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...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/173986 |
| Acceso en línea: | https://hdl.handle.net/2117/173986 https://dx.doi.org/10.1080/00036811.2019.1698721 |
| Access Level: | acceso abierto |
| Palabra clave: | Elastic solids -- Mechanical properties Viscoelasticity Mixtures viscoelasticity Finite element approximations Error estimates Numerical simulations Sòlids elàstics -- Propietats mecàniques Viscoelasticitat Classificació AMS::74 Mechanics of deformable solids::74E Material properties given special treatment Classificació AMS::74 Mechanics of deformable solids::74D Materials of strain-rate type and history type, other materials with memory Classificació AMS::65 Numerical analysis::65M Partial differential equations, initial value and time-dependent initial-boundary value problems Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències |
| Sumario: | 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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