Modelling the curing process in particle-filled electro-active polymers with a dispersion anisotropy
- 19 Downloads
Abstract
Even for a moderate actuation, a large electric voltage requirement hinders the application of electro-active polymers (EAPs) in many areas. Hence, among other mechanisms, the actuation enhancement in EAPs is performed via inclusions of high-dielectric-permittivity fillers in the matrix material in the uncured stage. Moreover, to obtain an optimum advantage from the high-dielectric-permittivity fillers, an electric field can be applied during the curing process which helps the particles to align in a preferred direction. To be specific, recent experimental evidences show that these particles form a dispersed anisotropy rather than a perfect transverse anisotropic structure. The polymer curing process is a complex (visco-) elastic phenomenon where a liquid polymer gradually transforms into a solid macromolecular structure due to cross-linking of the initial solution of short polymer chains. This phase transition comes along with an increase in the material stiffness and a volume shrinkage. In this paper we present a phenomenologically inspired large strain framework for simulating the curing process of particle-filled electro-active polymers with a dispersion-type anisotropy that can work under the influence of an electro-mechanically coupled load. The application of the proposed approach is demonstrated with some numerical examples. These examples illustrate that the model can predict common features in particle-filled dispersed electro-active polymers undergoing curing processes in the presence of an electro-mechanically coupled load.
Keywords
Electro-active polymers Polymer curing Electro-mechanically coupled problem Dispersion anisotropy Electro-elasticity Curing shrinkagePreview
Unable to display preview. Download preview PDF.
Notes
References
- 1.Adolf, D.B., Martin, J.E., Chambers, R.S., Burchett, S.N., Guess, T.N.: Stresses during thermoset cure. J. Mater. Res. 13, 530–550 (1998)ADSGoogle Scholar
- 2.Alastrue, V., Martinez, M., Doblare, M., Menzel, M.: Anisotropic micro-sphere-based finite elasticity applied to blood vessel modeling. Int. J. Mech. Phys. Solids 57, 178–203 (2009)ADSzbMATHGoogle Scholar
- 3.Ask, A., Menzel, A., Ristinma, M.: Phenomenological modeling of viscous electrostrictive polymers. Int. J. Nonlinear Mech. 47(2), 156–165 (2012)ADSGoogle Scholar
- 4.Bazant, Z.P., Oh, B.H.: Efficient numerical integration on the surface of a sphere. Z. Angew. Math. Mech. 66, 37–49 (1986)MathSciNetzbMATHGoogle Scholar
- 5.Büschel, A., Klinkel, S., Wagner, W.: Dielectric elastomers—numerical modeling of nonlinear visco-elasticity. Int. J. Numer. Methods Eng. 93, 834–856 (2013)zbMATHGoogle Scholar
- 6.Bustamante, B.: Transversely isotropic nonlinear electro-active elastomers. Acta Mech. 206(3–4), 237–259 (2009)zbMATHGoogle Scholar
- 7.Carpi, F., Rossi, D.D.: Improvement of electromechanical actuating performances of a silicone dielectric elastomer by dispersion of titanium dioxide powder. IEEE Trans. Dielectr. Electr. Insul. 12, 835–843 (2005)Google Scholar
- 8.Carpi, F., Gallone, G., Galantini, F., Rossi, D.D.: Silicone-poly(hexylthiophene) blends as elastomers with enhanced electromechanical transduction properties. Adv. Funct. Mater. 18, 235–241 (2008)Google Scholar
- 9.Cortes, D.H., Lake, S.P., Kadlowec, J.A., Soslowsky, L.J., Elliot, D.M.: Characterizing the mechanical contribution of fiber angular distribution in connective tissue: comparison of two modeling approaches. Biomech. Model Mechanobiol. 9, 651–658 (2010)Google Scholar
- 10.Dorfmann, A., Ogden, R.W.: Nonlinear electroelasticity. Acta Mech. 174(3), 167–183 (2005)zbMATHGoogle Scholar
