Numerical modeling of nonlinear deformation of polymer composites based on hyperelastic constitutive law

Abstract

Fiber reinforced polymer (FRP) composites exhibit nonlinear and hyperelastic characteristics under finite deformation. This paper investigates the macroscopic hyperelastic behavior of fiber reinforced polymer composites using a micromechanical model and finite deformation theory based on the hyperelastic constitutive law. The local stress and deformation of a representative volume element are calculated by the nonlinear finite element method. Then, an averaging procedure is used to find the homogenized stress and strain, and the macroscopic stress-strain curves are obtained. Numerical examples are given to demonstrate hyperelastic behavior and deformation of the composites, and the effects of the distribution pattern of fibers are also investigated to model the mechanical behavior of FRP composites.

Keywords

composites / hyperelastic / finite deformation / homogenization / micromechanics

References

[1] DeBotton G, Hariton I, Socolsky E A. Neo-Hookean fiber-reinforced composites in finite elasticity. Journal of the Mechanics and Physics of Solids, 2006, 54: 533–559

[2] Guiot B, Nadot-Martin C, Dragon A. Towards a non-linear micromechanics-based analysis for particulate composites. Composites Science and Technology, 2006 ( to appear)

[3] Milani A S, Nemes J A. An intelligent inverse method for characterization of textile reinforced thermoplastic composites using a hyperelastic constitutive model. Composites Science and Technology, 2004, 64: 1565–1576

[4] Guz I A, Herrmann K P. On the lower bounds for critical loads under large deformations in non-linear hyperelastic composites with imperfect interlaminar adhesion. European Journal of Mechanics A/Solids, 2003, 22: 837–849

[5] Castañeda P P. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—Theory. Journal of the Mechanics and Physics of Solids, 2002, 50: 737–757

[6] Lopez-Pamies O, Castañeda P P. Second-order estimates for the large-deformation response of particle-reinforced rubbers. Mecanique, 2003, 331: 1–8

[7] Lahellec N, Mazerolle F, Michel J C. Second-order estimate of the macroscopic behavior of periodic hyperelastic composites: theory and experimental validation. Journal of the Mechanics and Physics of Solids, 2004, 52: 27–49

[8] Yin H M, Sun L Z, Chen J S. Micromechanics-based hyperelastic constitutive modeling of magnetostrictive particle-filled elastomers. Mechanics of Materials, 2002, 34: 505–516

[9] Pruchnicki E. Overall properties of thin hyperelastic plate at finite strain with edge effects using asymptotic method. International Journal of Engineering Science, 1998, 36: 973–1000

[10] Li M, Tucker III C L. Modeling and simulation of two-dimensional consolidation for thermoset matrix composites. Composites: Part A, 2002, 33: 877–892

[11] Dubouloz-Monnet F, Mele P, Alberola N D. Glass fibre aggregates: consequences on the dynamic mechanical properties of polypropylene matrix composites. Composites Science and Technology, 2005, 65: 437–443

[12] Yang Q S, Becker W. A comparative investigation of different homogenization methods for prediction of the macroscopic properties of composites. Computer Modeling in Engineering & Science, 2004, 6(4): 319–332

[13] Yang Q S, Qin Q H. Modelling the effective elasto-plastic properties of unidirectional composites reinforced by fibre bundles under transverse tension and shear loading. Materials Science and Engineering A, 2003, 344: 140–145

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg