Editing Topology optimization (section)

=== Internal contact ===
[[File:3D Topology Optimization with Internal Contact.webm|thumb|3D Topology Optimization with Internal Contact for a hook mechanism.]]
[[File:Topology optimization of contact problem problem with the third medium approach..gif|thumb|Design development and deformation of self-engaging hooks resulting from topology optimization of a contact problem using the TMC method <ref name=":0" />.]]
Internal contact can be included in topology optimization by applying the [[third medium contact method]].<ref>{{Cite journal |last1=Wriggers |first1=P. |last2=Schröder |first2=J. |last3=Schwarz |first3=A. |date=2013-03-30 |title=A finite element method for contact using a third medium |url=http://dx.doi.org/10.1007/s00466-013-0848-5 |journal=Computational Mechanics |volume=52 |issue=4 |pages=837–847 |doi=10.1007/s00466-013-0848-5 |bibcode=2013CompM..52..837W |s2cid=254032357 |issn=0178-7675}}</ref><ref>{{Cite journal |last1=Frederiksen |first1=Andreas H. |last2=Rokoš |first2=Ondřej |last3=Poulios |first3=Konstantinos |last4=Sigmund |first4=Ole |last5=Geers |first5=Marc G. D. |date=2024-12-01 |title=Adding friction to Third Medium Contact: A crystal plasticity inspired approach |journal=Computer Methods in Applied Mechanics and Engineering |volume=432 |pages=117412 |doi=10.1016/j.cma.2024.117412 |issn=0045-7825|doi-access=free |bibcode=2024CMAME.43217412F }}</ref> The third medium contact (TMC) method is an implicit contact formulation that is continuous and differentiable. This makes TMC suitable for use with gradient-based approaches to topology optimization. Monolithic<ref>{{Cite journal |last1=Bluhm |first1=Gore Lukas |last2=Sigmund |first2=Ole |last3=Poulios |first3=Konstantinos |date=2021-03-04 |title=Internal contact modeling for finite strain topology optimization |url=http://dx.doi.org/10.1007/s00466-021-01974-x |journal=Computational Mechanics |volume=67 |issue=4 |pages=1099–1114 |arxiv=2010.14277 |bibcode=2021CompM..67.1099B |doi=10.1007/s00466-021-01974-x |issn=0178-7675 |s2cid=225076340}}</ref> as well as staggerede approaches,<ref name=":0">{{Cite journal |last1=Frederiksen |first1=Andreas Henrik |last2=Sigmund |first2=Ole |last3=Poulios |first3=Konstantinos |date=2023-10-07 |title=Topology optimization of self-contacting structures |url=https://doi.org/10.1007/s00466-023-02396-7 |journal=Computational Mechanics |language=en |volume=73 |issue=4 |pages=967–981 |arxiv=2305.06750 |bibcode=2023CompM..73..967F |doi=10.1007/s00466-023-02396-7 |issn=1432-0924}}</ref><ref>{{Cite journal |last1=Frederiksen |first1=Andreas H. |last2=Dalklint |first2=Anna |last3=Sigmund |first3=Ole |last4=Poulios |first4=Konstantinos |date=2025-03-01 |title=Improved third medium formulation for 3D topology optimization with contact |journal=Computer Methods in Applied Mechanics and Engineering |volume=436 |pages=117595 |doi=10.1016/j.cma.2024.117595 |issn=0045-7825|doi-access=free |bibcode=2025CMAME.43617595F }}</ref> which are more common in topology optimization, have been used to create various design with internal contact. Recently, thermal contact has been included in the TMC topology optmization framework. <ref>{{Cite journal |last1=Dalklint |first1=Anna |last2=Alexandersen |first2=Joe |last3=Frederiksen |first3=Andreas Henrik |last4=Poulios |first4=Konstantinos |last5=Sigmund |first5=Ole |date=2025 |title=Topology Optimization of Contact-Aided Thermo-Mechanical Regulators |url=https://onlinelibrary.wiley.com/doi/full/10.1002/nme.7661 |journal=International Journal for Numerical Methods in Engineering |language=en |volume=126 |issue=2 |pages=e7661 |doi=10.1002/nme.7661 |issn=1097-0207|arxiv=2406.00865 }}</ref>