Dynamics of uniaxial tension of a viscoelastic strain-hardening body in a system with one degree of freedom. Part 1. Prescribed motion
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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.
KeywordsStrain Hardening Viscous Flow Elasticity Limit Rheological Model Constant Strain Rate
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