An Efficient Finite Element Algorithm in Elastography

2016 ◽  
Vol 08 (03) ◽  
pp. 1650037 ◽  
Author(s):  
Eric Li ◽  
W. H. Liao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Soft Tissues ◽  
Tetrahedral Mesh ◽  
Tetrahedral Elements ◽  
Time Harmonic ◽  
Smoothed Finite Element Method ◽  
Complicated Geometry ◽  
First Time ◽  
Element Method

Elastography is an imaging approach to measure the stiffness of tissues to provide diagnostic information. Currently, finite element method (FEM) has been widely used in elastography. However, FEM tends to an overly stiff model that sometimes gives unsatisfactory accuracy, particularly using triangular elements in 2D or tetrahedral elements in 3D. In general, it is difficult or even impossible to generate quadrilateral or brick elements to precisely capture the anatomic details for mechanobiologic modeling as the biologic system can be rather sophisticated. In addition, biologic soft tissues are often considered as “incompressible” materials, where conventional FEM could suffer from volumetric locking in numerical solution. On the other hand, linear triangular and tetrahedral mesh can be automatically generated for complicated geometry, which significantly saves the time for the creation of model. With these reasons, for the first time, smoothed finite element method (SFEM) is developed to analyze elastography problems. A range of numerical examples, including static, dynamic, viscoelastic and time harmonic cases have exemplified herein to validate that SFEM is able to provide more accurate and stable solutions using the same set of mesh compared with the standard FEM. Furthermore, SFEM is also effective to inversely compute the mechanical properties of abnormal tissue.

A Sub-Domain Inverse Finite Element Characterization of Hyperelastic Membranes Including Soft Tissues

2003 ◽  
Vol 125 (3) ◽  
pp. 363-371 ◽  
Author(s):  
Padmanabhan Seshaiyer ◽  
Jay D. Humphrey
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Soft Tissues ◽  
Nonlinear Behavior ◽  
Local Stress ◽  
Biological Tissues ◽  
Material Behavior ◽  
Inverse Finite Element Method ◽  
Complicated Geometry ◽  
Element Method

Quantification of the mechanical behavior of hyperelastic membranes in their service configuration, particularly biological tissues, is often challenging because of the complicated geometry, material heterogeneity, and nonlinear behavior under finite strains. Parameter estimation thus requires sophisticated techniques like the inverse finite element method. These techniques can also become difficult to apply, however, if the domain and boundary conditions are complex (e.g. a non-axisymmetric aneurysm). Quantification can alternatively be achieved by applying the inverse finite element method over sub-domains rather than the entire domain. The advantage of this technique, which is consistent with standard experimental practice, is that one can assume homogeneity of the material behavior as well as of the local stress and strain fields. In this paper, we develop a sub-domain inverse finite element method for characterizing the material properties of inflated hyperelastic membranes, including soft tissues. We illustrate the performance of this method for three different classes of materials: neo-Hookean, Mooney Rivlin, and Fung-exponential.

Development of SFEM-Pre: A Novel Preprocessor for Model Creation for the Smoothed Finite Element Method

2019 ◽  
Vol 17 (02) ◽  
pp. 1845002 ◽  
Author(s):  
J. F. Zhang ◽  
R. P. Niu ◽  
Y. F. Zhang ◽  
C. Q. Wang ◽  
M. Li ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Complex Geometry ◽  
Three Dimensional ◽  
Efficient Computation ◽  
Practical Engineering ◽  
Smoothed Finite Element Method ◽  
2D And 3D ◽  
First Time ◽  
Element Method

Smoothed finite element method (S-FEM) is a new general numerical method which has been applied to solve various practical engineering problems. It combines standard finite element method (FEM) and meshfree techniques based on the weaken-weak (W2) formulation. This project, for the first time, develops a preprocessor software package SFEM-Pre for creating types of two-dimensional (2D) and three-dimensional (3D) S-FEM models following strictly the S-FEM theory. Because the software architecture of our 3D processor is the same as our 2D preprocessor, we will mainly introduce the 2D preprocessor in terms of software design for easier description, but the examples will include both 2D and 3D cases to fully demonstrate and validate the whole preprocessor of S-FEM. Our 2D preprocessor package is equipped with a graphical user interface (GUI) for easy use, and with a connectivity database for efficient computation. Schemes are developed for not only automatically meshes the problem domains using our GUI, but also accepts various geometry files made available from some existing commercial software packages, such as ABAQUS®and HyperMesh®. In order to improve the efficiency of our preprocessor, a parallel triangulation mesh generator has also been developed based on the advancing front technique (AFT) to create triangular meshes for complex geometry, and at the same time to create six types of connectivity needed for various S-FEM models. In addition, a database is implemented in our code to record all these connectivity to avoid duplicated calculation. Finally, intensive numerical experiments are conducted to validate the efficiency, accuracy and stability of our preprocessor codes. It is shown that with our preprocessor, an S-FEM can be created automatically without much human intervention for geometry of arbitrary complexity.

