On microstructure evolution in fiber-reinforced elastomers and implications for their mechanical response and stability

O. LOPEZ-PAMIES; M. I. IDIART; Z. LI

JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY-TRANSACTIONS OF THE ASME

ASME-AMER SOC MECHANICAL ENG

Año: 2011 vol. 133 p. 110071 - 1100710

0094-4289

Lopez-Pamies and Idiart [Lopez-Pamies, O., Idiart, M.I., 2010, Fiber-reinforced hyperelastic solids: A realizable homogenization constitutive theory. Journal of Engineering Mathematics, doi:10.1007/s10665-009-9359-y.] have recently put forward a homogenization theory with the capability to generate exact results not only for the macroscopic response and stability, but also for the evolution of the microstructure in fiber-reinforced hyperelastic solids subjected to finite deformations. In this paper, we make use of this new theory to construct exact, closed-form solutions for the change in size, shape, and orientation undergone by the underlying fibers in a model class of fiber-reinforced hyperelastic solids along arbitrary 3D loading conditions. Making use of these results we then establish connections between the evolution of the microstructure and the overall stress-strain relation and macroscopic stability in fiber-reinforced elastomers. In particular, we show that the rotation of the fibers may lead to the softening of the overall stiffness of  fiber-reinforced elastomers under certain loading conditions. Furthermore, we show that this geometric mechanism is intimately related to the development of long-wavelength instabilities. These findings are discussed in light of comparisons with recent results for related material systems.