Eric Abercrombie, J Gregory McDaniel, Timothy Walsh
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A generalized time-domain constitutive finite element approach for viscoelastic materials
Despite the existence of time domain finite element formulations for viscoelastic materials, there are still substantial ways to improve the analysis. To the authors’ knowledge, the formulation of the problem is always done with respect to a single constitutive relation and so limits the implementer to a single scheme with which to model relaxation. Furthermore, all current constitutive relations involve the finding of fitting parameters for an analytical function, which is a sufficiently painful process to warrant the study of best fitting procedures to this day. In contrast, this effort is the first full derivation of the two dimensional problem from fundamental principles. It is also the first generalization of the problem, which frees users to select constitutive relations without re-derivation or re-expression of the problem. This approach is also the first approach to the problem that could lead to the elimination of constitutive relations for representing relaxation in viscoelastic materials. Following, the full derivation, several common constitutive relations are outlined with analysis of how they may best be implemented in the generalized form. Several expressions for viscoelastic terms are also provided given linear, quadratic, and exponential interpolation assumptions.
期刊介绍:
Serving the multidisciplinary materials community, the journal aims to publish new research work that advances the understanding and prediction of material behaviour at scales from atomistic to macroscopic through modelling and simulation.
Subject coverage:
Modelling and/or simulation across materials science that emphasizes fundamental materials issues advancing the understanding and prediction of material behaviour. Interdisciplinary research that tackles challenging and complex materials problems where the governing phenomena may span different scales of materials behaviour, with an emphasis on the development of quantitative approaches to explain and predict experimental observations. Material processing that advances the fundamental materials science and engineering underpinning the connection between processing and properties. Covering all classes of materials, and mechanical, microstructural, electronic, chemical, biological, and optical properties.