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Research Papers

An Exact Result for the Macroscopic Response of Particle-Reinforced Neo-Hookean Solids

[+] Author and Article Information
Oscar Lopez-Pamies

Department of Mechanical Engineering, State University of New York, Stony Brook, NY 11794-2300oscar.lopez-pamies@sunysb.edu

These include the restriction that the rigid particles can only undergo rigid body rotations.

The shape and orientation of the particles is arbitrary at this stage.

That is, G is an operator (e.g., a differential operator) with respect to the stored-energy function W, so that it can depend, for instance, not just on W but also on any derivative nW/FnnN.

Here and subsequently, the order of the asymptotic correction terms will be omitted for notational simplicity.

J. Appl. Mech 77(2), 021016 (Dec 14, 2009) (5 pages) doi:10.1115/1.3197444 History: Received April 21, 2009; Revised July 07, 2009; Published December 14, 2009; Online December 14, 2009

Making use of an iterated homogenization procedure in finite elasticity, an exact and explicit result is derived for the macroscopic response of Neo-Hookean solids reinforced by a random and isotropic distribution of rigid particles. The key theoretical and practical features of the result are discussed in light of comparisons with recent approximations and full-field simulations.

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Figures

Grahic Jump Location
Figure 1

The effective shear modulus μ¯/μ at zero strain of isotropic particle-reinforced Neo-Hookean solids, as a function of the volume fraction of particles c. Plots are shown for the IH result 18 (solid line), the LAM, and LC results as given by the left-hand side of inequality 19 (dashed line), and the boundary element simulations of Eischen and Torquato (18) (filled circles).

Grahic Jump Location
Figure 2

Macroscopic response of isotropic particle-reinforced Neo-Hookean solids with random microstructures and various values of volume fraction of particles c. The macroscopic stress t¯/μ=(1/μ)∂Φ¯/∂λ¯ for c=0.2,0.4,0.6 ((a), (b), (c)), as a function of applied stretch λ¯. Results are shown for the IH result 16 (solid line), the LAM result 12 of deBotton (2) (dashed line), the LC estimate 20 of Lopez-Pamies and Ponte Castañeda (6) (dashed-dotted line), and the FE simulations of Moraleda (17) (circles).

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