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A computational framework for polyconvex large strain elasticity for geometrically exact beam theory

A computational framework for polyconvex large strain elasticity for geometrically exact beam theory

Ortigosa, Rogelio, Gil, Antonio J., Bonet, Javier ORCID: 0000-0002-0430-5181 and Hesch, Christian (2016) A computational framework for polyconvex large strain elasticity for geometrically exact beam theory. Computational Mechanics, 57 (2). pp. 277-303. ISSN 0178-7675 (Print), 1432-0924 (Online) (doi:https://doi.org/10.1007/s00466-015-1231-5)

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Abstract

In this paper, a new computational framework is presented for the analysis of nonlinear beam finite elements subjected to large strains. Specifically, the methodology recently introduced in Bonet et al. (Comput Methods Appl Mech Eng 283:1061–1094, 2015) in the context of three dimensional polyconvex elasticity is extended to the geometrically exact beam model of Simo (Comput Methods Appl Mech Eng 49:55–70, 1985), the starting point of so many other finite element beam type formulations. This new variational framework can be viewed as a continuum degenerate formulation which, moreover, is enhanced by three key novelties. First, in order to facilitate the implementation of the sophisticated polyconvex constitutive laws particularly associated with beams undergoing large strains, a novel tensor cross product algebra by Bonet et al. (Comput Methods Appl Mech Eng 283:1061–1094, 2015) is adopted, leading to an elegant and physically meaningful representation of an otherwise complex computational framework. Second, the paper shows how the novel algebra facilitates the re-expression of any invariant of the deformation gradient, its cofactor and its determinant in terms of the classical beam strain measures. The latter being very useful whenever a classical beam implementation is preferred. This is particularised for the case of a Mooney–Rivlin model although the technique can be straightforwardly generalised to other more complex isotropic and anisotropic polyconvex models. Third, the connection between the two most accepted restrictions for the definition of constitutive models in three dimensional elasticity and beams is shown, bridging the gap between the continuum and its degenerate beam description. This is carried out via a novel insightful representation of the tangent operator.

Item Type: Article
Additional Information: © The Author(s) 2015. This article is published with open access at Springerlink.com
Uncontrolled Keywords: Polyconvexity; Geometrically exact beam theory; Continuum degenerate beam formulation; Finite elements
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Faculty / Department / Research Group: Vice-Chancellor's Group
Last Modified: 21 Dec 2016 14:45
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/14189

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