Anisotropic viscoelastic body subjected to the pulsating load

Jozef Sumec; Mária Minárová; Ľuboš Hruštinec

Applications of Mathematics (2023)

  • Volume: 68, Issue: 6, page 829-844
  • ISSN: 0862-7940

Abstract

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Constitutive equations of continuum mechanics of the solid phase of anisotropic material is focused in the paper. First, a synoptic one-dimensional Maxwell model is explored, subjected to arbitrary deformation load. The explicit form is derived for stress on strain dependence. Further, the analogous explicit constitutive equation is taken in three spatial dimensions and treated mathematically. Later on, a simply supported straight concrete beam reinforced by the steel fibres is taken as an investigated domain. The reinforcement is considered and dealt as scattered within the beam. Material characteristics are determined in line with the theory of the reinforcement. Sinusoidal load is taken as the action, stress reaction function is observed. By exploitation of the Fourier transform within the stress-strain relation analysis, both time and frequency interpretation of the constitutive relation can be performed.

How to cite

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Sumec, Jozef, Minárová, Mária, and Hruštinec, Ľuboš. "Anisotropic viscoelastic body subjected to the pulsating load." Applications of Mathematics 68.6 (2023): 829-844. <http://eudml.org/doc/299433>.

@article{Sumec2023,
abstract = {Constitutive equations of continuum mechanics of the solid phase of anisotropic material is focused in the paper. First, a synoptic one-dimensional Maxwell model is explored, subjected to arbitrary deformation load. The explicit form is derived for stress on strain dependence. Further, the analogous explicit constitutive equation is taken in three spatial dimensions and treated mathematically. Later on, a simply supported straight concrete beam reinforced by the steel fibres is taken as an investigated domain. The reinforcement is considered and dealt as scattered within the beam. Material characteristics are determined in line with the theory of the reinforcement. Sinusoidal load is taken as the action, stress reaction function is observed. By exploitation of the Fourier transform within the stress-strain relation analysis, both time and frequency interpretation of the constitutive relation can be performed.},
author = {Sumec, Jozef, Minárová, Mária, Hruštinec, Ľuboš},
journal = {Applications of Mathematics},
keywords = {linear viscoleasticity theory; constitutive equation; Duhamel hereditary integral; convolution; complex relaxation modulus of structural element; Fourier integral transform},
language = {eng},
number = {6},
pages = {829-844},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Anisotropic viscoelastic body subjected to the pulsating load},
url = {http://eudml.org/doc/299433},
volume = {68},
year = {2023},
}

TY - JOUR
AU - Sumec, Jozef
AU - Minárová, Mária
AU - Hruštinec, Ľuboš
TI - Anisotropic viscoelastic body subjected to the pulsating load
JO - Applications of Mathematics
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 6
SP - 829
EP - 844
AB - Constitutive equations of continuum mechanics of the solid phase of anisotropic material is focused in the paper. First, a synoptic one-dimensional Maxwell model is explored, subjected to arbitrary deformation load. The explicit form is derived for stress on strain dependence. Further, the analogous explicit constitutive equation is taken in three spatial dimensions and treated mathematically. Later on, a simply supported straight concrete beam reinforced by the steel fibres is taken as an investigated domain. The reinforcement is considered and dealt as scattered within the beam. Material characteristics are determined in line with the theory of the reinforcement. Sinusoidal load is taken as the action, stress reaction function is observed. By exploitation of the Fourier transform within the stress-strain relation analysis, both time and frequency interpretation of the constitutive relation can be performed.
LA - eng
KW - linear viscoleasticity theory; constitutive equation; Duhamel hereditary integral; convolution; complex relaxation modulus of structural element; Fourier integral transform
UR - http://eudml.org/doc/299433
ER -

References

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  21. Sumec, J., Hruštinec, ., Modeling of some effects in the viscoelastic selected type of materials, Proceedings of the 13th International Conference on New Trends in Statics and Dynamics of Buildings Slovak University of Technology, Bratislava (2017), 61-78. (2017) 
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