Abstract
Tailoring adhesive properties between surfaces is of great importance for micro-scale systems, ranging from managing stiction in MEMS devices to designing wall-scaling gecko-like robots. A methodology is introduced for designing adhesive interfaces between structures using topology optimization. Structures subjected to external loads that lead to delamination are studied for situations where displacements and deformations are small. Only the effects of adhesive forces acting normal to the surfaces are considered. An interface finite element is presented that couples a penalty contact formulation and a Lennard–Jones model of van der Waals adhesive forces. Two- and three dimensional design optimization problems are presented in which adhesive force distributions are designed such that load-displacement curves of delaminating structures match target responses. The design variables describe the adhesive energy per area of the interface between the surfaces, as well as the geometry of the delaminating structure. A built-in length scale in the formulation of the adhesion forces eliminates the need for filtering to achieve comparable optimal adhesive designs over a range of mesh densities. The resulting design problem is solved by gradient based optimization algorithms evaluating the design sensitivities by the adjoint method. Results show that the delamination response can be effectively manipulated by the method presented. Varying simultaneously both adhesive and geometric parameters yields a wider range of reachable target load-displacement curves than in the case varying adhesive energy alone.
Similar content being viewed by others
References
Bendsoe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer
Bhate D, Dunn M (2007) Adhesion of arbitrary-shaped thin-film microstructures. Microelectron Reliab 47(12):2014–2024
Cho SS, Park S (2004) Finite element modeling of adhesive contact using molecular potential. Tribol Internat 37:763–769. doi:10.1016/j.triboint.2004.04.007
DelRio FW, de Boer MP, Knapp JA, Reedy Jr ED, Clews PJ, Dunn ML (2005) The role of van der Waals forces in adhesion of micromachined surfaces. Nat Mater 4:629–634. doi:10.1038/nmat1431
DelRio FW, Dunn ML, Boyce BL, Corwin AD, de Boer MP (2006) The effect of nanoparticles on rough surface adhesion. J Appl Phys 99(10):104304–104309
DelRio FW, Dunn ML, Phinney LM, Bourdon CJ, de Boer MP (2007) Rough surface adhesion in the presence of capillary condensation. Appl Phys Lett 90(16):163104
Fancello EA (2006) Topology optimization for minimum mass design considering local failure constraints and contact boundary conditions. Struct Multidisc Optim 32:229–240. doi:10.1007/s00158-006-0019-9
Gao H, Wang X, Yao H, Gorb S, Arzt E (2005) Mechanics of hierarchical adhesion structures of geckos. Mech Mater 37:275–285. doi:10.1016/j.mechmat.2004.03.008
Geim AK, Dubonos SV, Grigorieva IV, Novoselov KS, Zhukov AA, Shapoval SY (2003) Microfabricated adhesive mimicking gecko foot-hair. Nat Mater 2:461–463. doi:10.1038/nmat917
Hertz H (1882) Ueber die Beruhrung fester elastischer Korper. J Reine Angew Math 92:156–171
Hilding D, Klarbring A, Petersson J (1999) Optimization of structures in unilateral contact. Appl Mech Rev 52(4):139–160
Knapp JA, de Boer MP (2002) Mechanics of microcantilever beams subject to combined electrostatic and adhesive forces. J. Microelectromechanical Syst. 11(6):754–764
Liu B, Huang Y, Jiang H, Qu S, Hwang K (2004) The atomic-scale finite element method. Comput Methods Appl Mech Engrg 193:1849–1864. doi:10.1016/j.cma.2003.12.037
Mankame ND, Ananthasuresh G (2004) Topology optimization for synthesis of contact-aided compliant mechanisms using regularized contact modeling. Comput Struct 82:1267–1290. doi:10.1016/j.compstruc.2004.02.024
Masuda Y, Tomimoto K, Koumoto K (2003) Two-dimensional self-assembly of spherical particles using a liquid mold and its drying process. Langmuir 19(13):5179–5183
Maugis D (2000) Contact, adhesion and rupture of elastic solids. No. 130 in Solid-State Sciences, Springer
Menon C, Sitti M (2006) A biomimetic climbing robot based on the gecko. J Bionic Eng 3:115–125
Militello C, Felippa CA (1991) The first andes elements: 9-dof plate bending triangles. Comput Methods Appl Mech Engrg 93(2):217–246
Northen MT, Turner KL (2005) A batch fabricated biomimetic dry adhesive. Nanotechnology 16:1159–1166. doi:10.1088/0957-4484/16/8/030
Petersson J, Patriksson M (1997) Topology optimization of sheets in contact by a subgradient method. Int J Numer Methods Eng 40:1295–1321
Raous M, Cangemi L, Cocu M (1999) A consistent model coupling adhesion, friction, and unilateral contact. Comput Methods Appl Mech Engrg 177:383–399
Rupp CJ, Evgrafov A, Maute K, Dunn ML (2007) Design of phononic materials/structures for surface wave devices using topology optimization. Struct Multidisc Optim 34:111–121. doi:10.1007/s00158-006-0076-0
Sitti M, Fearing R (2003) Synthetic gecko foot-hair micro/nano-structures as dry adhesives. J Adhesion Sci Technol 17:1055–1073
Svanberg K (1995) A globally convergent version of MMA without linesearch. In: Proceedings of the first world congress of structural and multidisciplinary optimization, 28 May–2 June 1995, pp 9–16
Sylves KT (2007) Modeling and design optimization of adhesion between surfaces at the microscale. Master’s thesis, University of Colorado at Boulder
Tayebi N, Polycarpou AA (2005) Reducing the effects of adhesion and friction in microelectromechanical systems (MEMSs) through surface roughening: comparison between theory and experiments. J Appl Phys 98(073528)
Tsibouklis J, Stone M, Thorpe AA, Graham P, Peters V, Heerlien R, Smith JR, Green KL, Nevel TG (1999) Preventing bacterial adhesion onto surfaces: the low-surface-energy approach. Biomaterials 20(13):1229–1235. doi:10.1016/S0142-9612(99)00023-X
Wriggers P (2002) Computational contact mechanics. Wiley
Yao H, Gao H (2006) Optimal shapes for adhesive binding between two elastic bodies. J Colloid Interface Sci 298:564–572. doi:10.1016/j.jcis.2005.12.059
Yee Y, Chun K, Lee JD, Kim CJ (1996) Polysilicon surface-modification technique to reduce sticking of microstructures. Sens Actuators A 52:145–150
Zhao YP, Wang LS, Yu TX (2003) Mechanics of adhesion in MEMS—a review. J Adhesion Sci Technol 17(4):519–546
Zhaoa Y, Tong T, Delzeit L, Kashani A, Meyyappan M, Majumdar A (2006) Interfacial energy and strength of multiwalled-carbon-nanotube-based dry adhesive. J Vac Sci Technol B 24(1):331–335. doi:10.1116/1.2163891
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sylves, K., Maute, K. & Dunn, M.L. Adhesive surface design using topology optimization. Struct Multidisc Optim 38, 455–468 (2009). https://doi.org/10.1007/s00158-008-0298-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-008-0298-4