- 11.Dorfmann, L., Ogden, R.W.: Nonlinear electroelasticity: material properties, continuum theory and applications. Proc. R. Soc. A 473, 20170311 (2017)ADSMathSciNetzbMATHGoogle Scholar
- 12.Diaconu, I., Dorohoi, D.O., Ciobanu, C.: Eletromechanical response of polyurethane films with different thickness. Roman. J. Phys. 53(1–2), 91–97 (2008)Google Scholar
- 13.Dang, Z.M., Yuan, J.K., Zha, J.W., Zhou, T., Li, S.T., Hu, G.H.: Fundamentals, processes and applications of high-permittivity polymer-matrix composites. Prog. Mater. Sci. 57, 660–723 (2012)Google Scholar
- 14.Dal, H., Zopf, C., Kaliske, M.: Micro-sphere based viscoplastic constitutive model for uncured green rubber. Int. J. Solids Struct. 132–133, 201–217 (2018)Google Scholar
- 15.Dal, H., Kaliske, M.: A micro-continuum-mechanical material model for failure of rubber-like materials: application to ageing-induced fracturing. Int. J. Mech. Phys. Solids 57(8), 1340–1356 (2009)ADSzbMATHGoogle Scholar
- 16.Dal, H., Cansiz, B., Miehe, C.: A three-scale compressible microsphere model for hyperelastic materials. Int. J. Numer. Methods Eng. 116, 412–433 (2018)MathSciNetGoogle Scholar
- 17.Ehret, A.E., Itskov, M., Schmid, H.: Numerical integration on the sphere and its effect on the material symmetry of constitutive equations—a comparative study. Int. J. Numer. Methods Eng. 81, 189–206 (2010)zbMATHGoogle Scholar
- 18.Fliege, J., Maier, U.: The distribution of points on the sphere and corresponding cubature formulae. IMA J. Numer. Anal. 19(2), 317–334 (1999)MathSciNetzbMATHGoogle Scholar
- 19.Gallone, G., Carpi, F., Rossi, D.D., Levita, G., Marchetti, A.: Dielectric constant enhancement in a silicone elastomer filled with lead magnesium niobate-leads titanate. Mater. Sci. Eng. C 27, 110–1162 (2007)Google Scholar
- 20.Gillen, K.T.: Effect of cross-links which occur during continuous chemical stress-relaxation. Macromolecules 21, 442–446 (1988)ADSGoogle Scholar
- 21.Hossain, M., Possart, G., Steinmann, P.: A small-strain model to simulate the curing of thermosets. Comput. Mech. 43, 769–779 (2009a)zbMATHGoogle Scholar
- 22.Hossain, M., Possart, G., Steinmann, P.: A finite strain framework for the simulation of polymer curing. Part I: elasticity. Comput. Mech. 44(5), 621–630 (2009b)MathSciNetzbMATHGoogle Scholar
- 23.Hossain, M., Possart, G., Steinmann, P.: A finite strain framework for the simulation of polymer curing. Part II: viscoelasticity and shrinkage. Comput. Mech. 46(3), 363–375 (2010)zbMATHGoogle Scholar
- 24.Hossain, M., Steinmann, P.: Degree of cure-dependent modelling for polymer curing processes at small-strain. Part I: consistent reformulation. Comput. Mech. 53(4), 777–787 (2014)MathSciNetzbMATHGoogle Scholar
- 25.Hossain, M., Steinmann, P.: Continuum physics of materials with time-dependent properties: reviewing the case of polymer curing. Adv. Appl. Mech. 48, 141–259 (2015)Google Scholar
- 26.Hossain, M., Saxena, P., Steinmann, P.: Modelling the mechanical aspects of the curing process of magneto-sensitive elastomeric materials. Int. J. Solids Struct. 58, 257–269 (2015)Google Scholar
- 27.Hossain, M., Saxena, P., Steinmann, P.: Modelling the curing process in magneto-sensitive materials: rate-dependence and shrinkage. Int. J. Nonlinear Mech. 74, 108–121 (2015)ADSGoogle Scholar
- 28.Hossain, M., Chatzigeorgiou, G., Meraghni, F., Steinmann, P.: A multi-scale approach to model the curing process in magneto-sensitive polymeric materials. Int. J. Solids Struct. 69–70, 34–44 (2015)Google Scholar
- 29.Hossain, M., Vu, D.K., Steinmann, P.: Experimental study and numerical modelling of VHB 4910 polymer. Comput. Mater. Sci. 59, 65–74 (2012)Google Scholar
- 30.Hossain, M., Vu, D.K., Steinmann, P.: A comprehensive characterization of the electro-mechanically coupled properties of VHB 4910 polymer. Arch. Appl. Mech. 85(4), 523–537 (2014)Google Scholar
