Topology optimization of degradable composite structures with time‐changeable stiffness
For effective bone healing, the stiffness of the bone plate should be adjusted to different bone‐healing processes. Thus, the design of stiffness‐changeable structures that take into account the time effect is of importance. To this end, this study introduces a novel topological optimization approac...
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| Published in | International journal for numerical methods in engineering Vol. 122; no. 17; pp. 4751 - 4773 |
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| Main Authors | , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Hoboken, USA
John Wiley & Sons, Inc
15.09.2021
Wiley Subscription Services, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0029-5981 1097-0207 |
| DOI | 10.1002/nme.6745 |
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| Abstract | For effective bone healing, the stiffness of the bone plate should be adjusted to different bone‐healing processes. Thus, the design of stiffness‐changeable structures that take into account the time effect is of importance. To this end, this study introduces a novel topological optimization approach for the composite structural layout design considering material degradation to realize structures with changeable stiffness over time. In this approach, two sets of variables are used: a density field that defines the material layout, and a time field that determines the effect of material degradation on mechanical performance. The continuous degradation update formula is proposed by integrating the Heaviside projected function and Kreisselmeier–Steinhauser function to guarantee its derivability. The objective is to minimize the summed compliance in some specified time steps subject to the constraints of volume fraction. The sensitivity of the aforementioned objective with respect to the design variable is deduced by considering the material degradation over time. The proposed design formulation is general and is demonstrated with several design analyses, considering different fix and degradable interface boundary conditions. Moreover, the results are compared with the results of not considering material degradation and demonstrate the effectiveness of the proposed method. |
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| AbstractList | For effective bone healing, the stiffness of the bone plate should be adjusted to different bone‐healing processes. Thus, the design of stiffness‐changeable structures that take into account the time effect is of importance. To this end, this study introduces a novel topological optimization approach for the composite structural layout design considering material degradation to realize structures with changeable stiffness over time. In this approach, two sets of variables are used: a density field that defines the material layout, and a time field that determines the effect of material degradation on mechanical performance. The continuous degradation update formula is proposed by integrating the Heaviside projected function and Kreisselmeier–Steinhauser function to guarantee its derivability. The objective is to minimize the summed compliance in some specified time steps subject to the constraints of volume fraction. The sensitivity of the aforementioned objective with respect to the design variable is deduced by considering the material degradation over time. The proposed design formulation is general and is demonstrated with several design analyses, considering different fix and degradable interface boundary conditions. Moreover, the results are compared with the results of not considering material degradation and demonstrate the effectiveness of the proposed method. |
| Author | Guo, Honghu Xu, Shipeng Takezawa, Akihiro Zhang, Heng Ding, Xiaohong Li, Hao |
| Author_xml | – sequence: 1 givenname: Heng orcidid: 0000-0001-5039-6865 surname: Zhang fullname: Zhang, Heng organization: Waseda University – sequence: 2 givenname: Akihiro orcidid: 0000-0001-8197-4306 surname: Takezawa fullname: Takezawa, Akihiro email: atakezawa@waseda.jp organization: Waseda University – sequence: 3 givenname: Xiaohong surname: Ding fullname: Ding, Xiaohong organization: University of Shanghai for Science and Technology – sequence: 4 givenname: Shipeng surname: Xu fullname: Xu, Shipeng organization: University of Shanghai for Science and Technology – sequence: 5 givenname: Hao orcidid: 0000-0003-4316-1253 surname: Li fullname: Li, Hao organization: Kyoto University – sequence: 6 givenname: Honghu surname: Guo fullname: Guo, Honghu organization: Waseda University |
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| Cites_doi | 10.1016/j.cma.2019.112702 10.1007/s001580050176 10.1680/jemmr.18.00048 10.1007/s00158-015-1370-5 10.1016/j.cma.2020.112886 10.1007/s00158-019-02420-6 10.1016/j.cma.2014.11.012 10.1016/j.actbio.2010.02.028 10.1016/j.mechmachtheory.2019.103622 10.1016/j.compstruct.2014.07.052 10.1155/2015/729076 10.1016/j.mser.2014.01.001 10.1016/j.actbio.2013.12.059 10.1002/nme.116 10.1002/nme.1620240207 10.1007/s10534-019-00170-y 10.1002/nme.5828 10.1007/978-3-662-05086-6 10.1016/j.actbio.2009.10.006 10.1016/j.msec.2009.03.003 10.1016/j.biomaterials.2013.07.010 10.1007/s00158-016-1495-1 10.1007/s004190050248 10.1016/j.cma.2010.05.013 10.1002/nme.6616 10.1016/j.cma.2008.10.008 10.1002/advs.201902443 10.1016/0168-874X(95)00043-S 10.1016/j.finel.2017.12.003 10.1016/j.finel.2016.09.006 10.1016/j.actbio.2011.05.032 10.1007/s00158-010-0594-7 10.1016/j.compstruct.2019.01.059 10.1016/j.applthermaleng.2016.10.134 10.1016/S0045-7825(02)00559-5 10.1016/0045-7949(95)00235-9 10.1016/j.finel.2007.06.006 10.1016/j.mattod.2018.05.018 10.1016/j.jcp.2003.09.032 10.1007/s00158-013-0978-6 10.1016/j.biomaterials.2016.10.017 10.1007/978-3-662-03115-5 10.1016/j.microc.2016.02.005 |
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| SubjectTerms | biodegradable materials Boundary conditions Composite structures Healing Layouts Mechanical properties Performance degradation Stiffness time‐changeable stiffness Topology optimization |
| Title | Topology optimization of degradable composite structures with time‐changeable stiffness |
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