Visco-elastic-plastic modelling

Koppová, Jana; Minárová, Mária; Sumec, Jozef

  • Proceedings of Equadiff 14, Publisher: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing(Bratislava), page 173-180

Abstract

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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.

How to cite

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Koppová, Jana, Minárová, Mária, and Sumec, Jozef. "Visco-elastic-plastic modelling." Proceedings of Equadiff 14. Bratislava: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, 2017. 173-180. <http://eudml.org/doc/294936>.

@inProceedings{Koppová2017,
abstract = {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.},
author = {Koppová, Jana, Minárová, Mária, Sumec, Jozef},
booktitle = {Proceedings of Equadiff 14},
keywords = {Rheological elements, constitutive equation, large deformations, hysteresis, dissipated energy},
location = {Bratislava},
pages = {173-180},
publisher = {Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing},
title = {Visco-elastic-plastic modelling},
url = {http://eudml.org/doc/294936},
year = {2017},
}

TY - CLSWK
AU - Koppová, Jana
AU - Minárová, Mária
AU - Sumec, Jozef
TI - Visco-elastic-plastic modelling
T2 - Proceedings of Equadiff 14
PY - 2017
CY - Bratislava
PB - Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing
SP - 173
EP - 180
AB - 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.
KW - Rheological elements, constitutive equation, large deformations, hysteresis, dissipated energy
UR - http://eudml.org/doc/294936
ER -

References

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  1. Ionescu, I. R., Sofonea, M., Functional and Numerical Methods in Viscoplasticity, , Oxford University Press, (1993). MR1244578
  2. Krejčí, P., Hysteresis, Convexity and Dissipation in Hyperbolic Equations, , Gakuto Intern. Ser.Math. Sci. Appl., Vol. 8, Gakkotosho, Tokyo (1996). MR2466538
  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). MR0165783
  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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