On the macroscopic response, microstructure evolution, and macroscopic stability of short-fiber-reinforced elastomers at finite strains: II – Representative examples

Abstract

In Part I of this work, we presented a homogenization-based constitutive model for the overall behavior of reinforced elastomers consisting of aligned, spheroidal particles distributed randomly in an incompressible, hyperelastic matrix. In particular, we provided analytical estimates for the effective stored-energy functions of the composites, as well as for the associated average particle rotations under finite deformations. The rotation of the particles is found to be very sensitive to the specific loading conditions applied, and is such that the particles tend to align themselves with the largest tensile direction. In addition, we obtained corresponding formulae for the detection of macroscopic instabilities in these composites. With the objective of illustrating the key features of the analytical results presented in Part I, we conduct here a more detailed study of these results for several representative values of the microstructural and loading parameters, as well as matrix properties. More specifically, this study deals with neo-Hookean and Gent elastomers reinforced with spheroidal particles of prolate and oblate shapes with various aspect ratios and volume fractions, subjected to aligned and non-aligned macroscopic loading conditions. In addition, to assess the accuracy of the model, we compare our results with corresponding finite element results available from the literature for the special case of spherical particles, and good agreement is found. For non-spherical particles, the results indicate that the possible rotation of the particles has a major influence on the overall response of the elastomeric composites. Furthermore, it is found that the composite may develop macroscopic shear localization instabilities, as a consequence of the geometric softening induced by the sudden rotation – or flopping – of the particles, when a sufficiently large amount of compression is applied along the long axes of the particles.

Keywords:

• microstructure
• large deformation
• bifurcation
• flopping-type instability
• geometric softening

Acknowledgments

Parts of this article were written while PPC was visiting IMDEA Materials Institute in Madrid, Spain.

Notes

1 The strain at which the composite locks up because of lock up in the elastomeric matrix phase

This material is based upon work supported by the National Science Foundation [grant number CMMI-0969570].