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A new two-point deformation tensor and its relation to the classical kinematical framework and the stress concept
2004 (English)In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 41, no 26, 7459-7469 p.Article in journal (Refereed) Published
Abstract [en]

Starting from the issue of what is the correct form for a Legendre transformation of the strain energy in terms of Eulerian and two-point tensor variables we introduce a new two-point deformation tensor, namely H = (F-F-T)/2, as a possible deformation measure involving points in two distinct configurations. The Lie derivative of H is work conjugate to the first Piola-Kirchhoff stress tensor P. The deformation measure H leads to straightforward manipulations within a two-point setting such as the derivation of the virtual work equation and its linearization required for finite element implementation. The manipulations are analogous to those used for the Lagrangian and Eulerian frameworks. It is also shown that the Legendre transformation in terms of two-point tensors and spatial tensors require Lie derivatives. As an illustrative example we propose a simple Saint Venant-Kirchhoff type of a strain-energy function in terms of H. The constitutive model leads to physically meaningful results also for the large compressive strain domain, which is not the case for the classical Saint Venant-Kirchhoff material.

Place, publisher, year, edition, pages
2004. Vol. 41, no 26, 7459-7469 p.
Keyword [en]
nonlinear continuum mechanics, finite element method, Legendre transformation, two-point tensor, Lie derivative, constitutive equation
URN: urn:nbn:se:kth:diva-23809DOI: 10.1016/j.ijsolstr.2004.06.008ISI: 000224489600012OAI: diva2:342508
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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Holzapfel, Gerhard A.
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