Abstract
Mechanical behaviour of a viscoelastic model is described by its constitutive equation, i.e. the stress–strain relation. This constitutive relation is determined by the particular physical equations of both (elastic and viscous) elementary members of the model; and the geometric equations matching with the configuration of the model. Initially, the governing equation is of an implicit differential form of the order corresponding to the number of the irreducible viscous members involved in the model. Given the action as a function in time, we can directly derive the reaction on action dependence in an implicit differential form. Sometimes there is a need to have the reaction function explicit expression for a general action function. Constitutive equations enable us to study the mechanical response of the materials, represented by these models, to predict their mechanical response to a current load with regard to the load history and memory of materials.
This work was supported by the Slovak Research and Development Agency under the contract no. APVV-17-0066, APVV-18-0052, VEGA 1/0522/20 and grant VEGA 1/0006/19.
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References
Boltzmann, L.: Zur Theorie der Elastischen Nachwirkung Sitzbrett. Akad. Wiss. 70, Wien, 1874
Brinson, H.F., Brinson, H.C.: Hereditary integral representations of stress and strain. In: Polymer Engineering Science and Viscoelasticity. Springer, Boston (2008)
Christensen, R.M.: Theory of Viscoelasticity an Introduction. Academic Press, N.Y., London (1974)
Hajek, J.: Deformations of Concrete Structures. Publishing House SAS, VEDA (1994)
Minárová Rheology, M.: Visco-Elastic and Visco-Elasto-Plastic Modeling: Habilitation thesis, 2018
Rabotnov, J.: Elements of Hreditary Mechanics of Solid Bodies, Moscow (1977)
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)
Urzhumcev, J.C.: Prognosis of Long-lasting Resiatance of Polymer Materials. Academic Press, N.Y., London (1974)
Volterra, V.: Theory of Functionals and of Integral and Integro-differential Equations. New York (1959)
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Minárová, M., Sumec, J. (2022). Duhamel Hereditary Integrals in Viscoelasticity. In: Harmati, I.Á., Kóczy, L.T., Medina, J., Ramírez-Poussa, E. (eds) Computational Intelligence and Mathematics for Tackling Complex Problems 3. Studies in Computational Intelligence, vol 959. Springer, Cham. https://doi.org/10.1007/978-3-030-74970-5_6
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DOI: https://doi.org/10.1007/978-3-030-74970-5_6
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