EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 29 (2023) ESAIM: COCV, 29 (2023) 24 References
Open Access
Issue
ESAIM: COCV
Volume 29, 2023
Article Number 24
Number of page(s) 46
DOI https://doi.org/10.1051/cocv/2023012
Published online 30 March 2023
  1. S.A. Abdullah, A. Jumahat, N.R. Abdullah and L. Frormann, Setermination of shape fixity and shape recovery rate of carbon nanotube-flled shape memory polymer nanocomposites. Procedia Eng. 41 (2012) 1641–1646. [CrossRef] [Google Scholar]
  2. M.H. Ali, A. Abilgaziyev and D. Adair, 4D printing: a critical review of current developments, and future prospects. Int. J. Adv. Mrnuf. Technol. 104 (2019) 701–717. [CrossRef] [Google Scholar]
  3. G. Allaire and B. Bogosel, Optimizing supports for additive manufacturing. Struct. Multidiscip. Optim. 58 (2018) 2493–2515. [CrossRef] [MathSciNet] [Google Scholar]
  4. S. Almi and U. Stefanelli, Topology optimization for incremental elastoplasticity: a phase-field approach. SIAM J. Control Optim. 59 (2021) 339–364. [CrossRef] [MathSciNet] [Google Scholar]
  5. H.W. Alt, Linear Functional Analysis, an Application Oriented Introduction. Springer, London, (2016). [CrossRef] [Google Scholar]
  6. P.R. Amestoy, T.A. Davis and I.S. Duff, Algorithm 837: AMD, an approximate minimum degree ordering algorithm. ACM Trans. Math. Softw. 30 (2004) 381–388. [CrossRef] [Google Scholar]
  7. S.E. Bakarich, E. Gorkin and G.M. Spinks, 4D printing with mechanically robust, thermally actuating hydrogels. Macromol. Rapid Commun. 36 (2015) 1211–1217. [CrossRef] [Google Scholar]
  8. S. Baldo, Minimal interface criterion for phase transitions in mixtures of Cahn–Hilliard fluids. Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990) 67–90. [CrossRef] [MathSciNet] [Google Scholar]
  9. L. Banas and R. Nurnberg, Finite element approximation of a three dimensional phase field model for void electromigration. J. Sci. Comp. 37 (2008) 202–232. [CrossRef] [Google Scholar]
  10. J.W. Barrett, R. Nürnberg and V. Styles, Finite element approximation of a phase field model for void electromigration. SIAM J. Numer. Anal. 42 (2004) 738–772. [CrossRef] [MathSciNet] [Google Scholar]
  11. G. Bellettini, A. Braides and G. Riey, Variational approximation of anisotropic functionals on partitions. Ann. Matemat. 184 (2005) 75–93. [CrossRef] [Google Scholar]
  12. A. Bhattacharyya and K.A. James, Topology optimization of shape memory polymers structures with programmable morphology. Struct. Multidiscip. Optim. 63 (2021) 1863–1887. [CrossRef] [Google Scholar]
  13. L. Blank, H. Garcke, M. Hassan Farshbaf-Shaker and V. Styles, Relating phase field and sharp interface approaches to structural topology optimization. ESAIM: COCV 20 (2014) 1025–1058. [CrossRef] [EDP Sciences] [Google Scholar]
  14. L. Blank, H. Garcke, C. Hecht and C. Rupprecht, Sharp interface limit for a phase field model in structural optimization. SIAM J. Control Optim. 54 (2016) 1558–1584. [CrossRef] [MathSciNet] [Google Scholar]
  15. L. Blank, H. Garcke, L. Sarbu, T. Srisupattarawanit, V. Styles and A. Voigt, Phase-field approaches to structural topology optimization, in Constrained optimization and optimal control for partial differential equations, vol. 160 of Internat. Ser. Numer. Math., Birkhäuser/Springer Basel AG, Basel (2012), pp. 245–256. [CrossRef] [Google Scholar]
