A topology optimization method for hyperelastic porous structures subject to large deformation
Source abstract
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.
Source: expertdata · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Topology Optimization in Engineering · Composite Structure Analysis and Optimization · Composite Material Mechanics
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (50)
Show source-provided references
1. Andreassen, E., Lazarov, B., Sigmund, O.: Design of manufacturable 3D extremal elastic microstructure. Mech. Mater. (2014). https://doi.org/10.1016/J.MECHMAT.2013.09.01810.1016/J.MECHMAT.2013.09.018 ↗
2. Behrou, R., Ghanem, M.A., Macnider, B.C., Verma, V., Alvey, R., Hong, J., Emery, A.F., Kim, H.A., Boechler, N.: Topology optimization of nonlinear periodically microstructured materials for tailored homogenized constitutive properties. Compos. Struct. 266, 113729 (2021). https://doi.org/10.1016/j.compstruct.2021.11372910.1016/j.compstruct.2021.113729 ↗
3. Belytschko, T., Liu, W.K., Moran, B., Elkhodary, K.I.: Nonlinear finite elements for continua and structures. Wiley, Chichester, West Sussex, United Kingdon (2014)
4. Bendsøe, M.P., Kikuchi, N.: Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Eng. 71, 197–224 (1988). https://doi.org/10.1016/0045-7825(88)90086-210.1016/0045-7825(88)90086-2 ↗
5. Bruns, T.E., Tortorelli, D.A.: An element removal and reintroduction strategy for the topology optimization of structures and compliant mechanisms. Int. J. Numer. Meth. Engng. 57, 1413–1430 (2003). https://doi.org/10.1002/nme.78310.1002/nme.783 ↗
6. Buhl, T., Pedersen, C.B.W., Sigmund, O.: Stiffness design of geometrically nonlinear structures using topology optimization. Struct Multidisc Optim. 19, 93–104 (2000). https://doi.org/10.1007/s00158005008910.1007/s001580050089 ↗
7. Chen, F., Wang, Y., Wang, M.Y., Zhang, Y.F.: Topology optimization of hyperelastic structures using a level set method. J. Comput. Phys. 351, 437–454 (2017). https://doi.org/10.1016/j.jcp.2017.09.04010.1016/j.jcp.2017.09.040 ↗
8. Das, S., Sutradhar, A.: Multi-physics topology optimization of functionally graded controllable porous structures: Application to heat dissipating problems. Mater. Des. 193, 108775 (2020). https://doi.org/10.1016/j.matdes.2020.10877510.1016/j.matdes.2020.108775 ↗
9. De Leon, D.M., Gonçalves, J.F., de Souza, C.E.: Stress-based topology optimization of compliant mechanisms design using geometrical and material nonlinearities. Struct Multidisc Optim. (2020). https://doi.org/10.1007/s00158-019-02484-410.1007/s00158-019-02484-4 ↗
10. Dou, S.: A projection approach for topology optimization of porous structures through implicit local volume control. Struct Multidisc Optim. 62, 835–850 (2020). https://doi.org/10.1007/s00158-020-02539-x10.1007/s00158-020-02539-x ↗
11. Fritzen, F., Xia, L., Leuschner, M., Breitkopf, P.: Topology optimization of multiscale elastoviscoplastic structures. Int. J. Numer. Meth. Eng. 106, 430–453 (2016). https://doi.org/10.1002/nme.512210.1002/nme.5122 ↗
12. Guest, J.K., Prévost, J.H.: Optimizing multifunctional materials: Design of microstructures for maximized stiffness and fluid permeability. Int. J. Solids Struct. 43, 7028–7047 (2006). https://doi.org/10.1016/j.ijsolstr.2006.03.00110.1016/j.ijsolstr.2006.03.001 ↗
13. Guo, X., Zhao, X., Zhang, W., Yan, J., Sun, G.: Multi-scale robust design and optimization considering load uncertainties. Comput. Methods Appl. Mech. Eng. 283, 994–1009 (2015). https://doi.org/10.1016/j.cma.2014.10.01410.1016/j.cma.2014.10.014 ↗
14. Ha, S.-H., Cho, S.: Level set based topological shape optimization of geometrically nonlinear structures using unstructured mesh. Comput. Struct. 86, 1447–1455 (2008). https://doi.org/10.1016/j.compstruc.2007.05.02510.1016/j.compstruc.2007.05.025 ↗
15. Han, Y., Xu, B., Liu, Y.: An efficient 137-line MATLAB code for geometrically nonlinear topology optimization using bi-directional evolutionary structural optimization method. Struct Multidisc Optim. (2021). https://doi.org/10.1007/s00158-020-02816-910.1007/s00158-020-02816-9 ↗
