Research Article
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Year 2023, Volume: 15 Issue: 4, 163 - 183, 24.12.2023

Mustafa Tekin Bahadır Alyavuz

https://doi.org/10.24107/ijeas.1386832

Abstract

References

  • Blacker, T., Automated conformal hexahedral meshing constraints, challenges and opportunities. Engineering with Computers, 17, 201-210, 2002.
  • Tadepalli, S.C., Erdemir, A. and Cavanagh, P.R., Comparison of hexahedral and tetrahedral elements in finite element analysis of the foot and footwear. Journal of Biomechanics, 44, 2337-2343, 2011.
  • Schneiders, R., A grid-based algorithm for the generation of hexahedral element meshes. Engineering with Computers, 12, 168-177, 1996.
  • Eppstein, E., Linear complexity hexahedral mesh generation. Computational Geometry Theory and Applications, 12, 3-16, 1999.
  • Baudouin, T.C., Remacle, J.F., Marchandise, E., Henrotte, F. and Geuzaine, C., A frontal approach to hex-dominant mesh generation. Advanced Modeling and Simulation in Engineering Sciences, 1-8,2014.
  • Staten, M.L., Canann, S.A. and Owen, S.J., BMSweep: Locating interior nodes during sweeping. Engineering with Computers, 15, 212-218, 1999.
  • Lai, M., Benzley, S. and White, D., Automated hexahedral mesh generation by generalized multiple source to multiple target sweeping. International Journal for Numerical Methods in Engineering, 49, 261-275, 2000.
  • Owen, S.J. and Saigal, S., H-Morph: an indirect approach to advancing front hex meshing. International Journal for Numerical Methods in Engineering, 49, 289-312, 2000.
  • Li, T.S., McKeag, R.M. and Armstrong, C.G., Hexahedral meshing using midpoint subdivision and integer programming. Computer Methods in Applied Mechanics and Engineering, 124, 171-193, 1995.
  • Schneiders, R., Refining quadrilateral and hexahedral element meshes, Proceedings of the Fifth International Conference on Numerical Grid Generation in Computational Field Simulations, 679-688, 1996.
  • Harris, N.J., Benzley, S.E. and Owen, S.J., Conformal refinement of all-hexahedral element meshes based on multiple twist plane insertion, Proceedings of the 13th International Meshing Roundtable (IMR), 157–168, 2004.
  • Parrish, M., Borden, M., Staten, M. and Benzley, S., A selective approach to conformal refinement of unstructured hexahedral finite element meshes, Proceedings of the 16th International Meshing Roundtable (IMR), Seattle, USA, 14-17 Oct 2007.
  • Huang, L., Zhao, G., Wang, Z. and Zhang, X., Adaptive hexahedral mesh generation and regeneration using an improve d grid-base d method. Advances in Engineering Software, 102, 49-70, 2016.
  • Huang, L., Zhao, G., Ma, X. and Wang, Z., Incorporating improved refinement techniques for a grid-based geometrically-adaptive hexahedral mesh generation algorithm. Advances in Engineering Software, 64, 20-32, 2013.
  • Tchon, K.F., Khachan, M., Guibault, F. and Camarero, R., Three-dimensional anisotropic geometric metrics based on local domain curvature and thickness. Computer-Aided Design, 37, 173-187, 2005.
  • Zhang, Y. and Bajaj, C., Adaptive and quality quadrilateral/hexahedral meshing from volumetric data. Computer Methods Applied Mechanics and Engineering, 195, 942–960, 2006.
  • Fernandes, J.L.M. and Martins, P.A.F., All-hexahedral remeshing for the finite element analysis of metal forming processes. Finite Elements in Analysis and Design, 43, 666 – 679, 2007.
  • Zhao, G., Zhang, H. and Cheng, L., Geometry-adaptive generation algorithm and boundary match method for initial hexahedral element mesh. Engineering with Computers, 24, 321–339, 2008.
  • Sun, L., Zhao, G. and Ma, X., Adaptive generation and local refinement methods of three-dimensional hexahedral element mesh. Finite Elements in Analysis and Design, 50, 184–200, 2012.
  • Zhu, J. and Zienkiewicz, C., Super convergence recovery technique and a posteriori error estimators. International Journal for Numerical Methods in Engineering, 30, 1321-1339, 1990.
  • Devloo, P. R., A three-dimensional adaptive finite element strategy. Computers and Structures, 38, 121-130, 1991.
  • Zienkiewicz, O.C. and Zhu, J.Z., The superconvergent patch recover (SPR) and adaptive finite element refinement. Computer Methods in Applied Mechanics and Engineering, 101, 207-224, 1992.
  • Wada, Y. and Okuda, H., Effective adaptation technique for hexahedral mesh. Concurrency and Computation: Practice And Experience, 14, 451-463, 2002.
  • Park, C.,H. and Yang, D.Y., Adaptive refinement of all-hexahedral elements for three-dimensional metal forming analysis. Finite Elements in Analysis and Design, 43, 22–35, 2006.
  • Moshfegh, R., Li, X. and Nilsson, L., Gradient-based refinement indicators in adaptive finite element analysis with special reference to sheet metal forming. Engineering Computations, 17, 910-932, 2000.
