Dear Colleagues,

Viscoelasticity denotes the joint properties of elasticity and viscosity, and hence describes materials with both fluid and solid properties at the same time. Well-known accounts of viscoelasticity can be traced back to Maxwell, Boltzmann, and Kelvin. While Maxwell and Kelvin models describe the viscoelastic behavior via first-order differential equations linking stress and strain (rheological models), in the Boltzmann theory, the stress is determined by a functional of the past history of the strain. Physically, these schemes are the prototypes forming the basis of current models of viscoelastic materials.

This Special Issue is devoted to recent advances in the modeling of viscoelastic materials, possibly interacting with electromagnetic fields and temperature fields, along with mathematical properties of the solution to associated evolution problems. The following are some topics to be investigated in this Special Issue.

The modeling of viscoelastic materials is developed within the domain of materials with fading memory. The model is based on the classical linear functional for the stress–strain constitutive relationship; to account for aging properties, the kernel is allowed to depend explicitly on time. The thermodynamic analysis yields a set of properties characterizing the functional for both aging and non-aging materials. Likewise, a rate-type (Maxwell) model is shown to account for hysteresis effects in viscoelasticity. Further, viscoelastic materials are considered with a singular kernel.

The interaction of deformation with the temperature field is investigated for a nonlinear viscoelastic beam with different conditions at the boundary; the existence and uniqueness of the solution are proven along with an exponential decay property.

More-involved models of viscoelastic materials are considered by accounting for the effects of magnetic or electric fields. Basic schemes for the modeling of such materials may contain rate-type equations (as with the Cattaneo–Maxwell law for heat flux) or fading memory functionals (as with the Boltzmann model) or possibly with two types of constitutive relations. Rate-type equations for the magnetization are considered in light of some customary evolution equations in the physical literature.

Prof. Dr. Angelo Morro
Guest Editor

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• constitutive relations
• materials with memory
• rate-type equations
• thermodynamic consistency
• relaxation and creep
• aging
• hysteresis
• existence and uniqueness