Nitsche’s method for non-conforming multipatch coupling in hyperelastic isogeometric analysis

Du, Xiaoxiao; Zhao, Gang; Wang, Wei; Fang, Hsu Wei

doi:10.1007/s00466-019-01789-x

Cited by 25 publications

(3 citation statements)

References 57 publications

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“…In a nonlinear system, the deformation gradient F is typically defined as the geometric relationship between the coordinates of the current geometry change x and the coordinates of the initial undeformed shape X [32][33][34]:…”

Section: Isogeometric Hyperelastic Numerical Formulamentioning

confidence: 99%

Isogeometric Analysis of Hyperelastic Material Characteristics for Calcified Aortic Valve

Chen,

Li,

Liu

et al. 2024

CMES

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This study explores the implementation of computed tomography (CT) reconstruction and simulation techniques for patient-specific valves, aiming to dissect the mechanical attributes of calcified valves within transcatheter heart valve replacement (TAVR) procedures. In order to facilitate this exploration, it derives pertinent formulas for 3D multi-material isogeometric hyperelastic analysis based on Hounsfield unit (HU) values, thereby unlocking foundational capabilities for isogeometric analysis in calcified aortic valves. A series of uniaxial and biaxial tensile tests is executed to obtain an accurate constitutive model for calcified active valves. To mitigate discretization errors, methodologies for reconstructing volumetric parametric models, integrating both geometric and material attributes, are introduced. Applying these analytical formulas, constitutive models, and precise analytical models to isogeometric analyses of calcified valves, the research ascertains their close alignment with experimental results through the close fit in displacement-stress curves, compellingly validating the accuracy and reliability of the method. This study presents a step-by-step approach to analyzing the mechanical characteristics of patient-specific valves obtained from CT images, holding significant clinical implications and assisting in the selection of treatment strategies and surgical intervention approaches in TAVR procedures.

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Section: Isogeometric Hyperelastic Numerical Formulamentioning

confidence: 99%

Isogeometric Analysis of Hyperelastic Material Characteristics for Calcified Aortic Valve

Chen,

Li,

Liu

et al. 2024

CMES

View full text Add to dashboard Cite

show abstract

“…The commonly used schemes for multiple patches are based on the mortar method, 56,57 penalty method, 58 and Nitsche's method. [59][60][61] The mortar method can be considered to be a type of Lagrange multiplier method, in which the resulting system is not positive definite. The penalty parameter should be adjusted according to the grid density during the penalty method.…”

Section: Introductionmentioning

confidence: 99%

“…The coupling of multiple patches is another problem that must be addressed. The commonly used schemes for multiple patches are based on the mortar method, 56,57 penalty method, 58 and Nitsche's method 59–61 . The mortar method can be considered to be a type of Lagrange multiplier method, in which the resulting system is not positive definite.…”

Section: Introductionmentioning

confidence: 99%

Generalized particle domain method: An extension of material point method generates particles from the CAD files

Wang,

Dong,

Zhang

et al. 2024

Numerical Meth Engineering

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SummaryIn this paper, a generalized particle domain method (GPDM) is proposed and developed within the framework of the convected particle domain interpolation method. This new method generates particles directly from non‐uniform rational B‐spline (NURBS)‐based CAD file of a continuum body. The particle domain corresponds to a NURBS element even for trimmed elements of solids with complex geometries. The shape functions and the gradient of shape functions are evaluated using NURBS basis functions to map material properties between particles and grid nodes. It approves that this proposed GPDM can track the domain of particles accurately and avoid the issue of cell‐crossing instability. Several numerical examples are presented to demonstrate the high performance of this proposed new particle domain method. It is shown that the results obtained using the proposed GPDM are consistent with the experimental data reported in the literature. Further development of the generalized particle domain method can provide a link to the material point method and isogeometric analysis.

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Virtual element method with adaptive refinement for problems of two-dimensional complex topology models from an engineering perspective

Wang

Zhao

et al. 2022

Comput Mech

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Nitsche’s method for non-conforming multipatch coupling in hyperelastic isogeometric analysis

Cited by 25 publications

References 57 publications

Isogeometric Analysis of Hyperelastic Material Characteristics for Calcified Aortic Valve

Isogeometric Analysis of Hyperelastic Material Characteristics for Calcified Aortic Valve

Generalized particle domain method: An extension of material point method generates particles from the CAD files

Virtual element method with adaptive refinement for problems of two-dimensional complex topology models from an engineering perspective

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