Experimental testing and nonlinear viscoelastic modeling of filled rubber

Owing to its unique physical properties, rubber plays a keyrole in countless industrial applications. Tires, vibration absorbers and shoe soles are only but a few of the myriad uses of natural and synthetic rubber in an industry which in 2009 had an estimated market value of 2 billion euro. Despite a peculiar internal structure, the macroscopic behavior of filled-rubber is reminiscent of several biological soft tissues. While rubber is internally constituted by flexible long chain molecules that intertwine with each other, a similar role is played, in soft-tissues, by collagen fiber bundles. As a consequence, both classes of materials are able to sustain large strains and exhibit the characteristics of a viscous fluid and an elastic solid. In industry, the requirement to model complex geometrical structures made of materials exhibiting a nonlinear constitutive behavior is a compelling reason to use Finite Element Analysis (FEA) software. The predictive capabilities of these numerical tools strongly rely upon the capabilities of the underlying model to describe the material’s rheological properties. The possibility of simulating accurately the material behavior over the entire working range avoids the use of excessive number of prototypes, thereby reducing the need for expensive and difficult experimental tests; consequently, development costs can be drastically reduced. The theory of viscoelasticity is crucial in describing materials, such as filled rubber, which exhibit time dependent stress-strain behavior. In many engineering applications, such as the estimate of the rolling resistance of tires and hysteretic losses in soft biological tissues, the energy dissipation is a primary feature to be predicted. In addition, in the usual operative range, tires, shock absorbers and other rubber components bear finite dynamic deformations. Therefore, a reliable constitutive equation must be assessed within the theory of nonlinear viscoelasticity. A review of the literature revealed significantly more well-established studies dealing with hyperelastic constitutive models, than those dealing with finite viscoelasticity. Over the years, many hyperelastic models able to describe all the relevant aspects of the quasi-static response have been introduced. Furthermore, the American norms (ASTM D412, ASTM D575, ASTM D945, ASTM D6147, ASTM D1456) establish all the experimental techniques to identify the material constitutive parameters. In this context, many authors have recently addressed the problem of finite amplitude wave propagation or focused their interest upon particular boundary value problems. On the other hand, there is a lack of well-established nonlinear viscoelastic models capable of describing all the relevant effects in the material response. Moreover, a standardization similar to that concerning the static norms is yet to be achieved. The usual methodology provides for small harmonic deformations superimposed on a large static displacement. However, such a prescription does not allow the capture of many of the relevant nonlinear phenomena. In the literature, experimental evidence concerning finite dynamic deformations is rarely reported.