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MSC: 00A79, 35J86
Rheological elements, constitutive equation, large deformations, hysteresis, dissipated energy
In this paper we deal with the mathematical modelling of rheological models with applications in various engineering disciplines and industry. We study the mechanical response of visco-elasto-plastic materials. We describe the basic rheological elements and focus our attention to the specific model of concrete, for which we derive governing equations and discuss its solution. We provide an application of rheological model involving rigid-plastic element as well - mechanical and mathematical model of failure of one dimensional construction member, straight beam. Herein, the physical model is considered with a homogeneous isotropic material of the beam, quasi static regime is supposed.
[1] Ionescu, I. R., Sofonea, M.: Functional and Numerical Methods in Viscoplasticity. Oxford University Press, (1993). MR 1244578
[2] Krejčí, P.: Hysteresis, Convexity and Dissipation in Hyperbolic Equations. Gakuto Intern. Ser.Math. Sci. Appl., Vol. 8, Gakkot{\bar o}sho, Tokyo (1996). MR 2466538
[3] Kuhnen, K.: Inverse Steuerung piezoelektrischer Aktoren mit Hysterese-, Kriech- und Superpositionsoperatoren (Berichte aus der Steuerungs- und Regelungstechnik). Gebundene Ausgabe, (2001).
[4] Minárová, M., Sumec, J.: Constitutive equations for selected rheological models in linear viscoelasticity. Advances and Trends in Engineering Sciences and Technologies II: Proc. of ESAT conference, CRC Press, (2016), pp.207-212.
[5] Minárová, M.: Mathematical Modeling of Phenomenological Material Properties - Differential Operator Forms of Constitutive equations. Slovak Journal of Civil Engineering Vol. 22/4(2014).
[6] Rabotnov, R. J.: Creep of Structural Elements. Moscow: Nauka, (1966). MR 0165783
[7] Sobotka, Z.: Reologie hmot a konstrukcí. Praha, Academia publishing house (1981).
[8] Sumec, J.: Mechanics - Mathematical Modeling of Materials Whose Physical Properties are Time Dependent. Internal Research Report, III-3-4/9.4 USTARCH-SAV Bratislava (1983).
[9] al., J. Sumec et: Elasticity and Plasticity in Civil Engineering. Slovak Technical University Bratislava (2007).
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