  16. J.F. Blowey and C.M. Elliott, Curvature dependent phase boundary motion and parabolic double obstacle problems, in Degenerate diffusions (Minneapolis, MN, 1991), vol. 47 of IMA Vol. Math. Appl., Springer, New York (1993) pp. 19–60. [Google Scholar]
  17. B. Bourdin and A. Chambolle, Design-dependent loads in topology optimization. ESAIM: COCV 9 (2003) 19–48. [CrossRef] [EDP Sciences] [Google Scholar]
  18. L. Bronsard, H. Garcke and B. Stoth, A multi-phase Mullins-Sekerka system: matched asymptotic expansions and an implicit time discretization for the geometric evolution problem. SIAM J. Appl. Math. 60 (1999) 295–315. [CrossRef] [Google Scholar]
  19. M. Burger and R. Stainko, Phase-field relaxation of topology optimization with local stress constraints. SIAM J. Control Optim. 45 (2006) 1447–1466. [CrossRef] [MathSciNet] [Google Scholar]
  20. S. Cacace, E. Cristiani and L. Rocchi, A level set based method for fixing overhangs in 3D printing. Appl. Math. Model. 44 (2017) 446–455. [CrossRef] [MathSciNet] [Google Scholar]
  21. M. Carraturo, E. Rocca, E. Bonetti, D. Hömberg, A. Reali and F. Auricchio, Graded-material design based phase-field and topology optimization. Comput. Mech. 64 (2019) 1589–1600. [CrossRef] [MathSciNet] [Google Scholar]
  22. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland Publishing Co., Amsterdam (1978), [Google Scholar]
  23. T.A. Davis, Algorithm 849: a concise sparse Cholesky factorization package. ACM Trans. Math. Software 31 (2005) 587–591. [CrossRef] [MathSciNet] [Google Scholar]
  24. Z. Ding, C. Yuan, X. Peng, T. Wang, JH.J. Qi and M.L. Dunn, Direct 4D printing via active composite materials. Sci. Adv. 3 (2017) e1602890. [CrossRef] [Google Scholar]
  25. P.C. Fife and O. Penrose, Interfacial dynamics for thermodynamically consistent phase-field models with nonconserved order parameter. J. Differ. Equ. 16 (1995) 1–49. [Google Scholar]
  26. H. Garcke, The Γ-limit of the Ginzburg–Landau energy in an elastic medium. AMSA 18 (2008) 345–379. [Google Scholar]
  27. H. Garcke and C. Hecht, Apply a phase field approach for shape optimization of a stationary Navier-Stokes flow. ESAIM: COCV 22 (2016) 309–337. [CrossRef] [EDP Sciences] [Google Scholar]
  28. H. Garcke and C. Hecht, Shape and topology optimization in Stokes flow with a phase field approach. Appl. Math. Optim. 73 (2016) 23–70. [CrossRef] [MathSciNet] [Google Scholar]
  29. H. Garcke, C. Hecht, M. Hinze, C. Kahle and K.F. Lam, Shape optimization for surface functionals in Navier–Stokes flow using a phase field approach. Interfaces Free Bound. 18 (2016) 219–261. [CrossRef] [MathSciNet] [Google Scholar]
  30. H. Garcke, P. Hüttl and P. Knopf, Shape and topology optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach. Adv. Nonlinear Anal. 11 (2022) 159–197. [Google Scholar]
  31. H. Garcke, K.F. Lam, R. Nurnberg and A. Signori, Overhang penalization in additive manufacturing via phase field structural topology optimization with anisotropic energies. Appl. Math. Optim. 87 (2023) 44. [CrossRef] [MathSciNet] [Google Scholar]
  32. H. Garcke, B. Nestler and B. Stoth, On anisotropic order parameter models for multi0phase systems and their sharp interface limits. Phys. D 115 (1998) 87–108. [CrossRef] [MathSciNet] [Google Scholar]
  33. H. Garcke and B. Stinner, Second order phase field asymptotics for multi-component systems. Interfaces Free Bound. 8 (2006) 131–157. [CrossRef] [MathSciNet] [Google Scholar]
  34. Q. Ge, C.K. Dunn, H.J. Qi and M.L. Dunn, Active origami by 4D printing. Smart Mater. Struct. 23 (2014) 094007. [CrossRef] [Google Scholar]