  • Niekamp, R. and Stein, E., An object-oriented approach for parallel two- and three-dimensional adaptive finite element computations. Computers and Structures, 80, 317–328, 2002.
  • Swanson, S. R., Large deformation finite element calculations for slightly compressible hyperelastic materials. Computers and Structures, 21, 81-88, 1985.
  • Pengt, S. H. and Cbang, W. V., A compressible approach in finite element analysis of rubber-elastic materials. Computers and Structures, 62, 573-593, 1997.
  • Suchocki, C., Finite element implementation of slightly compressible and incompressible first invariant-based hyperelasticity: theory, coding, exemplary problems. Journal of Theoretical and Applied Mechanics, 55, 787-800, 2017.
  • Herrmann, L. R., Elasticity equations for incompressible and nearly incompressible materials by a variational theorem. American Institute of Aeronautics and Astronautics (AIAA) Journal, 3, 1896-1900, 1965.
  • Bonet, J. and Bhargava, P., A uniform deformation gradient hexahedron element with artificial hourglass control. International Journal For Numerical Methods in Engineering, 38, 2809-2828, 1995.
  • Neto, E. A. S., Peril D., Dutko M. and Owen D. R. J., Design of simple low order finite elements for large strain analysis of nearly incompressible solids. International Journal of Solids and Structures, 33, 3211-3296, 1996.
  • Pascon, J. P., Large deformation analysis of plane‑stress hyperelastic problems via triangular membrane finite elements. International Journal of Advanced Structural Engineering, 11, 331–350, 2019.
  • Medri, G. and Strozzl, A., Mechanical analysis of elastomeric seals by numerical methods. Industrial and Engineering Chemistry Product Research and Development, 23, 596-600, 1984.
  • Kato, K., Lee, N.S. and Bathe K.J., Adaptive finite element analysis of large strain elastic response. Computers and Structures, 47, 829-855, 1993.
  • Chamberland, E., Fortin, A. and Fortin, M., Comparison of the performance of some finite element discretizations for large deformation elasticity problems. Computers and Structures, 88, 664–673, 2010.
  • O’Shea, D. J., Attard, M. M., Kellermann, D.C. and Sansour, C., Nonlinear finite element formulation based on invariant-free hyperelasticity for orthotropic materials. International Journal of Solids and Structures, 185, 191-201, 2000.
  • Nguyen, T. D., Huynh, T. T. H., Nguyen, N. T., Nguyen, H. T. M. and Truong, T. T., Finite element analysis for three-dimensional hyper-elastic problems. Science and Technology Development Journal, 24, 43-50, 2022.
  • Schönherr, J. A., Schneider, P. and Mittelstedt, C., Robust hybrid/mixed finite elements for rubber-likematerials under. Computational Mechanics, 70, 101–122, 2022.
  • Onishi, Y. and Amaya, K., A locking-free selective smoothed finite element method using tetrahedral and triangular elements with adaptive mesh rezoning for large deformation problems. International Journal for Numerical Methods in Engineering, 99, 354-371, 2014.
  • Léger, S., Fortin, A., Tibirna, C. and Fortin, M., An updated Lagrangian method with error estimation and adaptive remeshing for very large deformation elasticity problems. International Journal For Numerical Methods in Engineering, 100, 1006–1030, 2014.
  • Ju, X., Mahnken, R., Xu, Y. and Liang, L., Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua. Computational Mechanics, 69, 847-863, 2022.
  • Jansaria, C., Natarajana, S., Beexb, L. and Kannana, K., Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua. Computational Mechanics, 69, 847–863, 2022.
  • Meyer, A., Error estimators and the adaptive finite element method on large strain deformation problems. Mathematical Methods in the Applied Sciences, 32, 2148-2159, 2009.
  • Léger, S. and Pepin, A., An updated Lagrangian method with error estimation and adaptive remeshing for very large deformation elasticity problems: The three-dimensional case. Computer Methods Applied Mechanics and Engineering, 309, 1–18, 2016.
  • Smith, M., ABAQUS/Standard User’s Manual, Version 6.9, Dassault Systemes, Simulia Corp, 2009.
  • Kim, N.H., Introduction to Nonlinear Finite Element Analysis, Springer, 2015.
  • Shabana, A.A. and Niamathullah, S.K., Total Lagrangian Formulation For Large-Displacement Analysis Of The Triangular Finite Elements. Computer Methods in Applied Mechanics And Engineering, 72, 195-199, 1989.
  • Wriggers, P., Nonlinear Finite Element Methods, Springer, 2008.
  • Zienkiewicz, O.C., Zhu, J.Z. and Gong, N.G., Effective and Practical h–p Adaptive Analysis Procedure for the Finite Element Method, International Journal for Numerical Methods in Engineering, 28, 879-891, 1989.

