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.
Highlights
A fundamental problem for particle-reinforced composites (PRC) is to predict the overall mechanical behavior of the composite based on the mechanical properties of the constituents and the microstructure of the composites. Guth (1945) extended Einstein’s linear estimate originally developed for viscous fluid and proposed a second order⇑ Corresponding authors
For composites with nonlinear phase(s), there is no theoretical estimates for the minimum Representative Volume Element (RVE) size, various numerical investigations showed that similar sizes of RVE models can be used to obtain predictions with the same degree of accuracy (Segurado and Llorca, 2005, 2006)
After the random distribution of the particles in the 16 RVE models is verified in the previous section, the isotropy of the mechanical behavior of the RVE models is doublechecked by direct simulations of the responses of the RVE models subjected to uniaxial tension/compression along various directions
Summary
A fundamental problem for particle-reinforced composites (PRC) is to predict the overall mechanical behavior of the composite based on the mechanical properties of the constituents and the microstructure of the composites. Guth (1945) extended Einstein’s linear estimate originally developed for viscous fluid and proposed a second order. Because of the fundamental difficulties caused by the related geometrical and material nonlinearity, even for the simplest PRC defined above, it is still very difficult (if not impossible) to derive an analytical expression for the strain energy field in the volume V under a general deformation state (e.g., the explicit strain energy approximation obtained in (Avazmohammadi and Castaneda, 2012) for incompressible neo-Hookean composite with rigid reinforcement has about 200 terms). Based on the macro-variables defined in Hill (1972), to determine the mechanical behavior of hyperelastic composites, for any given ‘‘overall’’ deformation (represented by the average deformation gradient F), appropriate displacement boundary conditions which satisfy (5) are applied to a geometrical representative model and the corresponding stress/strain fields can be computed numerically (usually by FEM). If sufficient values of W are computed numerically, for some simple composites, the data might suggest a simple function Wðk; k2Þ or WðI1; I2Þ, as illustrated later in the paper
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