  35. Q. Ge, H.J. Qi and M.L. Dunn, Active materials by four-dimension printing. Appl. Phys. Lett. 103 (2013) 131901. [CrossRef] [Google Scholar]
  36. Q. Ge, A.H. Sakhaei, H. Lee, C.K. Dunn, N.X. Fang and M.L. Dunn, Multimaterial 4D printing with tailorable shape memory polymers. Sci. Rep. 6 (2016) 31110. [CrossRef] [Google Scholar]
  37. M.J. Geiss, N. Boddeti, O. Weeger, K. Maute and M.L. Dunn, Combined level-set-XFEM-density topology optimization of four-dimensional printed structures undergoing large deformation. J. Mech. Des. 141 (2019) 051405. [CrossRef] [Google Scholar]
  38. C. Hecht, Shape and topology optimization in fluids using a phase field approach an application in structural optimization. Ph.D. thesis. University of Regensburg, Regensburg, Germany (2014). https://epub.uni-regensburg.de/29869/1/Dissertation_ClaudiaHecht.pdf [Google Scholar]
  39. M. Howard, J. Pajot, K. Maute and M.L. Dunn, A computational design methodology for assembly and actuation of thin-film structures via patterning of eigenstrains. J. Microelectromech. Syst. 18 (2009) 1137–1148. [CrossRef] [Google Scholar]
  40. J. Jiang, X. Xu and J. Stringer, Support structures for additive manufacturing: a review. J. Mauf. Mater. Process. 2 (2008) 64 (23 pages). [Google Scholar]
  41. R. Kornhuber, Monotone multigrid methods for elliptic variational inequalities II. Numer. Math. 72 (1996) 481–499. [CrossRef] [MathSciNet] [Google Scholar]
  42. O. Kuksenok and A.C. Balazs, Stimuli-responsive behavior of composites integating thermo-responsive gels with photo- responsive fibers. Mater. Horizons 3 (2016) 53–62. [CrossRef] [Google Scholar]
  43. M. Langelaar, Combined optimization of part topology, support structure layout and build orientation for additive manufacturing. Struct. Multidiscip. Optim. 57 (2018) 1985–2004. [CrossRef] [MathSciNet] [Google Scholar]
  44. M. Leray, L. Merli, F. Torti, M. Mazur and M. Bandt, Optimal topology for additive manufacturing: a method for enabling additive manufacture of support-free optimal structures. Mater. Des. 63 (2014) 678–690. [CrossRef] [Google Scholar]
  45. H. Li, X. Gao and Y. Luo, Multi-shape memory polymers achieved by the spatio-assembly of 3D printable thermoplastic building blocks. Soft Matter 12 (2016) 3226–3233. [CrossRef] [PubMed] [Google Scholar]
  46. J.L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications. Springer (1972). [Google Scholar]
  47. J. Liu, A.T. Gaynor, S. Chen, Z. Kang, K. Suresh, A. Takezawa, L. Li, J. Kato, J. Tang, C.C.L. Wang, L. Cheng, X. Liang and A.C. To, Current and future trends in topology optimization for additive manufacturing. Struct. Multi. Optim. 57 (2018) 2457–2483. [CrossRef] [Google Scholar]
  48. J. Liu and H. Yu, Self-supporting topology optimization with horizontal overhangs for additive manufacturing. J. Manuf. Sci. Eng. 142 (2020) 091003 (14 pages). [CrossRef] [Google Scholar]
  49. T.S. Lumpe and K. Shea, Computational design of 3D-printed active lattice structures for reversible shape morphing. J. Mater. Res. 36 (2021) 3642–3655. [CrossRef] [Google Scholar]
  50. K. Maute, A. Tkachuk, J. Wu, H.J. Qi, Z. Ding and M.L. Dunn, Level set topology optimization of printed active composites. J. Mech. Des. 137 (2015) 111402 (13 pages). [CrossRef] [Google Scholar]
  51. A.M. Mirzendehdel and K. Suresh, Support structure constrained topology optimization for additive manufacturing. Comput. Aided Des. 1 (2016) 1–13. [CrossRef] [Google Scholar]
