Elsevier

Mechanics of Materials

Volume 70, March 2014, Pages 1-17
Mechanics of Materials

Mechanical modeling of incompressible particle-reinforced neo-Hookean composites based on numerical homogenization

https://doi.org/10.1016/j.mechmat.2013.11.004Get rights and content
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Highlights

  • Mechanical behavior of particle reinforced neo-Hookean composite is studied numerically.

  • Classical three-phase model can be extended to finite deformation regime.

  • Effects of volume fraction and stiffness contrast are investigated.

Abstract

In this paper, the mechanical response of incompressible particle-reinforced neo-Hookean composites (IPRNC) under general finite deformations is investigated numerically. Three-dimensional Representative Volume Element (RVE) models containing 27 non-overlapping identical randomly distributed spheres are created to represent neo-Hookean composites consisting of incompressible neo-Hookean elastomeric spheres embedded within another incompressible neo-Hookean elastomeric matrix. Four types of finite deformation (i.e., uniaxial tension, uniaxial compression, simple shear and general biaxial deformation) are simulated using the finite element method (FEM) and the RVE models with periodic boundary condition (PBC) enforced. The simulation results show that the overall mechanical response of the IPRNC can be well-predicted by another simple incompressible neo-Hookean model up to the deformation the FEM simulation can reach. It is also shown that the effective shear modulus of the IPRNC can be well-predicted as a function of both particle volume fraction and particle/matrix stiffness ratio, using the classical linear elastic estimation within the limit of current FEM software.

Keywords

Particle-reinforced composite
Representative volume element (RVE)
Neo-Hookean
Numerical homogenization
Hyperelasticity

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