We analyze approximate approaches to the modeling of the thermomechanical behavior of physically nonlinear materials under harmonic loading. The approaches are based on various harmonic-linearization schemes and the concept of complex moduli. Mechanical and mathematical features of various schemes are considered. Some modifications of the model are proposed to account for various aspects of material behavior under harmonic loading. The problems of vibration and dissipative heating of physically nonlinear bodies are formulated. The main thermomechanical characteristics are analyzed for some classes of problems.Introduction. Many structural elements and technological objects experience cyclic deformation during use or treatment [2,3,[30][31][32]61]. Loads are sometimes so high that the deformation process becomes nonlinear and mechanical elements may suffer low-cycle fatigue. Apart from purely mechanical fatigue failure, polymeric products may undergo thermal failure, i.e., softening or even melting due to vibrational heating, which is because of high hysteresis losses and low heat conductivity [32,59,60].In the cases mentioned, modeling the thermomechanical behavior of nonlinearly dissipative materials is one of the major tasks to be accomplished in evaluating the durability or working characteristics of cyclically deformed bodies.There are currently two approaches to solve such problems. One employs the constitutive equations valid for arbitrary or, at least, rather wide classes of loading histories. Quasistatic problems for inelastic bodies, specifically beams and plates, were addressed in [77,81,82]; and vibration problems for viscoplastic structures in [66,73,78,79].This approach was used to solve problems for thin-walled structural members (mainly beams) in a practically important formulation that allows for the elastoviscoplasticity and geometrical nonlinearity of the material. Such formulations in combination with well-tested computational schemes allow us to analyze mechanical effects of the interaction of physical and geometrical nonlinearities, specifically snap buckling of initially curved elements [92] and chaotic motions in such elements under harmonic loading [42,89].By using exact models under harmonic loading, we can study a number of effects accompanying vibrations such as snap buckling, drift of average plastic strain, dynamic buckling, chaotic motions, etc. Study of such processes is difficult because of
The vibrations and self-heating of a viscoelastic prism with a cylindrical inclusion under harmonic loading are studied through numerical simulation. The effects of the stiffness of the inclusion and the mechanical and kinematic types of loading on kinetics, spatial temperature distribution, and thermal instability parameters are examined Keywords: viscoelastic material, vibrations heating, rectangular prism, cylindrical inclusion Introduction. Intensive vibrations of viscoelastic bodies are generally accompanied by vibrational heating, which is because of the conversion of mechanical energy into heat. Heating can noticeably reduce the performance and life of structural members such as rubber shock absorbers, solid-propellant engines [11,26], etc. Also, vibrational heating is a crucial factor for some high-intensity processes such as ultrasonic plastic welding [7][8][9]. The stationary vibrations and vibrational heating of linear viscoelastic bodies were studied and associated models were validated in [20][21][22]. The results obtained there were generalized in [2,11,[16][17][18][19]25]. The cited publications employed the concept of complex moduli, which was convincingly substantiated, both experimentally and theoretically, during the early development of the theory of linear thermoviscoelasticity in [1, 12, 14, 15, etc.].One of the special features of vibrational heating is the effect of thermal instability. It manifests itself as abrupt increase in temperature and leads to thermal fatigue failure of structural members [6,14,15,26]. Relevant results are reviewed in [3,4,16,18,19,23].Fracture usually sets in near stress concentrators. It is these areas that become sources of vibrational heating. Such processes in bodies with cylindrical inclusions under compressive and shear loading of kinematic type were studied in [8,9]. Vibrational heating in laminated prisms acted upon by a vibrating punch was addressed in [13,16].Intensive high-frequency loading of a rectangular prism with an inclusion produces a number of specific effects. The major effect is concentration of stress, dissipation rate, and temperature. It was established that the level of vibrational heating is strongly dependent on the type of loading and the stiffness of the inclusion.The present paper studies the kinetics of vibrational heating and thermal instability of a rectangular prism with an inclusion under harmonic compressive loading of mechanical type. We will compare the mechanical and kinematic types of excitation and examine the cases of rigid and soft inclusion.
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