A topology optimization method for hyperelastic porous structures subject to large deformation
Porous infill, rather than the solids, can provide high stiffness-to-weight ratio, energy absorption, thermal insulation, and many other outstanding properties. However, porous structure design to date have been majorly performed with topology optimization under small deformation assumption. The eff...
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| Published in | International journal of mechanics and materials in design Vol. 18; no. 2; pp. 289 - 308 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Dordrecht
Springer Netherlands
01.06.2022
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1569-1713 1573-8841 |
| DOI | 10.1007/s10999-021-09576-4 |
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| Abstract | Porous infill, rather than the solids, can provide high stiffness-to-weight ratio, energy absorption, thermal insulation, and many other outstanding properties. However, porous structure design to date have been majorly performed with topology optimization under small deformation assumption. The effect of porosity control under large deformation is not explored yet. Hence, this paper exploits the topological design method of porous infill structures under large deformational configuration. Specifically, the neo-Hookean hyperelasticity model is adopted to simulate the large structural deformation, and the adjoint sensitivity analysis is performed accordingly with the governing equation and constraint. The maximum local volume fractions before and after deformation are concurrently constrained and especially for the latter, the representative volume points (RVPs) are modeled and tracked for evaluating the local volume fractions subject to the distorted mesh configuration. The local volume constraints are then aggregated with the P-norm method for a global expression. Iterative corrections are made to the P-norm function to rigorously restrict the upper bound of the maximum local volume. Finally, several benchmark cases are investigated, which validate the effectiveness of the proposed method. |
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| AbstractList | Porous infill, rather than the solids, can provide high stiffness-to-weight ratio, energy absorption, thermal insulation, and many other outstanding properties. However, porous structure design to date have been majorly performed with topology optimization under small deformation assumption. The effect of porosity control under large deformation is not explored yet. Hence, this paper exploits the topological design method of porous infill structures under large deformational configuration. Specifically, the neo-Hookean hyperelasticity model is adopted to simulate the large structural deformation, and the adjoint sensitivity analysis is performed accordingly with the governing equation and constraint. The maximum local volume fractions before and after deformation are concurrently constrained and especially for the latter, the representative volume points (RVPs) are modeled and tracked for evaluating the local volume fractions subject to the distorted mesh configuration. The local volume constraints are then aggregated with the P-norm method for a global expression. Iterative corrections are made to the P-norm function to rigorously restrict the upper bound of the maximum local volume. Finally, several benchmark cases are investigated, which validate the effectiveness of the proposed method. |
| Author | Liu, Jikai Ma, Yongsheng Huang, Jiaqi Xu, Shuzhi |
| Author_xml | – sequence: 1 givenname: Jiaqi surname: Huang fullname: Huang, Jiaqi organization: Center for Advanced Jet Engineering Technologies (CaJET), Key Laboratory of High Efficiency and Clean Mechanical Manufacture (Ministry of Education), School of Mechanical Engineering, Shandong University – sequence: 2 givenname: Shuzhi surname: Xu fullname: Xu, Shuzhi organization: Department of Mechanical Engineering, University of Alberta – sequence: 3 givenname: Yongsheng surname: Ma fullname: Ma, Yongsheng organization: Department of Mechanical Engineering, University of Alberta – sequence: 4 givenname: Jikai surname: Liu fullname: Liu, Jikai email: jikai_liu@sdu.edu.cn organization: Center for Advanced Jet Engineering Technologies (CaJET), Key Laboratory of High Efficiency and Clean Mechanical Manufacture (Ministry of Education), School of Mechanical Engineering, Shandong University, Key National Demonstration Center for Experimental Mechanical Engineering Education, Shandong University |
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| Keywords | Topology optimization Porous infill Hyperelastic material Nonlinear analysis SIMP |
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| SubjectTerms | Characterization and Evaluation of Materials Classical Mechanics Configurations Constraints Deformation effects Energy absorption Engineering Engineering Design Finite element method Iterative methods Sensitivity analysis Solid Mechanics Stiffness Thermal insulation Topology optimization Upper bounds |
| Title | A topology optimization method for hyperelastic porous structures subject to large deformation |
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