Large Deformation Analysis of Hyperelastic Continuum with Hexahedral Adaptive Finite Elements

Year 2023, Volume: 15 Issue: 4, 163 - 183, 24.12.2023

Mustafa Tekin Bahadır Alyavuz

https://doi.org/10.24107/ijeas.1386832

Abstract

The use of hyperelastic materials capable of large deformations, such as elastomeric bearings used to reduce seismic effects, is quite common in civil engineering. Such environments are, in most cases, addressed by numerical solution techniques such as the finite element method. In case of large deformations, nonlinear analysis is used in the solution. In the study presented here, large deformations of a hyperelastic continuum expressed by the Mooney-Rivlin material model are calculated using hexahedral adaptive finite elements. A code was written in MATLAB using the total Lagrangian formulation for the nonlinear adaptive finite element solution. Comparisons were made with Abaqus software to check the consistency of the results obtained from this program. It has been observed that local refinements in the adaptive element mesh occur in the regions where they are needed. Considering the variation of maximum displacement and maximum stress with the number of elements, it has been observed that mesh refinement creates a convergent solution.

Keywords

Hyperelasticity adaptive finite element method hexahedral elements

References

  • Blacker, T., Automated conformal hexahedral meshing constraints, challenges and opportunities. Engineering with Computers, 17, 201-210, 2002.
  • Tadepalli, S.C., Erdemir, A. and Cavanagh, P.R., Comparison of hexahedral and tetrahedral elements in finite element analysis of the foot and footwear. Journal of Biomechanics, 44, 2337-2343, 2011.
  • Schneiders, R., A grid-based algorithm for the generation of hexahedral element meshes. Engineering with Computers, 12, 168-177, 1996.
  • Eppstein, E., Linear complexity hexahedral mesh generation. Computational Geometry Theory and Applications, 12, 3-16, 1999.
  • Baudouin, T.C., Remacle, J.F., Marchandise, E., Henrotte, F. and Geuzaine, C., A frontal approach to hex-dominant mesh generation. Advanced Modeling and Simulation in Engineering Sciences, 1-8,2014.
  • Staten, M.L., Canann, S.A. and Owen, S.J., BMSweep: Locating interior nodes during sweeping. Engineering with Computers, 15, 212-218, 1999.
  • Lai, M., Benzley, S. and White, D., Automated hexahedral mesh generation by generalized multiple source to multiple target sweeping. International Journal for Numerical Methods in Engineering, 49, 261-275, 2000.
  • Owen, S.J. and Saigal, S., H-Morph: an indirect approach to advancing front hex meshing. International Journal for Numerical Methods in Engineering, 49, 289-312, 2000.
  • Li, T.S., McKeag, R.M. and Armstrong, C.G., Hexahedral meshing using midpoint subdivision and integer programming. Computer Methods in Applied Mechanics and Engineering, 124, 171-193, 1995.
  • Schneiders, R., Refining quadrilateral and hexahedral element meshes, Proceedings of the Fifth International Conference on Numerical Grid Generation in Computational Field Simulations, 679-688, 1996.
  • Harris, N.J., Benzley, S.E. and Owen, S.J., Conformal refinement of all-hexahedral element meshes based on multiple twist plane insertion, Proceedings of the 13th International Meshing Roundtable (IMR), 157–168, 2004.
  • Parrish, M., Borden, M., Staten, M. and Benzley, S., A selective approach to conformal refinement of unstructured hexahedral finite element meshes, Proceedings of the 16th International Meshing Roundtable (IMR), Seattle, USA, 14-17 Oct 2007.
