A simple and efficient BEM implementation of quasistatic linear visco-elasticity
| Autor: | Christos Panagiotopoulos, Vladislav Mantic, Tomáš Roubíček |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Unilateral contact
Discretization Quasistatic linear visco-elasticity Kelvin–Voigt rheology Jeffreys rheology symbols.namesake Materials Science(all) Modelling and Simulation FOS: Mathematics Fundamental solution Boundary element method Applied mathematics General Materials Science Mathematics - Numerical Analysis Algebraic number Mathematics Implicit time discretisation Burgers rheology Maxwell rheology Mechanical Engineering Applied Mathematics Standard linear solids Inverse Laplace transform Numerical Analysis (math.NA) Condensed Matter Physics Condensed Matter::Soft Condensed Matter Mechanics of Materials Modeling and Simulation Boltzmann constant symbols Quasistatic process |
| Zdroj: | International Journal of Solids and Structures. 51(13):2261-2271 |
| ISSN: | 0020-7683 |
| DOI: | 10.1016/j.ijsolstr.2014.02.028 |
| Popis: | A simple yet efficient procedure to solve quasistatic problems of special linear visco-elastic solids at small strains with equal rheological response in all tensorial components, utilizing boundary element method (BEM), is introduced. This procedure is based on the implicit discretisation in time (the so-called Rothe method) combined with a simple “algebraic” transformation of variables, leading to a numerically stable procedure (proved explicitly by discrete energy estimates), which can be easily implemented in a BEM code to solve initial-boundary value visco-elastic problems by using the Kelvin elastostatic fundamental solution only. It is worth mentioning that no inverse Laplace transform is required here. The formulation is straightforward for both 2D and 3D problems involving unilateral frictionless contact. Although the focus is to the simplest Kelvin–Voigt rheology, a generalization to Maxwell, Boltzmann, Jeffreys, and Burgers rheologies is proposed, discussed, and implemented in the BEM code too. A few 2D and 3D initial-boundary value problems, one of them with unilateral frictionless contact, are solved numerically. |
| Databáze: | OpenAIRE |
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