A MODIFIED TRIANGULATION ALGORITHM TAILORED FOR THE SMOOTHED FINITE ELEMENT METHOD (S-FEM)

2013 ◽  
Vol 11 (01) ◽  
pp. 1350069 ◽  
Author(s):  
Y. LI ◽  
M. LI ◽  
G. R. LIU
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
The Finite Element Method ◽  
Advancing Front ◽  
Stiffness Matrices ◽  
Smoothed Finite Element Method ◽  
Complicated Geometry ◽  
Discrete Domains ◽  
Volume Method ◽  
Element Method

Meshing is one of the key tasks in using the finite element method (FEM), the smoothed finite element method (S-FEM), finite volume method (FVM), and many other discrete numerical methods. Linear triangular (T3) mesh is one of the most widely used mesh, because it can be generated and refined automatically for discrete domains of complicated geometry, and hence save significantly the time for model creation. This paper presents a modified triangulation algorithm based on the advancing front technique to provide a comprehensive linear triangular mesh generator with six connectivity lists, including element–node (Ele–N) connectivity, element–edge (Ele–Eg) connectivity, edge–node (Eg–N) connectivity, edge–element (Eg–Ele) connectivity, node–edge (N–Eg) connectivity and node–element (N–Ele) connectivity. These six connectivity lists are generated along the way when the T3 elements are created, and hence it is done in a most efficient fashion. The connectivity is recorded in the usual counter-clockwise convention for convenient utilization in various S-FEM models for effective analyses. In addition, an algorithm is developed for renumbering the nodes in the T3 mesh to obtain a minimized bandwidth of stiffness matrices for both FEM and S-FEM models.

F-Bar Aided Edge-Based Smoothed Finite Element Method with 4-Node Tetrahedral Elements for Static Large Deformation Elastoplastic Problems

2019 ◽  
Vol 16 (05) ◽  
pp. 1840010 ◽  
Author(s):  
Yuki Onishi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Element Formulation ◽  
Tetrahedral Elements ◽  
Smoothed Finite Element Method ◽  
New Type ◽  
Displacement Based ◽  
Edge Based ◽  
Element Method

A new type of smoothed finite element method (S-FEM), F-barES-FEM-T4, is demonstrated in static large deformation elastoplastic cases. F-barES-FEM-T4 combines the edge-based S-FEM (ES-FEM) and the node-based S-FEM (NS-FEM) for 4-node tetrahedral (T4) elements with the aid of the F-bar method in order to resolve the major issues of Selective ES/NS-FEM-T4. As well as most of the other S-FEMs, F-barES-FEM-T4 inherits pure displacement-based formulation and thus has no increase in DOF. Moreover, the cyclic smoothing procedure introduced in F-barES-FEM-T4 is effective to adjust the smoothing level so that pressure checkerboarding (oscillation) is suppressed reasonably. Some examples of static large deformation analyses for elastoplastic materials proof the excellent performance of F-barES-FEM-T4 in contrast to the conventional hybrid T4 element formulation.

Hexahedral-Based Smoothed Finite Element Method Using Volumetric-Deviatoric Split for Contact Problem

2018 ◽  
Vol 940 ◽  
pp. 84-88 ◽  
Author(s):  
Kai Oshiro ◽  
Hiroka Miyakubo ◽  
Masaki Fujikawa ◽  
Chobin Makabe
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Contact Problem ◽  
Large Strain ◽  
Deformation Gradient ◽  
Deformation Analysis ◽  
Tetrahedral Elements ◽  
Incompressible Materials ◽  
Smoothed Finite Element Method ◽  
Element Method

A first-order hexahedral (H8)-element-based smoothed finite element method (S-FEM) with a volumetric-deviatoric split for nearly incompressible materials was developed for highly accurate deformation analysis of large-strain problems. In the proposed method, the isovolumetric part of the deformation gradient at the integration point is derived from F based on the beta finite element method (i.e., an S-FEM), whereas the volumetric part of the deformation gradient is derived from F on the basis of the standard FEM with reduced integration elements. This method targets H8 elements that are automatically generated from tetrahedral elements, which makes it quite practical. This is because the FE mesh can be created automatically even if the targeted object has a complex shape. This method eliminates the phenomena of volumetric and shear locking, and reduces pressure oscillations. The proposed method was implemented in the commercial FE software Abaqus and applied to the large-deformation contact problem to verify its effectiveness.

SMOOTHED FINITE ELEMENTS LARGE DEFORMATION ANALYSIS

2010 ◽  
Vol 07 (03) ◽  
pp. 513-524 ◽  
Author(s):  
S. J. LIU ◽  
H. WANG ◽  
H. ZHANG
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Large Deformations ◽  
Meshfree Methods ◽  
Deformation Analysis ◽  
The Finite Element Method ◽  
Smoothed Finite Element Method ◽  
First Time ◽  
Element Method

The smoothed finite element method (SFEM) was developed in order to eliminate certain shortcomings of the finite element method (FEM). SFEM enjoys some of the flexibilities of meshfree methods. One advantage of SFEM is its applicability to modeling large deformations. Due to the absence of volume integration and parametric mapping, issues such as negative volumes and singular Jacobi matrix do not occur. However, despite these advantages, SFEM has never been applied to problems with extreme large deformation. For the first time, we apply SFEM to extreme large deformations. For two numerical problems, we demonstrate the advantages of SFEM over FEM. We also show that SFEM can compete with the flexibility of meshfree methods.

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