Finite viscoelasticity of filled rubber: experiments and numerical simulation (Q1403056)

The authors derive constitutive equations for isothermal behavior of unfilled and particle-reinforced elastomers at finite strain. The time-dependent behavior of elatomers is described within the concept of transient networks that treats a rubbery polymer as a network of chains bridged by junctions (chemical and physical cross-links and entanglements). A filled rubber is thought of as a composite medium where inclusions with high and low concentration of junctions between chains are randomly distributed in the bulk material. The bulk medium is treated as a permanent network of long chains bridged by junctions. The time-dependent response of elastomer is attributed to termally activated rearrangement of strands in the domains with low concentration of junctions. The composite is treated as an incompressible and isotropic elastic medium having the density of the free energy of the form \(\psi= \psi^0+ V+ W\), where \(\psi^0\) is the free energy density in the stress-free state at the reference temperature, \(V\) is the free energy density corresponding to the thermal motion of chains, and \(W\) is the density of the strain energy. Constitutive equations are derived by using the standard procedure resulting from the laws of thermodynamics. These constitutive equations are applied to analyze stresses at uniaxial extension of a bar, and fair agreement is made clear between the results of numerical simulation and the observations in relaxation tests. To form a more exact idea of this paper, we present its contents: 1. Introduction; 2. Free energy density of filled rubber (2.1. Mechanical energy of host matrix; 2.2. Mechanical energy of regions with low concentration of junctions; 2.3. Mechanical energy of regions with high concentration of junctions); 3. Constitutive equations; 4. Uniaxial extension of a specimen; 5. Comparison with experimental data; 7. Discussion; 8. Concluding remarks; References.