16. Huang, X., Radman, A., Xie, Y.M.: Topological design of microstructures of cellular materials for maximum bulk or shear modulus. Comput. Mater. Sci. 50, 1861–1870 (2011). https://doi.org/10.1016/j.commatsci.2011.01.03010.1016/j.commatsci.2011.01.030 ↗
17. Huang, X., Xie, Y.M., Jia, B., Li, Q., Zhou, S.W.: Evolutionary topology optimization of periodic composites for extremal magnetic permeability and electrical permittivity. Struct Multidisc Optim. 46, 385–398 (2012). https://doi.org/10.1007/s00158-012-0766-810.1007/s00158-012-0766-8 ↗
18. Huang, X., Zhou, S., Sun, G., Li, G., Xie, Y.M.: Topology optimization for microstructures of viscoelastic composite materials. Comput. Methods Appl. Mech. Eng. 283, 503–516 (2015). https://doi.org/10.1016/j.cma.2014.10.00710.1016/j.cma.2014.10.007 ↗
19. Kim, N.-H.: Introduction to nonlinear finite element analysis. Springer, New York, NY (2015)10.1007/978-1-4419-1746-1 ↗
20. Kim, S., Yun, G.J.: Microstructure topology optimization by targeting prescribed nonlinear stress-strain relationships. Int. J. Plast 128, 102684 (2020). https://doi.org/10.1016/j.ijplas.2020.10268410.1016/j.ijplas.2020.102684 ↗
21. Klarbring, A., Strömberg, N.: Topology optimization of hyperelastic bodies including non-zero prescribed displacements. Struct Multidisc Optim. 47, 37–48 (2013). https://doi.org/10.1007/s00158-012-0819-z10.1007/s00158-012-0819-z ↗
22. Li, H., Gao, L., Li, H., Tong, H.: Spatial-varying multi-phase infill design using density-based topology optimization. Comput. Method. Appl. Mech. Eng. 372, 113354 (2020). https://doi.org/10.1016/j.cma.2020.11335410.1016/j.cma.2020.113354 ↗
23. Liu, L., Xing, J., Yang, Q., Luo, Y.: Design of large-displacement compliant mechanisms by topology optimization incorporating modified additive hyperelasticity technique. Math. Probl. Eng. 2017, 1–11 (2017). https://doi.org/10.1155/2017/467974610.1155/2017/4679746 ↗
24. Liu, J., Gaynor, A.T., Chen, S., Kang, Z., Suresh, K., Takezawa, A., Li, L., Kato, J., Tang, J., Wang, C.C.L., Cheng, L., Liang, X., To, Albert.C.: Current and future trends in topology optimization for additive manufacturing. Struct. Multidisc. Optim. 57, 2457–2483 (2018). https://doi.org/10.1007/s00158-018-1994-310.1007/s00158-018-1994-3 ↗
25. Liu, B., Cao, W., Zhang, L., Jiang, K., Lu, P.: A design method of Voronoi porous structures with graded relative elasticity distribution for functionally gradient porous materials. Int J Mech Mater Des. (2021). https://doi.org/10.1007/s10999-021-09558-610.1007/s10999-021-09558-6 ↗
26. Long, K., Wang, X., Liu, H.: Stress-constrained topology optimization of continuum structures subjected to harmonic force excitation using sequential quadratic programming. Struct. Multidisc. Optim. 59, 1747–1759 (2019). https://doi.org/10.1007/s00158-018-2159-010.1007/s00158-018-2159-0 ↗
27. Luo, Y., Wang, M.Y., Kang, Z.: Topology optimization of geometrically nonlinear structures based on an additive hyperelasticity technique. Comput. Methods Appl. Mech. Eng. 286, 422–441 (2015). https://doi.org/10.1016/j.cma.2014.12.02310.1016/j.cma.2014.12.023 ↗
28. Ortigosa, R., Ruiz, D., Gil, A.J., Donoso, A., Bellido, J.C.: A stabilisation approach for topology optimisation of hyperelastic structures with the SIMP method. Comput. Method. Appl. Mech. Eng. 364, 112924 (2020). https://doi.org/10.1016/j.cma.2020.11292410.1016/j.cma.2020.112924 ↗
29. Schmidt, M.-P., Pedersen, C.B.W., Gout, C.: On structural topology optimization using graded porosity control. Struct. Multidisc. Optim. 60, 1437–1453 (2019). https://doi.org/10.1007/s00158-019-02275-x10.1007/s00158-019-02275-x ↗
30. Sigmund, O.: A new class of extremal composites. J. Mech. Phys. Solids 48, 397–428 (2000). https://doi.org/10.1016/S0022-5096(99)00034-410.1016/S0022-5096(99)00034-4 ↗
31. Svanberg, K.: The method of moving asymptotes—a new method for structural optimization. Int. J. Numer. Meth. Eng. 24, 359–373 (1987). https://doi.org/10.1002/nme.162024020710.1002/nme.1620240207 ↗
32. van Dijk, N.P., Langelaar, M., van Keulen, F.: Element deformation scaling for robust geometrically nonlinear analyses in topology optimization. Struct Multidisc Optim. 50, 537–560 (2014). https://doi.org/10.1007/s00158-014-1145-410.1007/s00158-014-1145-4 ↗
