Microscopic and macroscopic modeling of linear viscoelastic vibration behavior of short fiber reinforced plastics

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A. Kriwet
F. Urban
D. Er
M. Stommel
P. Middendorf


More and more components made of short-fiber reinforced plastics are being used in modern powertrains. A reason for this is the good acoustic properties due to the lower stiffness and higher damping compared to classic metallic materials. To meet the increased customer demand regarding the acoustic sound comfort of internal combustion or electric powertrains, it is necessary to precisely predict the vibration behavior of components that are responsible for the transmission of structure-borne noise into the vehicle structure. Today’s simulations often cannot satisfactorily predict the actual vibration behavior of short-fiber reinforced plastics. The required material data, in particular damping, is often obtained from static tests or considered unknown. Frequency-dependent material properties are required for a reliable prediction of the special viscoelastic properties of the short-fiber reinforced plastics. By means of a new test method based on flexural resonance vibrations, viscoelastic material data can be characterized in a frequency range between 100 Hz and 10 kHz, considering environmental conditions such as temperature and humidity. Using these material data, a simulation of the structural dynamic behavior can be performed using either of two modeling approaches: microscopic or macroscopic. The basis is the orientation of the fibers from an injection molding simulation. The microscopic modeling approach uses a two-step homogenization of the properties of the matrix, fiber and matrix-fiber-interphase followed by a spatial discretization into material databases, whilst the macroscopic modeling approach uses a one-step homogenization based on directly measured viscoelastic material data with different fiber orientation. The necessary assumptions and challenges are discussed to categorize the usage of the models in proper cases.

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How to Cite
Microscopic and macroscopic modeling of linear viscoelastic vibration behavior of short fiber reinforced plastics. (2023). Engineering Modelling, Analysis and Simulation, 1. https://doi.org/10.59972/kp48t0yu

How to Cite

Microscopic and macroscopic modeling of linear viscoelastic vibration behavior of short fiber reinforced plastics. (2023). Engineering Modelling, Analysis and Simulation, 1. https://doi.org/10.59972/kp48t0yu


M. Stommel, M. Stojek and W. Korte, FEM zur Berechnung von Kunststoff- und Elastomerbauteilen. Carl Hanser Verlag GmbH Co KG, 2018.

H. Kremer, „Materialdatenermittlung thermoplastischer Kunststoffe für Körperschallsimulationen auf Basis von Reverse Engineering“, PhD Thesis, 2014.

K. Raschke and W. Korte, „Faserverstärkte Motorbauteile besser berechnen“, Kunststoffe, vol. 109, pp. 184-189, 2019.

W. Michaeli, C. Hopmann and H. Kremer, „Materialdatenermittlung für Akustiksimulationen mittels Reverse Engineering: Akustisches Verhalten von Kunststoffen“, Kunststoffe, vol. 102, pp. 5-7, 2012.

M. op de Laak and M. Hauth, “Noch schneller zur Zylinderkopfhaube”, Kunststoffe, vol. 94, pp. 126-130, 2004.

K. P. Menard, Dynamic Mechanical Analysis. Boca Raton: Crc Press, 2020.

E. T. J. Klompen and L. E. Govaert, Mechanics of Time-Dependent Materials, vol. 3, no. 1, pp. 49–69, 1999, doi: https://doi.org/10.1023/a:1009853024441.

B. Wampfler, S. Affolter, A. Ritter and M. Schmid, Messunsicherheit in der Kunststoffanalytik. Carl Hanser Verlag GmbH Co KG, 2017.

Standard Test Method for Plastics: Dynamic Mechanical Properties: In Flexure (Three-Point Bending). ASTM D5023-15, 2016, doi: https://doi.org/10.1520/D5023-15.

M. Giersbeck, K. Hornberger and A. Kech, „Virtuelle Bauteilentwicklung“, Kunststoffe, vol. 101, pp. 50-53, 2011.

C. Hopmann, W. Michaeli and H. Kremer, „Frequenzabhängiges Verhalten von Kunststoffen“, Kunststoffe, vol. 102, pp. 64-66, 2012.

S. Pischinger, W. Michaeli, M. Joerres, C. Steffens, M. Atzler and T. Arping, “Verfahren zur akustischen Simulation von Kunststoffbauteilen”, MTZ - Motortechnische Zeitschrift, vol. 70, no. 9, pp. 692–701, Sep. 2009, doi: https://doi.org/10.1007/bf03225522.

H. J. Böhm, A short introduction into basic aspects of continuum micromechanics. Institute of Lightweight Design and Structural Biomechanics (ILSB), 2008.

O. Pierard, “Micromechanics of inclusion-reinforced composites in elasto-plasticity and elasto-viscoplasticity modeling and computation”, PhD Thesis, Katholische Universität Löwen, 2006.

R. Hill, “Elastic properties of reinforced solids: Some theoretical principles”, Journal of the Mechanics and Physics of Solids, vol. 11, no. 5, pp. 357–372, Sep. 1963, doi: https://doi.org/10.1016/0022-5096(63)90036-x.

“The determination of the elastic field of an ellipsoidal inclusion, and related problems”, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, vol. 241, no. 1226, pp. 376–396, Aug. 1957, doi: https://doi.org/10.1098/rspa.1957.0133.

T. Mori and K. Tanaka, “Average stress in matrix and average elastic energy of materials with misfitting inclusions,” Acta Metallurgica, vol. 21, no. 5, pp. 571–574, May 1973, doi: https://doi.org/10.1016/0001-6160(73)90064-3.

