Calculating the Critical Parameters Characterizing the Thermal Instability of a Viscoelastic Prism with a Stress Concentrator under Harmonic Compression

Thermal and mechanical response of particulate composite plates under inertial excitation

“…Prior investigations have highlighted, for example, the fact that heating within materials due to cyclic deformation is often attributable to a phase delay between fluctuating stress and strain fields. 4 Likewise, in the context of vibrothermography, Renshaw 5 and others [6][7][8] have shown that high-frequency excitation is highly effective at eliciting thermal responses near stress concentrations, such as cracks, voids, and inclusions. While most of the prior work in thermography specifically targets heating near defects, research in this area has also highlighted stressinduced heating along the modal structure of various systems.…”

Thermal instability of a layered rectangular viscoelastic prism under high-frequency compressive loading

“…The vibrational heating of bodies with stress concentrators such as notches or cylindrical inclusions was studied in [9][10][11]. It was revealed that heating localizes around stress concentrators.…”

“…Relevant results are reviewed in [10][11][12]14]. The thermal instability of a rectangular prism with a cylindrical inclusion was examined in [10].…”

“…The physical and mechanical characteristics of the polymers are assumed temperature-dependent. The critical values of the load parameter are determined by the method of stationary diagrams developed in [11].…”

Dissipative heating of a viscoelastic cylinder steadily rolling over a rigid foundation

“…where the dissipative function is defined by the following formula [5][6][7]: 9) and the complex equations of state σ rr = λ∆ + 2µε rr , σ ϕϕ = λ∆ + 2µε ϕϕ , σ rϕ = 2µε rϕ , (1.10) where all quantities are complex, so that λ = λ′ + iλ″ and µ = µ′ + iµ″, and ∆ is the coefficient of volumetric expansion. The above relations should be supplemented with the mechanical boundary conditions 12) and the thermal boundary conditions (convective heat exchange)…”