  • Huang, L., Zhao, G., Wang, Z. and Zhang, X., Adaptive hexahedral mesh generation and regeneration using an improve d grid-base d method. Advances in Engineering Software, 102, 49-70, 2016.
  • Huang, L., Zhao, G., Ma, X. and Wang, Z., Incorporating improved refinement techniques for a grid-based geometrically-adaptive hexahedral mesh generation algorithm. Advances in Engineering Software, 64, 20-32, 2013.
  • Tchon, K.F., Khachan, M., Guibault, F. and Camarero, R., Three-dimensional anisotropic geometric metrics based on local domain curvature and thickness. Computer-Aided Design, 37, 173-187, 2005.
  • Zhang, Y. and Bajaj, C., Adaptive and quality quadrilateral/hexahedral meshing from volumetric data. Computer Methods Applied Mechanics and Engineering, 195, 942–960, 2006.
  • Fernandes, J.L.M. and Martins, P.A.F., All-hexahedral remeshing for the finite element analysis of metal forming processes. Finite Elements in Analysis and Design, 43, 666 – 679, 2007.
  • Zhao, G., Zhang, H. and Cheng, L., Geometry-adaptive generation algorithm and boundary match method for initial hexahedral element mesh. Engineering with Computers, 24, 321–339, 2008.
  • Sun, L., Zhao, G. and Ma, X., Adaptive generation and local refinement methods of three-dimensional hexahedral element mesh. Finite Elements in Analysis and Design, 50, 184–200, 2012.
  • Zhu, J. and Zienkiewicz, C., Super convergence recovery technique and a posteriori error estimators. International Journal for Numerical Methods in Engineering, 30, 1321-1339, 1990.
  • Devloo, P. R., A three-dimensional adaptive finite element strategy. Computers and Structures, 38, 121-130, 1991.
  • Zienkiewicz, O.C. and Zhu, J.Z., The superconvergent patch recover (SPR) and adaptive finite element refinement. Computer Methods in Applied Mechanics and Engineering, 101, 207-224, 1992.
  • Wada, Y. and Okuda, H., Effective adaptation technique for hexahedral mesh. Concurrency and Computation: Practice And Experience, 14, 451-463, 2002.
  • Park, C.,H. and Yang, D.Y., Adaptive refinement of all-hexahedral elements for three-dimensional metal forming analysis. Finite Elements in Analysis and Design, 43, 22–35, 2006.
  • Moshfegh, R., Li, X. and Nilsson, L., Gradient-based refinement indicators in adaptive finite element analysis with special reference to sheet metal forming. Engineering Computations, 17, 910-932, 2000.
  • Niekamp, R. and Stein, E., An object-oriented approach for parallel two- and three-dimensional adaptive finite element computations. Computers and Structures, 80, 317–328, 2002.
  • Swanson, S. R., Large deformation finite element calculations for slightly compressible hyperelastic materials. Computers and Structures, 21, 81-88, 1985.
  • Pengt, S. H. and Cbang, W. V., A compressible approach in finite element analysis of rubber-elastic materials. Computers and Structures, 62, 573-593, 1997.
  • Suchocki, C., Finite element implementation of slightly compressible and incompressible first invariant-based hyperelasticity: theory, coding, exemplary problems. Journal of Theoretical and Applied Mechanics, 55, 787-800, 2017.
  • Herrmann, L. R., Elasticity equations for incompressible and nearly incompressible materials by a variational theorem. American Institute of Aeronautics and Astronautics (AIAA) Journal, 3, 1896-1900, 1965.
  • Bonet, J. and Bhargava, P., A uniform deformation gradient hexahedron element with artificial hourglass control. International Journal For Numerical Methods in Engineering, 38, 2809-2828, 1995.