  52. F. Momeni, S.M. Hassani, N.X. Liu and J. Ni, A review of 4D printing. Mater. Des. 122 (2017) 42–79. [CrossRef] [Google Scholar]
  53. N.C. Owen, J. Rubinstein, and P. Sternberg, Minimizers and gradient flows for singularly perturbed bi-stable potentials with a Dirichlet condition. Proc. R. Soc. Lond. A 429 (1990) 505–532. [CrossRef] [Google Scholar]
  54. J.M. Pajot, K. Maute, Y. Zhang and M.L. Dunn, Design of patterned multilayer films with eigenstrains by topology optimization. Int. J. Solids Struct. 43 (2006) 1832–1853. [CrossRef] [Google Scholar]
  55. P. Penzler, M. Rumpf and B. Wirth, A phase-field model for compliance shape optimization in nonlinear elasticity. ESAIM: COCV 18 (2012) 229–258. [CrossRef] [EDP Sciences] [Google Scholar]
  56. A. Schmidt and K.G. Siebert, Design of adaptive finite element software: the finite element toolbox ALBERTA. vol. 42 of Lecture Notes in Computational Science and Engineering, Springer-Verlag, Berlin (2005). [Google Scholar]
  57. J. Sokolowski and J.-P. Zolesio. Introduction to Shape Optimization. Springer series in computational mathematics, Vol. 16, Springer-Verlag, Berlin Heidelberg (1991). [Google Scholar]
  58. L. Sun and W.M. Huang, Mechanisms of the multi-shape memory effect and temperature memory effect in shape memory polymers. Soft Matter 6 (2010) 4403–4406. [CrossRef] [Google Scholar]
  59. Y. Sun, W. Ouyang, Z. Liu, N. Ni, Y. Savoye, P. Song and L. Liu, Computational design of self-actuated deformable solids via shape memory material. IEEE Trans. Vis. Comput. Graph. 28 (2022) 2577–2588. [CrossRef] [PubMed] [Google Scholar]
  60. A. Takezawa, S. Nishiwaki and M. Kitamura, Shape and topology optimization based on the phase field method and sensitivity analysis. J. Comput. Phys. 229 (2010) 2697–2718. [CrossRef] [MathSciNet] [Google Scholar]
  61. S. Tibbits, 4D printing: Multi-material shape change. Archit. Des. 84 (2014) 116–121. [Google Scholar]
  62. X. Wan, Y. He, Y. Liu and J. Leng, 4D printing of multiple shape memory polymer and nanocomposites with biocompatible programmable and selectively actuated properties. Addit. Manuf. 53 (2022) 102689. [Google Scholar]
  63. M.Y. Wang and S. Zhou, Phase field: a variational method for structural topology optimization. CMES Comput. Model. Eng. Sci. 6 (2004) 547–566. [MathSciNet] [Google Scholar]
  64. G. Wang, H. Yang, Z. Yan, N.G. Ulu, Y. Tao, J. Gu, L.B. Kara and L. Yao, 4DMesh: 4d printing morphing non- developable mesh surfaces, in the 31st Annual ACM Symposium on User Interface Software and Technology (2018) 623–635. [CrossRef] [Google Scholar]
  65. Y. Wei, P. Huang, Z. Li, P. Wang and X. Feng, Design of active materials distributions for four-dimensional printing based on multi-material topology optimization. Smart Mater. Struct. 30 (2021) 095002. [CrossRef] [Google Scholar]
  66. J. Wu, C. Yuan, Z. Ding, M. Isakov, Y. Mao, T. Wang, M.L. Dunn and H.J. Qi, Multi-shape active composites by 3D printing of digital shape memory polymers. Sci. Rep. 6 (2016) 24224. [CrossRef] [Google Scholar]
  67. C. Yuan, T. Lu and T.J. Wang, Mechanics-based design strategies for 4D printing: a review. Forces Mech. 7 (2022) 100081. [CrossRef] [Google Scholar]
  68. Q. Zhang, K. Zhang and G. Hu, Smart three-dimensional lightweight structure triggered from a thin composite sheet via 3D printing technique. Sci. Rep. 6 (2016) 22431. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.