Modeling the response of filled elastomers at finite strains by rigid-rod networks |
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Authors: | A D Drozdov A Dorfmann |
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Institution: | (1) Institute for Industrial Mathematics, 4 Hanachtom Street, 84311 Beersheba, Israel e-mail: aleksey@cs.bgu.ac.il, IL;(2) Institute of Structural Engineering, 82 Peter Jordan Street, 1190 Vienna, Austria, AT |
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Abstract: | Summary A constitutive model is developed for the isothermal response of particle-reinforced elastomers at finite strains. An amorphous
rubbery polymer is treated as a network of long chains bridged to permanent junctions. A strand between two neighboring junctions
is thought of as a sequence of rigid segments connected by bonds. In the stress-free state, a bond may be in one of two stable
conformations: flexed and extended. The mechanical energy of a bond in the flexed conformation is treated as a quadratic function
of the local strain, whereas that of a bond in the extended conformation is neglected. An explicit expression is developed
for the free energy of a network. Stress–strain relations and kinetic equations for the concentrations of bonds in various
conformations are derived using the laws of thermodynamics. In the case of small strains, these relations are reduced to the
constitutive equation for the standard viscoelastic solid. At finite strains, the governing equations are determined by four
adjustable parameters which are found by fitting experimental data in uniaxial tensile, compressive and cyclic tests. Fair
agreement is demonstrated between the observations for several filled and unfilled rubbery polymers and the results of numerical
simulation. We discuss the effects of the straining state, filler content, crosslink density and temperature on the adjustable
constants.
Received 3 January 2001; accepted for publication 12 July 2001 |
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Keywords: | Elastomer Finite Strain Constitutive Equation Viscoelasticity Cyclic Test |
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