- 31.Hossain, M., Steinmann, P.: Modelling electro-active polymers with a dispersion-type anisotropy. Smart Mater. Struct. 27(2), 1–17 (2018)Google Scholar
- 32.Heinrich, C., Aldridge, M., Wineman, A.S., Kieffer, J., Waas, A.M., Shahwan, K.W.: The role of curing stresses in subsequent response, damage and failure of textile polymer composites. J. Mech. Phys. Solids 61, 1241–1264 (2013)ADSMathSciNetGoogle Scholar
- 33.Horgan, C.O., Saccomandi, G.: Constitutive models for compressible nonlinearly elastic materials with limiting chain extensibility. J. Elast. 77, 123–138 (2004)MathSciNetzbMATHGoogle Scholar
- 34.Itskov, M.: On the accuracy of numerical integration over the unit sphere applied to full network models. Comput. Mech. 57(5), 859–865 (2016)MathSciNetzbMATHGoogle Scholar
- 35.Itskov, M., Khiem, V.N., Waluyo, S.: Electroelasticity of dielectric elastomers based on molecular chain statistics. Math. Mech. Solids (2018). https://doi.org/10.1177/1081286518755846 Google Scholar
- 36.Johlitz, M., Steeb, H., Diebels, S., Chatzouridou, A., Batal, J., Possart, W.: Experimental and theoretical investigation of nonlinear viscoelastic polyurethane systems. J. Mater. Sci. 42, 9894–9904 (2007)ADSGoogle Scholar
- 37.Koh, S.J.A., Keplinger, C., Li, T., Bauer, S., Suo, Z.: Dielectric elastomer generators: how much energy can be converted? IEEE/ASME Trans Mechatron 16(1), 33–41 (2011)Google Scholar
- 38.Kashani, M.R., Javadi, S., Gharavi, N.: Dielectric properties of silicone rubber-titanium dioxide composites prepared by dielectrophoretic assembly of filler particles. Smart Mater. Struct. 19, 1–7 (2010)Google Scholar
- 39.Kussmaul, B., Risse, S., Kofod, G., Wache, R., Wegener, M., McCarthy, D.N., Krueger, H., Gerhard, R.: Enhancement of dielectric permittivity and electromechanical response in silicone elastomers: molecular grafting of organic dipoles to the macromolecular network. Adv. Funct. Mater. 21, 4589–4594 (2011)Google Scholar
- 40.Keip, M.A., Steinmann, P., Schröder, J.: Two-scale computational homogenization of electro-elasticity at finite strains. Comput. Methods Appl. Mech. Eng. 278, 62–79 (2014)ADSMathSciNetzbMATHGoogle Scholar
- 41.Kiasat, M.: Curing Shrinkage and Residual Stresses in Viscoelastic Thermosetting Resins and Composites. TU Delft, Delft (2000). PhD ThesisGoogle Scholar
- 42.Landgraf, R., Scherzer, R., Rudolph, M., Ihlemann, J.: Modelling and simulation of adhesive curing processes in bonded piezo metal composites. Comput. Mech. 54(2), 547–565 (2014)zbMATHGoogle Scholar
- 43.Landgraf, R.: Modeling and simulation of the curing of polymeric materials. Ph.D. dissertation, TU Chemnitz, Germany (2015)Google Scholar
- 44.Lion, A., Höfer, P.: On the phenomenological representation of curing phenomena in continuum mechanics. Arch. Mech. 59, 59–89 (2007)zbMATHGoogle Scholar
- 45.Liu, B., Shaw, M.T.: Electrorheology of filled silicone elastomers. J. Rheol. 45, 641–657 (2011)ADSGoogle Scholar
- 46.Mehnert, M., Hossain, M., Steinmann, P.: On nonlinear thermo-electro-elasticity. Proc. R. Soc. A 472(2190), 20160170 (2016)ADSMathSciNetzbMATHGoogle Scholar
- 47.Monk, P.: Finite Element Methods for Maxwell Equations. Oxford University Press, Oxford (2003)zbMATHGoogle Scholar
- 48.Molberg, M., Crespy, D., Rupper, P., Nesch, F., Manson, J.A.E., Loewe, C., Opris, D.M.: High breakdown field dielectric elastomer actuators using encapsulated polyaniline as high dielectric constant filler. Adv. Funct. Mater. 20, 3280–3291 (2010)Google Scholar
- 49.Miehe, C., Göktepe, S., Lulei, F.: A micro–macro approach to rubber-like materials: part I, the non-affine micro-sphere model of rubber elasticity. J. Mech. Phys. Solids 52, 2617–2660 (2004)ADSMathSciNetzbMATHGoogle Scholar
- 50.Mahnken, R.: Thermodynamic consistent modeling of polymer curing coupled to viscoelasticity at large strains. Int. J. Solids Struct. 50(13), 2003–2021 (2013)Google Scholar
