Abstract
In case of classical continuum mechanics the set of basic equations consists of the equation of motion, the kinematic equation and the constitutive equations. Constitutive equations form a material model. However, such equations are the addition, which constructs a mathematically solvable system of equations. We concentrate on the stability problems and the effects of discretization on material modeling. The method of investigation is analytic, the linear mapping operator of the discrete dynamical system is studied. We study how discretization, stability and anticipation act on one another. As results we show cases, when the incursive nature of a material model leads to instability.
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Acknowledgments
This work was supported by the National Scientific Research Funds of Hungary (OTKA contract number: K81531). The paper has been presented during 12th Conference on Dynamical Systems - Theory and Applications.
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Béda, P.B. Dynamical systems and incursive effects in continuum mechanics. Int. J. Dynam. Control 3, 58–62 (2015). https://doi.org/10.1007/s40435-014-0063-z
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DOI: https://doi.org/10.1007/s40435-014-0063-z