations, and as a consequence, no separations or penetrations at the contact points are allowed. For both formulations, the contact surfaces are described in a parametric form using surface parameters that enter into the ANCF finite element geometric description. A set of nonlinear algebraic equations that depend on the surface parameters is developed and used to determine the location of the contact points. These two contact formulations are implemented in a general MBS algorithm that allows for modeling rigid and flexible body dynamics.

Use of Finite Element and Finite Segment Methods in Modeling Rail Flexibility: A Comparative Study

2012 ◽  
Vol 7 (4) ◽  
Author(s):  
Martin B. Hamper ◽  
Antonio M. Recuero ◽  
José L. Escalona ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Element Mesh ◽  
Finite Segment ◽  
Safety Requirements ◽  
Contact Points ◽  
Rigid Finite Element Method ◽  
Contact Formulation ◽  
Finite Segment Method ◽  
Railroad Vehicle

Safety requirements and optimal performance of railroad vehicle systems require the use of multibody system (MBS) dynamics formulations that allow for modeling flexible bodies. This investigation will present three methods suited for the study of flexible track models while conclusions about their implementations and features are made. The first method is based on the floating frame of reference (FFR) formulation which allows for the use of a detailed finite element mesh with the component mode synthesis technique in order to obtain a reduced order model. In the second method, the flexible body is modeled as a finite number of rigid elements that are connected by springs and dampers. This method, called finite segment method (FSM) or rigid finite element method, requires the use of rigid MBS formulations only. In the third method, the FFR formulation is used to obtain a model that is equivalent to the FSM model by assuming that the rail segments are very stiff, thereby allowing the exclusion of the high frequency modes associated with the rail deformations. This FFR/FS model demonstrates that some rail movement scenarios such as gauge widening can be captured using the finite element FFR formulation. The three procedures FFR, FSM, and FFR/FS will be compared in order to establish differences among them and analyze the specific application of the FSM to modeling track flexibility. Convergence of the methods is analyzed. The three methods proposed in this investigation for modeling the movement of three-dimensional tracks are used with a three-dimensional elastic wheel/rail contact formulation that predicts contact points online and allows for updating the creepages to account for the rail deformations. Several conclusions will be drawn in view of the results obtained in this investigation.

Component Mode Synthesis Order-Reduction for Dynamic Analysis of Structure Modeled With NURBS Finite Element

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
K. Zhou ◽  
G. Liang ◽  
J. Tang
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Large Scale ◽  
Order Reduction ◽  
Reduction Technique ◽  
Component Mode Synthesis ◽  
Original Structure ◽  
Surface Geometry ◽  
Compatibility Conditions ◽  
B Splines

Nonuniform rational B-splines (NURBS) finite element has advantages in analyzing the structure with curved surface geometry. In this research, we develop a component mode synthesis (CMS) based order-reduction technique which can be applied to large-scale NURBS finite element dynamic analysis. In particular, we establish a new substructure division scheme. The underlying idea is to optimally construct interface between adjacent substructures that can maximize the geometry consistency between the original structure and the divided substructures and at the meantime facilitate the compatibility conditions needed in mode synthesis. Case studies are carried out to validate the performance of the order-reduction formulation.

Modeling Rail Flexibility Using Finite Element and Finite Segment Methods

2011 ◽  
Author(s):  
Martin B. Hamper ◽  
Antonio M. Recuero ◽  
Jose´ L. Escalona ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Low Frequency ◽  
Mode Shapes ◽  
Finite Segment ◽  
Safety Requirements ◽  
Contact Points ◽  
Contact Formulation ◽  
Modes Of Vibration ◽  
Floating Frame

Safety requirements and optimal performance of railroad systems require the utilization of multibody System (MBS) formulations that allow for modeling flexible bodies. This investigation will present three methods suited for the study of flexible track models while conclusions about their implementations and features are made. A validated method combining Floating Frame of Reference (FFR) and Finite Element (FE) to model flexible rails is utilized for comparison. In this procedure, component mode synthesis is used to extract a number of low-frequency modes of vibration which describe the deformation of the rail. Likewise, a method that discretizes the flexible body as a finite number of rigid elements that are linked by springs and dampers is applied for railroad simulations. This method, called Finite Segment or Rigid Finite Element (FS), can in turn be combined with FFR through the extraction of mode shapes of the FS model. Convergence of the methods is analyzed. A comparison will be made between these three procedures establishing differences among them and analyzing the specific application of FS to modeling track flexibility. The three aforementioned procedures may be applied to three-dimensional track models and will be used together with three-dimensional wheel/rail contact formulation that predicts contact points online and allows for updating the creepages to account for the rail movements and deformations. Several comparisons and conclusions will be drawn in view of the results obtained in this investigation.

