Considering the viscoelastic material behavior in a solid-shell element for thermoforming simulation

Considering the viscoelastic material behavior in a solid-shell element for thermoforming simulation

MITSCH Johannes, SCHÄFER Bastian, WANK Jan Paul, KÄRGER Luise

download PDF

Abstract. To predict manufacturing effects in the thermoforming process for fiber reinforced plastics the Finite Element Method is widely used. Most macroscopic simulation methods are based on conventional two-dimensional shell elements which are not capable of modeling the material behavior in thickness direction using constitutive equations. At the same time, standard three-dimensional element formulations are not suitable for the forming simulation of thin textiles due to numerical locking phenomena and the lack of a possible membrane-bending-decoupling. Previous studies focused on a specialized solid-shell element formulation which provides anisotropic but purely elastic material modeling. Since purely elastic approaches cannot accurately describe the deformation behavior in the thermoforming process, the provided element formulation is enhanced to rate-dependent viscoelastic material modeling. Numerical studies are carried out that reveal that the membrane-bending-decoupling is preserved for the viscoelastic material model. Virtual coupon tests demonstrate the rate-dependent material behavior in the solid-shell element. The obtained results show that the general approach of the viscoelastic material behavior within the solid-shell element is suitable to address out-of-plane phenomena in thermoforming simulations.

Keywords
Solid-Shell, Thermoforming, Process Simulation, Finite Element-Analysis

Published online 4/24/2024, 10 pages
Copyright © 2024 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: MITSCH Johannes, SCHÄFER Bastian, WANK Jan Paul, KÄRGER Luise, Considering the viscoelastic material behavior in a solid-shell element for thermoforming simulation, Materials Research Proceedings, Vol. 41, pp 457-466, 2024

