A problem with viscoelastic mixtures: numerical analysis and computational experiments

In this paper, we study, from the numerical point of view, a dynamic problem involving a mixture of two viscoelastic solids. The mechanical problem is written as a system of two coupled partial differential equations. Its variational formulation is derived and an existence and uniqueness result, and...

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Bibliographic Details
Published in:Applicable analysis Vol. 100; no. 12; pp. 2684 - 2705
Main Authors: Fernández, J. R., Masid, M., Magaña, A., Quintanilla, R.
Format: Journal Article Publication
Language:English
Published: Abingdon Taylor & Francis 10.09.2021
Taylor & Francis Ltd
Subjects:
65 Numerical analysis
65M Partial differential equations, initial value and time-dependent initial-boundary value problems
74 Mechanics of deformable solids
74D Materials of strain-rate type and history type, other materials with memory
74E Material properties given special treatment
Algorithms
Classificació AMS
Elastic solids
Error estimates
Finite element approximations
Finite element method
Matemàtica aplicada a les ciències
Matemàtiques i estadística
Mathematical analysis
Mechanical properties
Mixtures
Numerical analysis
Numerical simulations
Partial differential equations
Propietats mecàniques
Sòlids elàstics
Viscoelasticitat
Viscoelasticity
Àrees temàtiques de la UPC
ISSN:0003-6811, 1563-504X
Online Access:Get full text
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Summary:In this paper, we study, from the numerical point of view, a dynamic problem involving a mixture of two viscoelastic solids. The mechanical problem is written as a system of two coupled partial differential equations. Its variational formulation is derived and an existence and uniqueness result, and an energy decay property, are recalled. Then, fully discrete approximations are introduced by using the classical finite element method and the implicit Euler scheme. A discrete stability property and a priori error estimates are shown, from which we deduce the linear convergence of the algorithm. Finally, some numerical simulations, including examples in one and two dimensions, are presented to show the accuracy of the approximation and the behaviour of the solution.
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ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2019.1698721