- 51.Nateghi, A., Dal, H., Keip, M.A., Miehe, C.: An affine microsphere approach to modeling strain-induced crystallization in rubbery polymers. Contin. Mech. Thermodyn. 30(3), 485–507 (2018)MathSciNetzbMATHGoogle Scholar
- 52.Opris, D.M., Molberg, M., Walder, C., Ko, Y.S., Fischer, B., Nuesch, F.A.: New silicone composites for dielectric elastomer actuator applications in competition with acrylic foil. Adv. Funct. Mater. 21, 3531–3539 (2011)Google Scholar
- 53.Oliva-Aviles, A.I., Aviles, F., Sosa, V.: Electrical and piezoresistive properties of multi-walled carbon nanotube/polymer composite films aligned by an electric field. Carbon 49, 2989–2997 (2011)Google Scholar
- 54.Pandolfi, A., Vasta, M.: Fiber distributed hyper elastic modelling of biological tissues. Mech. Mater. 44, 151–162 (2012)Google Scholar
- 55.Brochu, P., Pei, Q.: Advances in dielectric elastomers for actuators and artificial muscles. Macromol. Rapid Commun. 31, 10–36 (2010)Google Scholar
- 56.Reese, S., Govindjee, S.: A theory of finite viscoelasticity and numerical aspects. Int. J. Solids Struct. 35, 3455–3482 (1998)zbMATHGoogle Scholar
- 57.Risse, S., Kussmaul, B., Krueger, H., Kofod, G.: Synergistic improvement of actuation properties with compatibilized high permittivity filler. Adv. Funct. Mater. 22, 3958–3962 (2012)Google Scholar
- 58.Risse, S., Kussmaul, B., Krueger, H., Kofod, G.: A versatile method for enhancement of electromechanical sensitivity of silicone elastomers. RSC Adv. 2, 9029–9035 (2012)Google Scholar
- 59.Romasanta, L.J., Lopez-Manchado, M.A., Verdejo, R.: Increasing the performance of dielectric elastomer actuators: a review from the materials perspective. Prog. Polym. Res. 51, 188–211 (2014)Google Scholar
- 60.Steinmann, P., Hossain, M., Possart, G.: Hyperelastic models for rubber-like materials: consistent tangent operators and suitability of Treloar’s data. Arch. Appl. Mech. 82(9), 1183–1217 (2012)ADSzbMATHGoogle Scholar
- 61.Spencer, A.J.M.: Theory of invariants. In: Eringen, A.C. (ed.) Continuum Physics, vol. 1, pp. 239–353. Academic, New York (1971)Google Scholar
- 62.Saxena, P., Vu, D.K., Steinmann, P.: On rate-dependent dissipation effects in electro-elasticity. Int. J. Nonlinear Mech. 62, 1–11 (2014)ADSGoogle Scholar
- 63.Saxena, P., Pelteret, J.-P., Steinmann, P.: Modelling of iron-filled magneto-active polymers with a dispersed chain-like microstructure. Eur. J. Mech. A Solids 50, 132–151 (2015)ADSMathSciNetzbMATHGoogle Scholar
- 64.Skacel, P., Bursa, J.: Comparison of constitutive models of arterial layers with distributed collagen fibre orientations. Acta Bioeng. Biomech. 16(3), 47–58 (2014)Google Scholar
- 65.Tomer, V., Randall, C.A.: High field dielectric properties of anisotropic polymer-ceramic composites. J Appl Phys 104, 074106/1–074106/7 (2008)ADSGoogle Scholar
- 66.Thylander, S.: Microsphere-based modeling of electro-active polymers. Ph.D. dissertation, Lund University, Sweden (2016)Google Scholar
- 67.Vogel, F.: On the modeling and computation of electro- and magneto-active polymers. Ph.D. dissertation, Friedrich-Alexander-University Erlangen-Nuremberg, Germany (2014)Google Scholar
- 68.Vu, D.K., Steinmann, P.: Numerical modeling of non-linear electroelasticity. Int. J. Numer. Methods Eng. 70, 685–704 (2007)zbMATHGoogle Scholar
- 69.Wissler, M., Mazza, E.: Mechanical behavior of an acrylic elastomer used in dielectric elastomer actuators. Sens. Actuators A 134, 494–504 (2007)Google Scholar
- 70.Yang, Ta-I, Kofinas, P.: Dielectric properties of polymer nanoparticle composites. Polymer 48, 791–798 (2009)Google Scholar
- 71.Womersley, R.S.: Interpolation and cubature on the sphere—UNSW Sydney. https://web.maths.unsw.edu.au/~rsw/Sphere/. Accessed 11 June 2017