Analysis of the Viscoelastic Sphere Impact against a Viscoelastic Uflyand-Mindlin Plate considering the Extension of Its Middle Surface

In the present paper, the problem on impact of a viscoelastic sphere against a viscoelastic plate is considered with due account for the extension of plate’s middle surface and local bearing of sphere and plate’s materials via the Hertz theory. The standard linear solid models with conventional derivatives and with fractional-order derivatives are used as viscoelastic models, respectively, outside and within the contact domain. As a result of impact, transient waves (surfaces of strong discontinuity) are generated in the plate, behind the wave fronts of which up to the boundaries of the contact domain the solution is constructed in terms of one-term ray expansions due to short-time duration of the impact process. The motion of the contact zone occurs under the action of extension forces acting in the plate’s middle surface, transverse force, and the Hertzian contact force. The suggested approach allows one to find the time-dependence of the impactor’s indentation into the target and the Hertzian contact force.

Research on the Thermal Cavitation Problem of a Preexisting Microvoid in a Viscoelastic Sphere

The cavitation problem of a preexisting microvoid in the incompressible viscoelastic sphere subjected to the uniform temperature field was studied in this paper. Based on the finite logarithmic strain measure for geometrically large deformation, the nonlinear mathematical model of this problem was established by employing the Kelvin-Voigt differential type constitutive equation of thermoviscoelasticity. Adopting the dimensionless transformation of each parameter, growth curves of the microvoid radius increasing with the temperature were given. And the results indicated that the generation of cavity could be regarded as the idealized model of microvoid growth. A parametric study, including the influences of the external temperature, the initial microvoid radius, and the material parameter on the microvoid radius, was also conducted. The sudden growth of infinitely large sphere with a preexisting microvoid could also achieved by the finitely large sphere.

Viscosity Measurement by the Free Vibrations of Homogeneous Viscoelastic Sphere

In this paper, a nondestructive method to measure bulk and shear viscosities of a homogeneous viscoelastic sphere using free vibration is investigated by taking into account a single Voigt model for viscous and elastic stress tensors. For the viscosity measurement, Q value characterizing the damping due to the viscous effect is used. The formulation of the Q value for spheroidal and torsional modes is theoretically made based on the redefinition of the coefficients of bulk and shear viscosities as positive values. Newly introduced coefficients A and B constituting Q value formula, which correspond to bulk and shear deformations in the free vibration, are numerically calculated for spheroidal and torsional modes, respectively. The method to measure the viscosity by using the observed values of vibration and coefficients A and B is presented, and the example to apply the method is also shown. This study may find applications in rheology of soft material where viscous effects of spherical structures matter.