Abstract
The paper presents an extension to viscoelastic composites of a former developed numerical homogenization procedure which was used for elastic and piezoelectric material systems. It is based on an unit cell model using the finite element method. In the paper a brief description of the basic equations and the homogenization algorithm with specific attention to the numerical model is given. The investigated composites consist of a viscoelastic matrix with unidirectional embedded cylindrical elastic fibers. Hence the homogenized behavior of the composite is also viscoelastic. Consequently the effective coefficients are time-dependent. The geometrical shape of the unit cell is rhombic which allows to analyze a wide range of nonstandard unidirectional fiber distributions. Otherwise it includes the special cases for square and hexagonal fiber arrangements which can be used for comparisons with other solutions. Here results are compared with an analytical homogenization method. Furthermore the influences of rhombic angle and fiber volume fraction on effective coefficients are investigated. In addition two limit cases are considered. One is with air as inclusions which is equivalent to a porous media and the other is the pure matrix without fibers.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berger H, Kari S, Gabbert U, Rodríguez-Ramos R, Bravo-Castillero J, Guinovart-Díaz R, Sabina FJ, Maugin GA (2006) Unit cell models of piezoelectric fiber composites for numerical and analytical calculation of effective properties. Smart Mater Struct 15:451–458
Cruz-González OL, Rodríguez-Ramos R, Otero JA, Bravo-Castillero J, Guinovart-Díaz R, Martínez-Rosado R, Sabina FJ, Dumont S, Lebon F, Sevostianov I (2018) Viscoelastic effective properties for composites with rectangular cross-section fibers using the asymptotic homogenization method. In: Altenbach H, Pouget J, Rousseau M, Collet B, Michelitsch T (eds) Generalized Models and Non-Classical Approaches in Complex Materials - Vol. 1, Springer, Singapore, Advanced Structured Materials, vol 92, pp 203–222
Daridon L, Licht C, Orankitjaroen S, Pagano S (2016) Periodic homogenization for Kelvin-Voigt viscoelastic media with a Kelvin-Voigt viscoelastic interphase. European Journal of Mechanics - A/Solids 58:163–171
Gutierrez-Lemini D (2014) Engineering Viscoelasticity. Springer, New York
Haasemann G, Ulbricht V (2009) Numerical evaluation of the viscoelastic and viscoplastic behavior of composites. Technische Mechanik 30:122–135
Kari S, Berger H, Rodríguez-Ramos R, Gabbert U (2007) Numerical evaluation of effective material properties of transversely randomly distributed unidirectional piezoelectric fiber composites. Journal of Intelligent Material Systems and Structures 18(4):361–372
Nguyen H, Pastor J, Muller D (1995) A method for predicting linear viscoelastic mechanical behavior of composites, a comparison with other methods and experimental validation. European Journal of Mechanics - A/Solids 14:939–960
Pathan MV, Tagarielli VL, Patsias S (2017) Numerical predictions of the anisotropic viscoelastic response of uni-directional fibre composites. Composites Part A: Applied Science and Manufacturing 93:18–32
Tang T, Felicelli SD (2016) Effective creep response and uniaxial tension behavior of linear viscoelastic polymer composites. In: Sano T, Srivatsan TS (eds) Advanced Composites for Aerospace, Marine, and Land Applications II, Springer International Publishing, Cham, pp 335–345
To QD, Nguyen ST, Bonnet G, Vu MN (2017) Overall viscoelastic properties of 2d and two-phase periodic composites constituted of elliptical and rectangular heterogeneities. European Journal of Mechanics - A/Solids 64:186–201
Würkner M, Berger H, Gabbert U (2011) On numerical evaluation of effective material properties for composite structures with rhombic fiber arrangements. International Journal of Engineering Science 49(4):322–332
Yancey RN, Pindera MJ (1990) Micromechanical analysis of the creep response of unidirectional composites. Journal of Engineering Materials and Technology 112(2):157–163
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Berger, H., Würkner, M., Otero, J.A., Guinovart-Díaz, R., Bravo-Castillero, J., Rodríguez-Ramos, R. (2018). Unit Cell Models of Viscoelastic Fibrous Composites for Numerical Computation of Effective Properties. In: Altenbach, H., Pouget, J., Rousseau, M., Collet, B., Michelitsch, T. (eds) Generalized Models and Non-classical Approaches in Complex Materials 1. Advanced Structured Materials, vol 89. Springer, Cham. https://doi.org/10.1007/978-3-319-72440-9_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-72440-9_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-72439-3
Online ISBN: 978-3-319-72440-9
eBook Packages: EngineeringEngineering (R0)