33. Wang, F.: Systematic design of 3D auxetic lattice materials with programmable Poisson’s ratio for finite strains. J. Mech. Phys. Solids 114, 303–318 (2018). https://doi.org/10.1016/j.jmps.2018.01.01310.1016/j.jmps.2018.01.013 ↗
34. Wang, F., Sigmund, O.: Numerical investigation of stiffness and buckling response of simple and optimized infill structures. Struct. Multidisc. Optim. 61, 2629–2639 (2020). https://doi.org/10.1007/s00158-020-02525-310.1007/s00158-020-02525-3 ↗
35. Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Struct. Multidisc. Optim. 43, 767–784 (2011). https://doi.org/10.1007/s00158-010-0602-y10.1007/s00158-010-0602-y ↗
36. Wang, F., Lazarov, B.S., Sigmund, O., Jensen, J.S.: Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems. Comput. Method. Appl. Mech. Eng. 276, 453–472 (2014a). https://doi.org/10.1016/j.cma.2014.03.02110.1016/j.cma.2014.03.021 ↗
37. Wang, F., Sigmund, O., Jensen, J.S.: Design of materials with prescribed nonlinear properties. J. Mech. Phys. Sol. 69, 156–174 (2014b). https://doi.org/10.1016/j.jmps.2014.05.00310.1016/j.jmps.2014.05.003 ↗
38. Wriggers, P.: Nonlinear finite element methods. Springer, Berlin (2008)
39. Wu, J., Clausen, A., Sigmund, O.: Minimum compliance topology optimization of shell–infill composites for additive manufacturing. Comput. Methods Appl. Mech. Eng. 326, 358–375 (2017). https://doi.org/10.1016/j.cma.2017.08.01810.1016/j.cma.2017.08.018 ↗
40. Wu, J., Aage, N., Westermann, R., Sigmund, O.: Infill optimization for additive manufacturing—approaching bone-like porous structures. IEEE Trans. Visual. Comput. Graphics. 24, 1127–1140 (2018). https://doi.org/10.1109/TVCG.2017.265552310.1109/TVCG.2017.2655523 ↗
41. Wu, J., Sigmund, O., Groen, J.P.: Topology optimization of multi-scale structures: a review. Struct. Multidisc. Optim. 63, 1455–1480 (2021). https://doi.org/10.1007/s00158-021-02881-810.1007/s00158-021-02881-8 ↗
42. Xu, S., Liu, J., Huang, J., Zou, B., Ma, Y.: Multi-scale topology optimization with shell and interface layers for additive manufacturing. Addit. Manuf. 37, 101698 (2021a). https://doi.org/10.1016/j.addma.2020.10169810.1016/j.addma.2020.101698 ↗
43. Xu, S., Liu, J., Zou, B., Li, Q., Ma, Y.: Stress constrained multi-material topology optimization with the ordered SIMP method. Comput. Methods Appl. Mech. Eng. 373, 113453 (2021b). https://doi.org/10.1016/j.cma.2020.11345310.1016/j.cma.2020.113453 ↗
44. Yan, J., Guo, X., Cheng, G.: Multi-scale concurrent material and structural design under mechanical and thermal loads. Comput Mech. 57, 437–446 (2016). https://doi.org/10.1007/s00466-015-1255-x10.1007/s00466-015-1255-x ↗
45. Yang, D., Liu, H., Zhang, W., Li, S.: Stress-constrained topology optimization based on maximum stress measures. Comput. Struct. 198, 23–39 (2018). https://doi.org/10.1016/j.compstruc.2018.01.00810.1016/j.compstruc.2018.01.008 ↗
46. Yoon, G.H., Kim, Y.Y.: Element connectivity parameterization for topology optimization of geometrically nonlinear structures. Int. J. Solids Struct. 42, 1983–2009 (2005). https://doi.org/10.1016/j.ijsolstr.2004.09.00510.1016/j.ijsolstr.2004.09.005 ↗
47. Zhang, Z., Zhao, Y., Du, B., Chen, X., Yao, W.: Topology optimization of hyperelastic structures using a modified evolutionary topology optimization method. Struct. Multidisc. Optim. (2020). https://doi.org/10.1007/s00158-020-02654-910.1007/s00158-020-02654-9 ↗
48. Zhang, C., Liu, J., Yuan, Z., Xu, S., Zou, B., Li, L., Ma, Y.: A novel lattice structure topology optimization method with extreme anisotropic lattice properties. J. Comput. Des. Eng. 8, 1367–1390 (2021a). https://doi.org/10.1093/jcde/qwab05110.1093/jcde/qwab051 ↗
49. Zhang, X., Xing, J., Liu, P., Luo, Y., Kang, Z.: Realization of full and directional band gap design by non-gradient topology optimization in acoustic metamaterials. Extreme. Mech. Lett. 42, 101126 (2021b). https://doi.org/10.1016/j.eml.2020.10112610.1016/j.eml.2020.101126 ↗
50. Zheng, J., Yang, X., Long, S.: Topology optimization with geometrically non-linear based on the element free Galerkin method. Int. J. Mech. Mater. Des. 11, 231–241 (2015). https://doi.org/10.1007/s10999-014-9257-y10.1007/s10999-014-9257-y ↗