Characteristics of spherical stress wave propagation in the standard linear solid material

Abstract

Based on the standard linear solid model, the solutions in Laplace domain, such as particle velocity v, particle displacement u, radial stress σr, tangential stress σθ, radial strain εr, tangential strain εθ, reduced velocity potential γ (RVP), and reduced displacement potential ψ (RDP), are derived from the spherical wave equations. The propagating characteristics of these physical quantities, as mentioned above, are calculated by using Crump algorithm for inverse Laplace transformation. The numerical inversion results reveal that the initial response to strong discontinuity spherical stress wave in viscoelastic material is purely elastic response. The strong discontinuities, such as σr, σθ, εr, εθ and v, contain geometrical attenuation and viscoelastic damping in the process of wave propagation. The variables, such as σr, σθ, εr, εθ,u and ψ, converge to steady values as time approaches to infinity. The peak values of RVP γ and RDP ψ, which are constant in a purely elastic material, are steadily reduced with the spreading distance increasing in viscoelastic material. The steady values of ψ are in inverse relation to the static shear modulus Ga, and directly proportional to the steady cavity pressure and the cube of the cavity radius r.