Hybrid Isogeometric-Finite Element Discretization Applied to Stress Concentration Problems

2018 ◽  
Vol 10 (08) ◽  
pp. 1850081 ◽  
Author(s):  
Saeed Maleki-Jebeli ◽  
Mahmoud Mosavi-Mashhadi ◽  
Mostafa Baghani
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Finite Elements ◽  
Field Variable ◽  
Higher Order ◽  
Stable Convergence ◽  
Order Continuity ◽  
Element Discretization ◽  
B Splines ◽  
Computer Methods

Isogeometric analysis (IGA) employs non-uniform rational B-splines (NURBS) or other B-spline-based variants to represent both the geometry and the field variable. Exact geometry representation and higher order global continuity (at least [Formula: see text] even on elements’ boundaries) are two favorable properties that would make IGA an appropriate discretization technique in problems with responses associated with the derivatives of the primary field variable. As a category of these problems, in this paper, 2D elastostatic problems involving stress concentration sites are analyzed with a hybrid isogeometric-finite element (IG-FE) discretization. To exploit higher order continuity of NURBS basis functions, IGA discretization is applied selectively at pre-identified locations of high displacement gradients where the stress concentration occurs. In addition, considering computational efficiency, the rest of problem domain is discretized by means of linear Lagrangian finite elements. The connection of NURBS and Lagrangian domain is carried out through employing specially devised elements [Corbett, C. J. and Sauer, R. A. [2014] “NURBS-enriched contact finite elements”, Computer Methods in Applied Mechanics and Engineering 275, 55–75]. The methodology is applied in some 2D elastostatic examples. Increasing the number of DOFs and comparing convergence of the concentrated stress value using different discretizations, it is shown that the hybrid IG-FE discretizations generally have faster and more stable convergence response compared with pure FE discretizations especially at lower DOFs.

scholarly journals Finite Elements Used in the Vertical Discretization of the Fully Compressible Core of the ALADIN System

2018 ◽  
Vol 146 (10) ◽  
pp. 3293-3310 ◽  
Author(s):  
Jozef Vivoda ◽  
Petra Smolíková ◽  
Juan Simarro
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Global Forecast System ◽  
The Finite Element Method ◽  
Forecast System ◽  
Dynamical Core ◽  
B Splines ◽  
The Finite Difference Method ◽  
Definition Of

Abstract The finite-element method with B splines is used for definition of vertical operators in the nonhydrostatic fully compressible dynamical core of the ALADIN system. It represents a generalization of the same method used in the hydrostatic dynamical core shared by the ALADIN system and the global forecast system ARPEGE/IFS. The method is shown to be robust enough in idealized academic tests and real simulations. Its theoretical superiority is shown when compared with the finite-difference method.

Effectiveness of Tetrahedral Finite Elements in Modeling Tread Patterns for Rolling Simulations

2014 ◽  
Vol 42 (2) ◽  
pp. 101-114
Author(s):  
Harish Surendranath
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Contact Stress ◽  
Contact Stresses ◽  
Time Saving ◽  
Tetrahedral Meshes ◽  
Tetrahedral Elements ◽  
Contact Formulation ◽  
Hexahedral Meshes ◽  
Slow Rolling

ABSTRACT Generating structured hexahedral finite element meshes on tread patterns is a challenging and laborious task due to the complex pattern geometry. However, creating good quality tetrahedral meshes on these geometries is relatively straightforward and can be fully automated. Despite the convenience and time saving, analysts have long avoided tetrahedral elements because of inadequate contact stress accuracy, which is critical for pattern wear prediction. Recent advances in contact formulation has vastly improved the accuracy of contact stresses predicted by tetrahedral meshes. This article presents a comparative study between the results predicted by tetrahedral and hexahedral meshes under slow rolling conditions. Comparisons are presented for footprint solution quantities such as contact stresses as well as global solution quantities such as residual aligning torque.

