Abstract
This chapter discusses constitutive relations for linear viscoelastic media with infinitesimal strains. The viscoelastic behavior is typical of a number of materials that are extremely important for applications: polymers and plastics. A brief survey is provided of differential and fractional differential models in linear visco-elasticity. The chapter explains linear differential and fractional differential models. The integral models, the concept of adaptive links, properties of creep and relaxation measures, and basic thermodynamic potentials for an aging viscoelastic medium are also discussed. A new constitutive model for an aging visco-elastic material is developed. Two types of relaxation measures are distinguished: regular and singular. A version of the model of adaptive links is derived for the mechanical behavior of linear visco-elastic materials subjected to physical aging. Two types of links are distinguished: links arising at the instant of quenching (type I), and links emerging in the quenched material at a constant temperature (type II). The mechanical reponse in an aging medium is determined by three material functions: annihilation of links of type I, the breakage of links of type II, and reformation of links of type II.
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