Strain smoothing for compressible and nearly-incompressible finite elasticity

Lee, Changkye; Mihai, L. Angela; Hale, Jack; Kerfriden, Pierre; Bordas, Stphane P.A.

doi:10.1016/j.compstruc.2016.05.004

Cited by 42 publications

(22 citation statements)

References 51 publications

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“…Moreover, the aforementioned approaches are restricted to conventional element types, ie, triangles/quadrilaterals in two dimensions and tetrahedra/hexahedral in three dimensions. With the introduction of the polygonal FEM (wherein, the elements can assume arbitrary shapes and sizes), there is a growing interest in using these elements for various problems in science and engineering . However, to the best of the authors' knowledge, an extension of the aforementioned approaches to arbitrary polytopes is scarcely reported in the literature.…”

Section: Introductionmentioning

confidence: 99%

“…With the introduction of the polygonal FEM (wherein, the elements can assume arbitrary shapes and sizes), there is a growing interest in using these elements for various problems in science and engineering. [9][10][11] However, to the best of the authors' knowledge, an extension of the aforementioned approaches to arbitrary polytopes is scarcely reported in the literature. system to a scaled boundary coordinate system, with the restriction that the entire boundary is visible from the origin of the scaled boundary coordinate system.…”

Section: Introductionmentioning

confidence: 99%

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Scaled boundary finite element method for compressible and nearly incompressible elasticity over arbitrary polytopes

Aladurthi

Natarajan

Ooi

et al. 2019

Numerical Meth Engineering

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Summary In this paper, a purely displacement‐based formulation is presented within the framework of the scaled boundary finite element method to model compressible and nearly incompressible materials. A selective reduced integration technique combined with an analytical treatment in the nearly incompressible limit is employed to alleviate volumetric locking. The stiffness matrix is computed by solving the scaled boundary finite element equation. The salient feature of the proposed technique is that it neither requires a stabilization parameter nor adds additional degrees of freedom to handle volumetric locking. The efficiency and the robustness of the proposed approach is demonstrated by solving various numerical examples in two and three dimensions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Scaled boundary finite element method for compressible and nearly incompressible elasticity over arbitrary polytopes

Aladurthi

Natarajan

Ooi

et al. 2019

Numerical Meth Engineering

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show abstract

“…Since Liu et al [3] introduced four different S-FEM approaches, i.e. cell-based S-FEM (CS-FEM), edge-based S-FEM (ES-FEM), node-based S-FEM (NS-FEM) and face-based S-FEM (FS-FEM), several approaches have been widely used in various engineering fields: plate (Nguyen-Xuan et al [4]), shell (Nguyen-Thanh et al [5]), nearly-incompressible elasticity (Lee et al [6] and Ong et al [7]), and coupled with extended FEM (Bordas et al [8,9]). Moreover, selective S-FEM [10], the hybrid S-FEM [11] and enriched-S-FEM [6] were introduced to improve conventional S-FEMs.…”

Section: Introductionmentioning

confidence: 99%

“…In the final section, the performance of the proposed method was conclude and some possible future works were prawn related to the present method. For the nonlinear CS-FEM approximation, the following smoothed infinitesimal strain tensor over smoothing domain Ω is given as [6]:…”

Section: Introductionmentioning

confidence: 99%

A Modified Cell-Based Strain Smoothing for Material Nonlinearity

Lee¹,

Natarajan²

2019

Preprint

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This work presents a linear smoothing scheme over high-order triangular elements in the framework of a cell-based strain smoothed finite element method for two-dimensional nonlinear problems. The main idea behind the proposed linear smoothing scheme for strain-smoothed finite element method (S-FEM) is no subdivision of finite element cells to sub-cells while the classical S-FEM needs sub-cells. Since the linear smoothing function is employed, S-FEM is able to use quadratic triangular or quadrilateral elements. The modified smoothed matrix obtained node-wise is evaluated. In the same manner with the computation of the strain-displacement matrix, the smoothed stiffness matrix and deformation graident are obtained over smoothing domains. A series of benchmark tests are investigated to demonstrate validity and stability of the proposed scheme. The validity and accuracy are confirmed by comparing the obtained numerical results with the standard FEM using 2nd-order triangular element and the exact solutions.

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“…Bonet and Burton proposed the average node pressure (ANP) tetrahedral mesh to achieve better results for nearly incompressible materials [9]. More recently, Leea et.al [34] present a robust and efficient form of the smoothed finite element method (SFEM) to prevent this issue.…”

Section: Mesh Typesmentioning

confidence: 99%

Virtual Reality Surgery Simulation: A Survey on Patient Specific Solution

Zhang

Chang

Yang

et al. 2017

Next Generation Computer Animation Techniques

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Abstract. For surgeons, the precise anatomy structure and its dynamics are important in the surgery interaction, which is critical for generating the immersive experience in VR based surgical training applications. Presently, a normal therapeutic scheme might not be able to be straightforwardly applied to a specific patient, because the diagnostic results are based on averages, which result in a rough solution. Patient Specific Modeling (PSM), using patient-specific medical image data (e.g. CT, MRI, or Ultrasound), could deliver a computational anatomical model. It provides the potential for surgeons to practice the operation procedures for a particular patient, which will improve the accuracy of diagnosis and treatment, thus enhance the prophetic ability of VR simulation framework and raise the patient care. This paper presents a general review based on existing literature of patient specific surgical simulation on data acquisition, medical image segmentation, computational mesh generation, and soft tissue real time simulation.

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Strain smoothing for compressible and nearly-incompressible finite elasticity

Cited by 42 publications

References 51 publications

Scaled boundary finite element method for compressible and nearly incompressible elasticity over arbitrary polytopes

Scaled boundary finite element method for compressible and nearly incompressible elasticity over arbitrary polytopes

A Modified Cell-Based Strain Smoothing for Material Nonlinearity

Virtual Reality Surgery Simulation: A Survey on Patient Specific Solution

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