Geodesic
Anisotropic viscoelastic body subjected to the pulsating load
Applications of Mathematics, Tome 68 (2023) no. 6, pp. 829-844.

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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.
DOI : 10.21136/AM.2023.0256-22
Classification : 42A38, 74-10
Keywords: linear viscoleasticity theory; constitutive equation; Duhamel hereditary integral; convolution; complex relaxation modulus of structural element; Fourier integral transform 
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Sumec, Jozef; Minárová, Mária; Hruštinec, Ľuboš. Anisotropic viscoelastic body subjected to the pulsating load. Applications of Mathematics, Tome 68 (2023) no. 6, pp. 829-844. doi : 10.21136/AM.2023.0256-22. http://geodesic.mathdoc.fr/articles/10.21136/AM.2023.0256-22/

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