  • Neto, E. A. S., Peril D., Dutko M. and Owen D. R. J., Design of simple low order finite elements for large strain analysis of nearly incompressible solids. International Journal of Solids and Structures, 33, 3211-3296, 1996.
  • Pascon, J. P., Large deformation analysis of plane‑stress hyperelastic problems via triangular membrane finite elements. International Journal of Advanced Structural Engineering, 11, 331–350, 2019.
  • Medri, G. and Strozzl, A., Mechanical analysis of elastomeric seals by numerical methods. Industrial and Engineering Chemistry Product Research and Development, 23, 596-600, 1984.
  • Kato, K., Lee, N.S. and Bathe K.J., Adaptive finite element analysis of large strain elastic response. Computers and Structures, 47, 829-855, 1993.
  • Chamberland, E., Fortin, A. and Fortin, M., Comparison of the performance of some finite element discretizations for large deformation elasticity problems. Computers and Structures, 88, 664–673, 2010.
  • O’Shea, D. J., Attard, M. M., Kellermann, D.C. and Sansour, C., Nonlinear finite element formulation based on invariant-free hyperelasticity for orthotropic materials. International Journal of Solids and Structures, 185, 191-201, 2000.
  • Nguyen, T. D., Huynh, T. T. H., Nguyen, N. T., Nguyen, H. T. M. and Truong, T. T., Finite element analysis for three-dimensional hyper-elastic problems. Science and Technology Development Journal, 24, 43-50, 2022.
  • Schönherr, J. A., Schneider, P. and Mittelstedt, C., Robust hybrid/mixed finite elements for rubber-likematerials under. Computational Mechanics, 70, 101–122, 2022.
  • Onishi, Y. and Amaya, K., A locking-free selective smoothed finite element method using tetrahedral and triangular elements with adaptive mesh rezoning for large deformation problems. International Journal for Numerical Methods in Engineering, 99, 354-371, 2014.
  • Léger, S., Fortin, A., Tibirna, C. and Fortin, M., An updated Lagrangian method with error estimation and adaptive remeshing for very large deformation elasticity problems. International Journal For Numerical Methods in Engineering, 100, 1006–1030, 2014.
  • Ju, X., Mahnken, R., Xu, Y. and Liang, L., Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua. Computational Mechanics, 69, 847-863, 2022.
  • Jansaria, C., Natarajana, S., Beexb, L. and Kannana, K., Goal-oriented error estimation and h-adaptive finite elements for hyperelastic micromorphic continua. Computational Mechanics, 69, 847–863, 2022.
  • Meyer, A., Error estimators and the adaptive finite element method on large strain deformation problems. Mathematical Methods in the Applied Sciences, 32, 2148-2159, 2009.
  • Léger, S. and Pepin, A., An updated Lagrangian method with error estimation and adaptive remeshing for very large deformation elasticity problems: The three-dimensional case. Computer Methods Applied Mechanics and Engineering, 309, 1–18, 2016.
  • Smith, M., ABAQUS/Standard User’s Manual, Version 6.9, Dassault Systemes, Simulia Corp, 2009.
  • Kim, N.H., Introduction to Nonlinear Finite Element Analysis, Springer, 2015.
  • Shabana, A.A. and Niamathullah, S.K., Total Lagrangian Formulation For Large-Displacement Analysis Of The Triangular Finite Elements. Computer Methods in Applied Mechanics And Engineering, 72, 195-199, 1989.
  • Wriggers, P., Nonlinear Finite Element Methods, Springer, 2008.
  • Zienkiewicz, O.C., Zhu, J.Z. and Gong, N.G., Effective and Practical h–p Adaptive Analysis Procedure for the Finite Element Method, International Journal for Numerical Methods in Engineering, 28, 879-891, 1989.
There are 50 citations in total.

