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Descripción
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| The hyperelastic nonlinear behaviour of many materials like composites, rubber and biological tissues present frequently a relevant viscous dissipative component which can be considered part of the Mullins effect. Most of these materials present a relevant anisotropic behavior which may be frequently modelled as orthotropic or transversely isotropic. There are many large-strain viscoelastic models available, some of them motivated on continuum mechanics principles and other models motivated on the micromechanics of the specific material. In this work we present a formulation that is purely phenomenological, without any insight (obtained but neither needed) in the micromechanics of the material being modelled. Currently there are two families of this type of large strain viscoelastic models that have success in finite element implementations. The first one comes mainly from the work of Simó and co-workers (see [1] and therein references), is valid for anisotropy and is based on stress-like internal variables. The implementation is a rather natural extension of a small strain framework. The needed storage for internal variables reduces to those of the previous step. This formulation was initially valid only for small deviations away from static thermodynamic equilibrium, hypothesis questionable at large strains and often referred to as finite linear viscoelasticity. However, the work has been extended to large deviations, but using linear non-equilibrated contributions [2]. The second family comes mainly from the work of Reese and Govindjee [3]. This finite (nonlinear) viscoelasticity model contains nonlinear equilibrated and non-equilibrated contributions, is based on a multiplicative (Sidoroff) decomposition (which viscous part can be considered as the internal variables) and is valid for large deviations from thermodynamical equilibrium. However, the model is restricted to isotropic stored energy functions. In this work we present a model with the following ingredients: (1) the stored energy is decomposed in unrelated equilibrated and non-equilibrated contributions, (2) both contributions may be nonlinear and orthotropic, (3) it uses a multiplicative decomposition, (4) it is valid far away from the thermodynamical equilibrium and (5) it uses logarithmic stress and strain measures. The model may be used with any isotropic, transversely isotropic or orthotropic stored energy function. However, a large benefit is obtained if teamed with spline-based stored energy functions in terms of logarithmic strains [4], [5]. These spline-based functions are purely phenomenological and are able to capture ?exactly? the nonlinear isotropic, transversely isotropic or orthotropic behaviour of a hyperelastic material. Using these functions, the user may then prescribe the instantaneous and quasi-static orthotropic behaviour and it is ?exactly? captured. Then the relaxation time establish the usual characteristic time to control the response relaxation from one constitutive relation to the other. | |
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Internacional
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Si |
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Nombre congreso
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9th European Solid Mechanics Conference (ESMC 2015) |
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Tipo de participación
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960 |
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Lugar del congreso
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Leganés-Madrid, Spain |
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Revisores
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Si |
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ISBN o ISSN
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1-84564-031-4 |
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DOI
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Fecha inicio congreso
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06/07/2015 |
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Fecha fin congreso
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10/07/2015 |
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Desde la página
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1 |
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Hasta la página
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14 |
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Título de las actas
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Proceedings 9th European Solid Mechanics Conference (ESMC 2015) |