Introduction

The engineering uses of rubber have expanded well beyond traditional products such as tires and seals. Today elastomeric, or rubber-like, components can be found in a diverse set of constructs including engine mounts, building foundations, belts, and fenders (see [13], [22]). Increasingly, the applications of rubber are becoming more sophisticated, as exemplified by the use of rubber bearings in bridges which allow for thermal expansions of the deck without placing excessive loads on the bridge supports (see [15]).

In current engineering applications, elastomer composites are typically filled with inactive particles such as carbon black or silica. If active fillers were used, such as piezoelectric, magnetic, or conductive particles, the resulting controllable elastomer could be used in products such as active or smart vibration suppression devices (e.g. see [8], [17], [18]). As these new materials are developed, the role of design will increase in both complexity and importance. In particular, the capability to predict the dynamic mechanical response of the components will become increasingly valuable.

The many desirable characteristics of rubber as a design component, which include the ability to undergo large elastic deformations and provide significant damping with near incompressibility, are also contributing factors to the complications arising in the process of formulating models. Damping is highly complex, and the strain history, rate of loading, environmental temperature, and amount and type of filler affect the mechanical response in a nontrivial manner. Additionally, many elastomers exhibit strong hysteresis characteristics similar to those found in shape-memory alloys and piezoceramic actuators. Hysteretic effects in an elastomer include a time-history-dependent stress–strain constitutive law.