Details

Primary Language English
Subjects Numerical Modelization in Civil Engineering
Journal Section Articles
Authors

Mustafa Tekin 0000-0003-2130-6407

Bahadır Alyavuz 0000-0003-4643-4368

Publication Date December 24, 2023
Submission Date November 6, 2023
Acceptance Date December 23, 2023
Published in Issue Year 2023 Volume: 15 Issue: 4

Cite

APA Tekin, M., & Alyavuz, B. (2023). Large Deformation Analysis of Hyperelastic Continuum with Hexahedral Adaptive Finite Elements. International Journal of Engineering and Applied Sciences, 15(4), 163-183. https://doi.org/10.24107/ijeas.1386832
AMA Tekin M, Alyavuz B. Large Deformation Analysis of Hyperelastic Continuum with Hexahedral Adaptive Finite Elements. IJEAS. December 2023;15(4):163-183. doi:10.24107/ijeas.1386832
Chicago Tekin, Mustafa, and Bahadır Alyavuz. “Large Deformation Analysis of Hyperelastic Continuum With Hexahedral Adaptive Finite Elements”. International Journal of Engineering and Applied Sciences 15, no. 4 (December 2023): 163-83. https://doi.org/10.24107/ijeas.1386832.
EndNote Tekin M, Alyavuz B (December 1, 2023) Large Deformation Analysis of Hyperelastic Continuum with Hexahedral Adaptive Finite Elements. International Journal of Engineering and Applied Sciences 15 4 163–183.
IEEE M. Tekin and B. Alyavuz, “Large Deformation Analysis of Hyperelastic Continuum with Hexahedral Adaptive Finite Elements”, IJEAS, vol. 15, no. 4, pp. 163–183, 2023, doi: 10.24107/ijeas.1386832.
ISNAD Tekin, Mustafa - Alyavuz, Bahadır. “Large Deformation Analysis of Hyperelastic Continuum With Hexahedral Adaptive Finite Elements”. International Journal of Engineering and Applied Sciences 15/4 (December 2023), 163-183. https://doi.org/10.24107/ijeas.1386832.
JAMA Tekin M, Alyavuz B. Large Deformation Analysis of Hyperelastic Continuum with Hexahedral Adaptive Finite Elements. IJEAS. 2023;15:163–183.
MLA Tekin, Mustafa and Bahadır Alyavuz. “Large Deformation Analysis of Hyperelastic Continuum With Hexahedral Adaptive Finite Elements”. International Journal of Engineering and Applied Sciences, vol. 15, no. 4, 2023, pp. 163-8, doi:10.24107/ijeas.1386832.
Vancouver Tekin M, Alyavuz B. Large Deformation Analysis of Hyperelastic Continuum with Hexahedral Adaptive Finite Elements. IJEAS. 2023;15(4):163-8.
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