Effects of occlusal scheme on All-on-Four abutments, screws and prostheses: A three-dimensional finite element study

2020 ◽  
Author(s):  
Nurullah Türker ◽  
Hümeyra Tercanlı Alkış ◽  
Steven J Sadowsky ◽  
Ulviye Şebnem Büyükkaplan
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Good Prognosis ◽  
Von Mises Stress ◽  
Element Analysis ◽  
Group Function ◽  
Occlusal Contact ◽  
Maximum Deformation ◽  
Contact Points ◽  
Von Mises

An ideal occlusal scheme plays an important role in a good prognosis of All-on-Four applications, as it does for other implant therapies, due to the potential impact of occlusal loads on implant prosthetic components. The aim of the present three-dimensional (3D) finite element analysis (FEA) study was to investigate the stresses on abutments, screws and prostheses that are generated by occlusal loads via different occlusal schemes in the All-on-Four concept. Three-dimensional models of the maxilla, mandible, implants, implant substructures and prostheses were designed according to the All-on-Four concept. Forces were applied from the occlusal contact points formed in maximum intercuspation and eccentric movements in canine guidance occlusion (CGO), group function occlusion (GFO) and lingualized occlusion (LO). The von Mises stress values for abutment and screws and deformation values for prostheses were obtained and results were evaluated comparatively. It was observed that the stresses on screws and abutments were more evenly distributed in GFO. Maximum deformation values for prosthesis were observed in the CFO model for lateral movement both in the maxilla and mandible. Within the limits of the present study, GFO may be suggested to reduce stresses on screws, abutments and prostheses in the All-on-Four concept.

scholarly journals A New Mixed Functional-probabilistic Approach for Finite Element Accuracy

2020 ◽  
Vol 20 (4) ◽  
pp. 799-813
Author(s):  
Joël Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Asymptotic Relation ◽  
Probabilistic Approach ◽  
Random Variable ◽  
High Order ◽  
Relative Accuracy ◽  
The Difference ◽  
New Perspective

AbstractThe aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble–Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements {P_{k}} and {P_{m}} ({k<m}). Then we analyze the asymptotic relation between these two probabilistic laws when the difference {m-k} goes to infinity. New insights which qualify the relative accuracy in the case of high order finite elements are also obtained.

scholarly journals Temporal coherency of mechanical stimuli modulates tactile form perception

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Masashi Nakatani ◽  
Yasuaki Kobayashi ◽  
Kota Ohno ◽  
Masaaki Uesaka ◽  
Sayako Mogami ◽  
...  
Keyword(s):  
Sensory Neuron ◽  
Sensory Neurons ◽  
Contact Surface ◽  
Relative Magnitude ◽  
Form Perception ◽  
Tangential Displacement ◽  
Surface Geometry ◽  
Tactile Stimuli ◽  
Surface Patterns ◽  
Temporal Coherency

AbstractThe human hand can detect both form and texture information of a contact surface. The detection of skin displacement (sustained stimulus) and changes in skin displacement (transient stimulus) are thought to be mediated in different tactile channels; however, tactile form perception may use both types of information. Here, we studied whether both the temporal frequency and the temporal coherency information of tactile stimuli encoded in sensory neurons could be used to recognize the form of contact surfaces. We used the fishbone tactile illusion (FTI), a known tactile phenomenon, as a probe for tactile form perception in humans. This illusion typically occurs with a surface geometry that has a smooth bar and coarse textures in its adjacent areas. When stroking the central bar back and forth with a fingertip, a human observer perceives a hollow surface geometry even though the bar is physically flat. We used a passive high-density pin matrix to extract only the vertical information of the contact surface, suppressing tangential displacement from surface rubbing. Participants in the psychological experiment reported indented surface geometry by tracing over the FTI textures with pin matrices of the different spatial densities (1.0 and 2.0 mm pin intervals). Human participants reported that the relative magnitude of perceived surface indentation steeply decreased when pins in the adjacent areas vibrated in synchrony. To address possible mechanisms for tactile form perception in the FTI, we developed a computational model of sensory neurons to estimate temporal patterns of action potentials from tactile receptive fields. Our computational data suggest that (1) the temporal asynchrony of sensory neuron responses is correlated with the relative magnitude of perceived surface indentation and (2) the spatiotemporal change of displacements in tactile stimuli are correlated with the asynchrony of simulated sensory neuron responses for the fishbone surface patterns. Based on these results, we propose that both the frequency and the asynchrony of temporal activity in sensory neurons could produce tactile form perception.

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