Stressed State of a Viscoelastic Layer on the Rigid Foundation Under the Action of Concentrated Cyclic Loads
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STRESSED STATE OF A VISCOELASTIC LAYER ON THE RIGID FOUNDATION UNDER THE ACTION OF CONCENTRATED CYCLIC LOADS І. S. Skorodyns’kyi1, 2 and О. V. Maksymuk3
UDC 539.37
By using a generalized two-parameter model, we study main regularities of the deformation of an infinite viscoelastic layer on the rigid foundation under the action of concentrated cyclic loads. The process of transition to the steady-state conditions of deformation under periodic nonharmonic loading is simulated. The possibility of taking into account residual strains (displacements) in a layer made of the Kelvin–Voigt material and their role in the evaluation of the rate of transition into the steady-state mode are analyzed. Keywords: viscoelastic layer, generalized two-parameter model, cyclic load, vertical displacements, steady-state conditions, residual strains.
Introduction Cyclic loads are among the most widespread loads encountered in nature and engineering. This is why it is important to study their action on the inelastic media and structural elements in the case where the delay of the response of materials to external mechanical actions, stress relaxation, creep (yield), irreversible residual strains, and hysteresis losses are observed [1–3]. In [4], one can find the results of theoretical and experimental investigations of the accumulation of irreversible residual strains in the road asphalt concrete under cyclic loads. In the cited work, asphalt concrete was studied either as a Maxwell solid liquid [1] or as a Boguslavskii viscoelastoplastic medium. The mechanical behavior of viscoelastic materials under the conditions of low-cycle deformation was studied in [5]. The time dependence of their subsidence (degree of consolidation) under the action of normal homogeneously distributed loads varying in time according to different laws was studied within the framework of the mechanics of soils (theory of one-dimensional consolidation) in [6–10]. Note that, in [6–8], the skeleton of soil was regarded as an elastic medium. Moreover, its viscoelastic properties were taken into account in [9, 10]. In the present paper, within the framework of a generalized two-parameter model [11–13], we study the mechanical behavior of an infinite viscoelastic layer on the rigid foundation under the action of concentrated cyclic loading. Moreover, we analyze the time dependence of the vertical displacements of loaded surfaces for different materials of the layer, the steady-state conditions of deformation, and residual strains under the action of periodic rectangular loading. 1 2 3
Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine. Corresponding author; e-mail: [email protected]. I. Franko Lviv National University, Lviv, Ukraine.
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 56, No. 1, pp. 82–88, January–February, 2020. Original article submitted December 12, 2018. 82
1068-820X/20/5601–0082
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Springer Science+Business Media, LLC
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