| Abstract: | The behavior of an open mechanical dissipative system formed by a viscoelastic hardening body and an elastic working element
used for the energy transfer between the testing machine and the deformed body is described by a third-order dynamic differential
equation with controlling parameters that depend on the reduced mass and stiffness of the system, its viscous resistance,
the degree of strain hardening, the type of the stressed state of the body, and the dissipation of energy in a viscous ambient
medium. We analyze the dynamics of uniaxial tension of the deformed body below and above its elasticity limit for the case
where the forces induced in the process of motion are determined by the kinematics of the testing machine with prescribed
motion. We establish the dynamic nature of the nonlinear section of the tensile stress-strain diagram beyond the elasticity
limit of the viscoelastic body corresponding to the so-called “nonlinear elasticity”. It is shown that the appearance of this
section is connected with a transient relaxation process. Upon the termination of this process, the forces acting in the system
are determined by the viscous flow of the body corresponding to its yield limit. Above the elasticity limit of the body, we
observe the formation of a bistable state of the system caused by changes in the controlling parameters and lag effects and
leading to its macroscopic acoustic activity.
I. N. Frantsevich Institute for Problems in Material Science, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated
from Problemy Prochnosti, No. 4, pp. 16–27, July–August, 1998. |
