Stability and Numerical Analysis of Micropolar Viscoelastic Systems

In this work, we consider two dynamic systems arising in micropolar viscoelasticity. In this sense, the material structure is assumed to have macroscopic and microscopic levels. First, an existence and uniqueness result is proved by using the theory of linear semigroups and, secondly, the decay of t...

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Published in:Journal of elasticity Vol. 157; no. 4; p. 83
Main Authors: Bazarra, Noelia, Fernández, José R., Fernández Sare, Hugo D., Quintanilla, Ramón
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.11.2025
Springer Nature B.V
Subjects:
Approximation
Biomechanics
Boundary conditions
Classical and Continuum Physics
Classical Mechanics
Convergence
Decay
Dynamical systems
Engineering
Equilibrium
Error analysis
Finite element analysis
Finite element method
Materials Science
Mathematical analysis
Mathematical Applications in the Physical Sciences
Mathematical problems
Numerical analysis
Operators (mathematics)
Partial differential equations
Polynomials
Stability
Theoretical and Applied Mechanics
Viscoelasticity
Viscoelasticity
65M15
Micropolar
Finite elements
Stability
Numerical analysis
35B35
74F99
65M60
35B40
Existence and uniqueness
ISSN:0374-3535, 1573-2681
Online Access:Get full text
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Summary:In this work, we consider two dynamic systems arising in micropolar viscoelasticity. In this sense, the material structure is assumed to have macroscopic and microscopic levels. First, an existence and uniqueness result is proved by using the theory of linear semigroups and, secondly, the decay of the solutions to the equilibrium state is shown. Then, the polynomial energy decay is obtained applying a characterization of the system operator. In a second part, we consider the numerical approximation of a variational version of the above problem. This is done by using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A discrete stability property is proved and an a priori error analysis is provided. The linear convergence of the approximations is deduced under some additional regularity conditions on the continuous solution. Finally, some numerical simulations are shown to demonstrate numerical convergence and the behavior of the discrete energy.
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ISSN:0374-3535
1573-2681
DOI:10.1007/s10659-025-10178-w