Article

NURBS-based Galerkin method and application to skeletal muscle modeling

Authors:

Jia LuAuthors Info & Claims

SPM '05: Proceedings of the 2005 ACM symposium on Solid and physical modeling

Pages 71 - 78

https://doi.org/10.1145/1060244.1060253

Published: 13 June 2005 Publication History

Abstract

Non-Uniform Rational B-spline (NURBS) is often used to construct the free-form boundary representation of three-dimensional objects. In this paper, we propose a method for mechanical analysis for deformable bodies by combining NURBS geometric representation and the Galerkin method. The NURBS surface bounding a 3D body is extended to a trivariate NURBS solid by adding another parametric domain represented by additional control points. The displacement field of the body is constructed using the NURBS shape representation with the control point being the generalized coordinates. The interpolated displacement field is directly used to facilitate finite element formulation. In this manner, traditional FEM meshing is not required. In this work, the NURBS-FEM is applied to skeletal muscle modeling. Muscle is modeled as anisotropic, active hyperelastic solids. The directions of the contractile fibers can be uniform or along the tangent direction of NURBS curves. Typical contractive motions of isolated muscle are simulated.

References

[1]

Belytschko, T., Krongauz, Y., Organ, D., Fleming, M., and Krysl, P. 1996. Meshless methods: an overview and recent developments, Computer Methods in Applied Mechanics and Engineering, special issue on Meshless Methods, 139:3--47.

[2]

Belytschko, T., Liu, W. K., and Mora, B. 2002. Nonlinear finite elements for continua and structure, J. Wiley & Sons, New York.

[3]

Chen, D. T., Zeltzer, D. 1992. Pump it up: computer animation of a biomechanically based model of muscle using the finite element method, ACM SIGGRAPH Computer Graphics, 26:89--98.

Digital Library

[4]

Chen, J. S. and Wang, H. P. 2000. Some Recent Improvements in Meshfree Methods for Incompressible Finite Elasticity Boundary Value Problems with Friction, Computational Mechanics, 25: 137--156.

[5]

de Boor, C. 2001. A practical Guide to Splines. Springer, New York.

[6]

Gibson, S., and Mirtich, B. 1997. A survey of deformable modeling in computer graphics, Tech. Report No. TR-97--19, Mitsubishi Electric Research Lab., Cambridge, MA.

[7]

Herzog, W. (ed.) 2000. Skeletal muscle mechanics: from mechanisms to function. Wiley & Sons, Chichester, UK.

[8]

Hollig, K. 2003. Finite Element Methods with B-Splines. SIAM, Philadelphia.

Digital Library

[9]

Hoschek, J., Lasser, D., and Schumaker, L. L. 1993. Fundamentals of Computer Aided Geometric Design, AK Peters, Ltd.

Digital Library

[10]

Lemors, R., Epstein, M., Herzog, W., Wyvill, B. 2001. Realistic skeletal muscle deformation using finite element analysis. Proceedings of the 14th Brazilian Symposium on Computer Graphics and Image Processing. IEEE Computer Society Press. 192--199.

Digital Library

[11]

Li, S. and Liu, W. K. 2002. Meshfree and particle methods and their applications. Applied Mechanics Review, 55: 1--34.

[12]

Liu, W. K., Chen, Y., Chang, C. T. and Belytschko, T. 1996. Advances in multiscale kernel particle methods. Computational Mechanics, 18:73--111.

[13]

Ma, D., Lin, F., and Chua, C. K. 2001. Rapid prototyping applications in medicine. Part 1: NURBS-based volume modeling, International Journal of Advanced Manufacturing Technology. 18(2):103--117.

[14]

Ng-Thow-Hing, V. 2000. Anatomically-based models for physical and geometric reconstruction of humans and other animals. Ph.D. Thesis, Department of Computer Science, University of Toronto.

Digital Library

[15]

Ng-Thow-Hing, V. and Fiume. E. 2002. Application-specific muscle representations. Proc. Graphics and Interface, 107--115. Eds. Sturzlinger and McCool M.

[16]

Oomens, C. W. J., Maenhout, M., van Oijen, C. H. G. A., Drost, M. R., and Baaijens, F. P.T. 2003. Fińite element modelling of contracting skeletal muscle, Phil Trans R Soc Lon B, 358(1437):1453--1460.

[17]

Piegl, L. and Tiller, W. 1997. The NURBS Book. Springer-Verlag, New York.

Digital Library

[18]

Porcher-Nedel, L., and Thalmann, D. 1998. Real time muscle deformation using mass-spring systems. Proc. CGI'98, IEEE Computer Society Press.

Digital Library

[19]

Sederberg, T., and Parry, S. 1986. Free-Form deformation of solid geometric models. ACM Computer Graphics (SIGGRAPH '86 Proc., 20:151--160.

Digital Library

[20]

Teran, J., Blemker, S., Ng-Thow-Hign, V., and Fedkiw, R. 2003. Finite volume method for the simulation of skeletal muscle. In Proc. of the 2003 SIGGRAPH/Eurographics Symp. on Computer Animation, 68--74.

