Higher-order and higher floating-point precision numerical approximations of finite strain elasticity moduli

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Connolly, Stephen John and MacKenzie, Donald and Gorash, Yevgen (2019) Higher-order and higher floating-point precision numerical approximations of finite strain elasticity moduli. International Journal for Numerical Methods in Engineering, 120 (10). pp. 1184-1201. ISSN 0029-5981 (https://doi.org/10.1002/nme.6176)

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Abstract

Two real‐domain numerical approximation methods for accurate computation of finite strain elasticity moduli are developed and their accuracy and computational efficiency investigated, with reference to hyperelastic constitutive models with known analytical solutions. The methods are higher‐order and higher floating‐point precision numerical approximation, the latter being novel in this context. A general formula for higher‐order approximation finite difference schemes is derived and a new procedure is proposed to implement increased floating‐point precision. The accuracy of the approximated elasticity moduli is investigated numerically using higher‐order approximations in standard double precision and increased quadruple precision. It is found that as the order of the approximation increases, the elasticity moduli tend towards the analytical solution. Using higher floating‐point precision, the approximated elasticity moduli for all orders of approximation are found to be more accurate than the standard double precision evaluation of the analytical moduli. Application of the techniques to a finite element problem shows that the numerically approximated methods obtain convergence equivalent to the analytical method but require greater computational effort. It is concluded that numerical approximation of elasticity moduli is a powerful and effective means of implementing advanced constitutive models in the finite element method without prior derivation of difficult analytical solutions.

ORCID iDs

Connolly, Stephen John ORCID logoORCID: https://orcid.org/0000-0001-6286-0469, MacKenzie, Donald ORCID logoORCID: https://orcid.org/0000-0002-1824-1684 and Gorash, Yevgen ORCID logoORCID: https://orcid.org/0000-0003-2802-7814;
  • Item type:Article
    ID code:69106
    Dates:
    Date
    Event
    7 December 2019
    Published
    25 July 2019
    Published Online
    22 July 2019
    Accepted
    Notes:This is the peer reviewed version of the following article: Connolly, SJ, MacKenzie, D & Gorash, Y 2019, 'Higher-order and higher floating-point precision numerical approximations of finite strain elasticity moduli' International Journal for Numerical Methods in Engineering, pp. 1-19., which has been published in final form at https://doi.org/10.1002/nme.6176. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.
    Subjects:Technology > Engineering (General). Civil engineering (General)
    Department:Faculty of Engineering > Mechanical and Aerospace Engineering
    Strategic Research Themes > Ocean, Air and Space
    Depositing user: Pure Administrator
    Date deposited:29 Jul 2019 13:40
    Last modified:17 Dec 2024 01:19
    URI:https://strathprints.strath.ac.uk/id/eprint/69106
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