DOI: https://doi.org/10.21741/9781644903131-51

The article was published as article 51 of the book Material Forming

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

References
[1] F. Henning, L. Kärger, D. Dörr, F.J. Schirmaier, J. Seuffert, A. Bernath, Fast processing and continuous simulation of automotive structural composite components, Composites Science and Technology 171 (2019) 261–279. https://doi.org/10.1016/j.compscitech.2018.12.007
[2] P. Bussetta, N. Correia, Numerical forming of continuous fibre reinforced composite material: A review, Composites Part A: Applied Science and Manufacturing 113 (2018) 12–31. https://doi.org/10.1016/j.compositesa.2018.07.010
[3] B. Schäfer, D. Dörr, L. Kärger, Reduced-Integrated 8-Node Hexahedral Solid-Shell Element for the Macroscopic Forming Simulation of Continuous Fibre-Reinforced Polymers, Procedia Manufacturing 47 (2020) 134–139. https://doi.org/10.1016/j.promfg.2020.04.154
[4] U. Sachs, R. Akkerman, Viscoelastic bending model for continuous fiber-reinforced thermoplastic composites in melt, Composites Part A: Applied Science and Manufacturing. https://doi.org/10.1016/j.compositesa.2017.05.032
[5] A. Margossian, S. Bel, R. Hinterhoelzl, Bending characterisation of a molten unidirectional carbon fibre reinforced thermoplastic composite using a Dynamic Mechanical Analysis system, Composites Part A: Applied Science and Manufacturing 77 (2015) 154–163. https://doi.org/10.1016/j.compositesa.2015.06.015
[6] S. Ropers, M. Kardos, T.A. Osswald, A thermo-viscoelastic approach for the characterization and modeling of the bending behavior of thermoplastic composites, Composites Part A: Applied Science and Manufacturing 90 (2016) 22–32. https://doi.org/10.1016/j.compositesa.2016.06.016
[7] D. Dörr, F. Henning, L. Kärger, Nonlinear hyperviscoelastic modelling of intra-ply deformation behaviour in Finite element forming simulation of continuously fibre-reinforced thermoplastics, Composites Part A: Applied Science and Manufacturing. https://doi.org/10.1016/j.compositesa.2018.03.037
[8] D. Dörr, F.J. Schirmaier, F. Henning, L. Kärger, A viscoelastic approach for modeling bending behavior in finite element forming simulation of continuously fiber reinforced composites, Composites Part A: Applied Science and Manufacturing 94 (2017) 113–123. https://doi.org/10.1016/j.compositesa.2016.11.027
[9] D. Dörr, T. Joppich, D. Kugele, F. Henning, L. Kärger, A coupled thermomechanical approach for finite element forming simulation of continuously fiber-reinforced semi-crystalline thermoplastics, Composites Part A: Applied Science and Manufacturing 125 (2019). https://doi.org/10.1016/j.compositesa.2019.105508
[10] Hu Xiong, Simulation of forming, compaction and consolidation of thermoplastic composites based on solid shell elements, 2018.
[11] H. Xiong, N. Hamila, P. Boisse, Consolidation Modeling during Thermoforming of Thermoplastic Composite Prepregs, Materials (Basel, Switzerland) 12 (2019). https://doi.org/10.3390/ma12182853
[12] P.D. Mulye, L. Morançay, C. Binetruy, S. Comas-Cardona, A. Leygue, D. Guillon, Unified numerical process modeling of forming and consolidation for thermoplastic composites with prepreg patches, Front. Mater. 10 (2023). https://doi.org/10.3389/fmats.2023.1176482
[13] B. Schäfer, D. Dörr, L. Kärger, Potential and challenges of a solid-shell element for the macroscopic forming simulation of engineering textiles, ESAFORM 2021. https://doi.org/10.25518/esaform21.883
[14] M. Schwarze, S. Reese, A reduced integration solid-shell finite element based on the EAS and the ANS concept-Geometrically linear problems, Int. J. Numer. Meth. Engng. 80 (2009) 1322–1355. https://doi.org/10.1002/nme.2653
[15] M. Schwarze, S. Reese, A reduced integration solid-shell finite element based on the EAS and the ANS concept-Large deformation problems, Int. J. Numer. Meth. Engng. 85 (2011) 289–329. https://doi.org/10.1002/nme.2966
[16] M. Pagani, S. Reese, U. Perego, Computationally efficient explicit nonlinear analyses using reduced integration-based solid-shell finite elements, Computer Methods In Applied Mechanics And Engineering 268 (2014) 141–159. https://doi.org/10.1016/j.cma.2013.09.005
[17] K. Jože, Multi-language and Multi-environment Generation of Nonlinear Finite Element Codes, Engineering with Computers 18 (2002) 312–327. https://doi.org/10.1007/s003660200028
[18] J.C. Simo, M.S. Rifai, A class of mixed assumed strain methods and the method of incompatible modes, Int. J. Numer. Meth. Engng. 29 (1990) 1595–1638. https://doi.org/10.1002/nme.1620290802
[19] J.C. Simo, F. Armero, Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes, Int. J. Numer. Meth. Engng. 33 (1992) 1413–1449. https://doi.org/10.1002/nme.1620330705
[20] J. Simo, F. Armero, R. Taylor, Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems, Computer Methods In Applied Mechanics And Engineering 110 (1993) 359–386.
[21] T.J.R. Hughes, T.E. Tezduyar, Finite Elements Based Upon Mindlin Plate Theory With Particular Reference to the Four-Node Bilinear Isoparametric Element, J. Appl. Mech 48 (1981) 587–596. https://doi.org/10.1115/1.3157679
[22] M. Schwarze, I.N. Vladimirov, S. Reese, On the implementation of the EAS and ANS concept into a reduced integration continuum shell element and applications to sheet forming, Int J Mater Form 2 (2009) 919–922. https://doi.org/10.1007/s12289-009-0634-2.
[23] A. Bertram, Elasticity and Plasticity of Large Deformations, Springer International Publishing, Cham, 2021.
[24] T. Belytschko, W.K. Liu, B. Moran, K.I. Elkhodary, Nonlinear finite elements for continua and structures, 2nd ed., Wiley, Chichester, 2014.
[25] C.W. Macosko, Rheology: Principles, measurements, and applications, Wiley-VCH, New York NY u.a., 1994.
[26] R. Hauptmann, K. Schweizerhof, S. Doll, Extension of the ‘solid-shell’ concept for application to large elastic and large elastoplastic deformations, Int. J. Numer. Meth. Engng. 49 (2000) 1121–1141. https://doi.org/10.1002/1097-0207(20001130)49:9<1121:AID-NME130>3.0.CO;2-F
[27] R. Courant, K. Friedrichs, H. Lewy, Über die partiellen Differenzengleichungen der mathematischen Physik, Math. Ann. 100 (1928) 32–74. https://doi.org/10.1007/BF01448839
[28] G. Cocchetti, M. Pagani, U. Perego, Selective mass scaling and critical time-step estimate for explicit dynamics analyses with solid-shell elements, Computers & Structures 127 (2013) 39–52. https://doi.org/10.1016/j.compstruc.2012.10.021