Wave propagation in continuous elastic and viscoelastic media: a comprehensive systematic review

Abstract

Wave propagation in continuous elastic and viscoelastic media is vast and has been adopted for long. It has played important roles in various areas of specialization, including structural dynamics, earthquake science, material testing, non-destructive evaluation, biomechanics, and energy systems. In conceptual elastic assumption, elastic media propagate mechanical waves with negligible energy loss while Viscoelastic media undergo elastic deformation, and time-dependent energy loss is defined by attenuation, dispersion and frequency-dependent phase velocity. Waves in complex media can now be simulated with the assistance of Numerical methods such as finite-difference, finite-element, spectral-element, homogenization and auxiliary-variable methods. This review considers mathematical models and very recent developments in the theory of wave propagation in continuous elastic and viscoelastic media. This review also focuses on classical elastic models versus Kelvin–Voigt, standard linear solid, generalized Zener, fractional and nonlocal viscoelastic formulations. The results shows that viscosity and heterogeneity of the material can greatly influence the amplitude, transmission, phase velocity and frequency response of the wave.  Viscoelasticity may reduce the energy of transmitted waves and create frequency-dependent attenuation and dispersion. This review draws the conclusion that viscoelastic effects must be included in the modelling of materials, where dissipation and time-dependent deformation are of importance. Advanced constitutive models and numerical techniques can present better description of the real wave behaviour and have important applications to structural health monitoring, seismic analysis, impact protection, composite materials and nondestructive evaluation. Research is moving towards combining physics and AI, where physics provides the foundation, and AI focuses on complex calculations.