G. P. Tandon and G. J. Weng, “The effect of aspect ratio of inclusions on the elastic properties of unidirectionally aligned composites”, Polymer Composites, vol. 5, no. 4, pp. 327–333, Oct. 1984, doi: https://doi.org/10.1002/pc.750050413.

M. Hori and S. Nemat-Nasser, “Double-inclusion model and overall moduli of multi-phase composites”, Mechanics of Materials, vol. 14, no. 3, pp. 189–206, Jan. 1993, doi: https://doi.org/10.1016/0167-6636(93)90066-z.

M. Schöneich, „Charakterisierung und Modellierung viskoelastischer Eigenschaften von kurzglasfaserverstärkten Thermoplasten mit Faser-Matrix Interphase“, PhD Thesis. Universität des Saarlandes, 2016, doi: http://dx.doi.org/10.22028/D291-23208

M. Bienert, “Warum der ganze Aufwand? Eine Einführung in die experimentelle Modalanalyse”, in Polytec Anwenderkonferenz, 2022.

M. Möser, Ed., Messtechnik der Akustik. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. doi: https://doi.org/10.1007/978-3-540-68087-1.

K. Magnus, K. Popp and W. Sextro, Schwingungen. Wiesbaden: Springer Fachmedien Wiesbaden, 2016. doi: https://doi.org/10.1007/978-3-658-13821-9.

P. Kumar, R. Chandra, and S. P. Singh, “Interphase Effect on Fiber-Reinforced Polymer Composites”, Composite Interfaces, vol. 17, no. 1, pp. 15–35, Jan. 2010, doi: https://doi.org/10.1163/092764409x12580201111502

A. Treviso, B. Van Genechten, D. Mundo and M. Tournour, “Damping in composite materials: Properties and models”, Composites Part B: Engineering, vol. 78, pp. 144–152, Sep. 2015, doi: https://doi.org/10.1016/j.compositesb.2015.03.081.

Plastics — Determination of dynamic mechanical properties — Part 3: Flexural vibration — Resonance-curve method. ISO 6721-3, 2021.

J.-M. Berthelot, M. Assarar, Y. Sefrani and A. E. Mahi, “Damping analysis of composite materials and structures”, Composite Structures, vol. 85, no. 3, pp. 189–204, Oct. 2008, doi: https://doi.org/10.1016/j.compstruct.2007.10.024.

P. Bonfiglio and F. Pompoli, “Determination of the dynamic complex modulus of viscoelastic materials using a time domain approach”, Polymer Testing, vol. 48, pp. 89–96, Dec. 2015, doi: https://doi.org/10.1016/j.polymertesting.2015.09.016.

R. M. Crane and J. W. Gillespie, “Characterization of the vibration damping loss factor of glass and graphite fiber composites”, Composites Science and Technology, vol. 40, no. 4, pp. 355–375, Jan. 1991, doi: https://doi.org/10.1016/0266-3538(91)90030-s.

J. Ilg, S. J. Rupitsch and R. Lerch, “Determination of frequency and temperature dependent mechanical material properties by means of an Inverse Method”, WIT Transactions on Engineering Sciences, Jun. 2013, doi: https://doi.org/10.2495/mc130091.

K. De Belder, R. Pintelon, C. Demol and P. Roose, “Estimation of the equivalent complex modulus of laminated glass beams and its application to sound transmission loss prediction”, Mechanical Systems and Signal Processing, vol. 24, no. 3, pp. 809–822, Apr. 2010, doi: https://doi.org/10.1016/j.ymssp.2009.11.001.

F. Cortés and M. J. Elejabarrieta, “Viscoelastic materials characterisation using the seismic response”, Materials & Design, vol. 28, no. 7, pp. 2054–2062, Jan. 2007, doi: https://doi.org/10.1016/j.matdes.2006.05.032.

F. Urban, B. Armbruster and P. Middendorf, “Development and validation of a method for linear-viscoelastic characterization of the dynamic complex modulus of short-fiber reinforced plastics using flexural resonances”, Polymer Testing, vol. 94, p. 107055, Feb. 2021, doi: https://doi.org/10.1016/j.polymertesting.2021.107055.

K. Breuer, M. Stommel, and W. Korte, “Analysis and Evaluation of Fiber Orientation Reconstruction Methods,” Journal of Composites Science, vol. 3, no. 3, p. 67, Jul. 2019, doi: https://doi.org/10.3390/jcs3030067.

A. Kriwet and M. Stommel, “Arbitrary-Reconsidered-Double-Inclusion (ARDI) Model to Describe the Anisotropic, Viscoelastic Stiffness and Damping of Short Fiber-Reinforced Thermoplastics”, Journal of Composites Science, vol. 4, no. 2, p. 37, Apr. 2020, doi: https://doi.org/10.3390/jcs4020037.

A. Kriwet and M. Stommel, “The Impact of Fiber Orientation on Structural Dynamics of Short-Fiber Reinforced, Thermoplastic Components—A Comparison of Simulative and Experimental Investigations”, Journal of Composites Science, vol. 6, no. 4, p. 106, Apr. 2022, doi: https://doi.org/10.3390/jcs6040106.

F. Urban and P. Middendorf, “Macroscopic Modeling of the Linear Viscoelastic Vibration Behavior of Short Fiber Reinforced Plastics,” SAMPE 2020 | Virtual Series, 2020, doi: https://doi.org/10.33599/382/s.20.0015.

P. Kohnke, ANSYS - engineering analysis system theoretical manual for Rev. 4.4, 5th ed. Houston: Swanson Analysis Systems Inc., 1989.