Digital Library

[21]

Terzopoulos D., and Qin, H. 1994. Dynamic nurbs with geometric constraints for interactive sculpting. ACM Transaction on Grpahics, 13(3):103--136.

Digital Library

[22]

U. S. National Library of Medicine. The visible human project, 1994. http://www.nlm.nih.gov/research/visible/.

[23]

Yang, J., Abdel-Malek, K, Farrell, K., and Nebel, K. 2004. The IOWA Interactive Digital-Human Virtual Environment, 2004 ASME International Engineering Congress, The 3rd Symposium on Virtual Manufacturing and Application, November 13--19, Anaheim, California.

[24]

Zajac, F. E., Topp, E. L., and Stevenson, P. J. 1986. A dimensionless musculotendon model. Proceedings IEEE Engineering in Medicine and Biology.

[25]

Zajac, F. E. 1989. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Critical Reviews in Biomedical Enginering, 17:359--411.

[26]

Zienkiewicz, O. C., and Taylor, R. L. 2000. The Finite Element Method(5th. Ed.), Butterworth-Heinemann, Oxford.

Cited By

Le QDeng YBu JZhu BDu T(2023)Second-Order Finite Elements for Deformable SurfacesSIGGRAPH Asia 2023 Conference Papers10.1145/3610548.3618186(1-10)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.1145/3610548.3618186
Schneider TPanozzo DZhou X(2021)Isogeometric high order mesh generationComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2021.114104386(114104)Online publication date: Dec-2021
https://doi.org/10.1016/j.cma.2021.114104
Luo SEdmonds MYi JZhou XShen Y(2020)Spline-Based Modeling and Control of Soft Robots2020 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM)10.1109/AIM43001.2020.9158917(482-487)Online publication date: Jul-2020
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Index Terms

NURBS-based Galerkin method and application to skeletal muscle modeling
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Conferences

SPM '05: Proceedings of the 2005 ACM symposium on Solid and physical modeling

June 2005

287 pages

ISBN:1595930159

DOI:10.1145/1060244

Program Chairs:
Leif Kobbelt
RWTH Aachen University, Germany
,
Vadim Shapiro
University of Wisconsin--Madison, USA

Copyright © 2005 ACM.

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Published: 13 June 2005

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SPM05: 2005 ACM Symposium on Solid and Physical Modeling

June 13 - 15, 2005

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Cited By

Le QDeng YBu JZhu BDu T(2023)Second-Order Finite Elements for Deformable SurfacesSIGGRAPH Asia 2023 Conference Papers10.1145/3610548.3618186(1-10)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.1145/3610548.3618186
Schneider TPanozzo DZhou X(2021)Isogeometric high order mesh generationComputer Methods in Applied Mechanics and Engineering10.1016/j.cma.2021.114104386(114104)Online publication date: Dec-2021
https://doi.org/10.1016/j.cma.2021.114104
Luo SEdmonds MYi JZhou XShen Y(2020)Spline-Based Modeling and Control of Soft Robots2020 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM)10.1109/AIM43001.2020.9158917(482-487)Online publication date: Jul-2020
https://doi.org/10.1109/AIM43001.2020.9158917
Kolo IAskes Hde Borst R(2017)Convergence analysis of Laplacian-based gradient elasticity in an isogeometric frameworkFinite Elements in Analysis and Design10.1016/j.finel.2017.07.006135:C(56-67)Online publication date: 1-Nov-2017
https://dl.acm.org/doi/10.1016/j.finel.2017.07.006
Soghrati SMerel R(2016)NURBS enhanced HIFEMFinite Elements in Analysis and Design10.1016/j.finel.2016.06.007120:C(68-79)Online publication date: 1-Nov-2016
https://dl.acm.org/doi/10.1016/j.finel.2016.06.007
Yijing Li Barbic J(2015)Stable Anisotropic MaterialsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2015.244810521:10(1129-1137)Online publication date: 1-Oct-2015
https://dl.acm.org/doi/10.1109/TVCG.2015.2448105
Sánchez CLloyd JFels SAbolmaesumi P(2014)Embedding digitized fibre fields in finite element models of musclesComputer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization10.1080/21681163.2013.8628612:4(223-236)Online publication date: 7-Feb-2014
https://doi.org/10.1080/21681163.2013.862861
Nguyen VKerfriden PBrino MBordas SBonisoli E(2014)Nitsche's method for two and three dimensional NURBS patch couplingComputational Mechanics10.1007/s00466-013-0955-353:6(1163-1182)Online publication date: 1-Jun-2014
https://dl.acm.org/doi/10.1007/s00466-013-0955-3
Chivukula VMousel JLu JVigmostad S(2014)Micro‐scale blood particulate dynamics using a non‐uniform rational B‐spline‐based isogeometric analysisInternational Journal for Numerical Methods in Biomedical Engineering10.1002/cnm.266630:12(1437-1459)Online publication date: 5-Oct-2014
https://doi.org/10.1002/cnm.2666
Li BLi XWang KQin H(2013)Surface Mesh to Volumetric Spline Conversion with Generalized PolycubesIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2012.17719:9(1539-1551)Online publication date: 1-Sep-2013
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