Explicit form of yield conditions dual to a class of dissipation potentials dependent on three invariants
Authors:
- Aleksander Szwed,
- Inez Donata Kamińska
Abstract
In the paper, a pragmatic approach to finding the dual formulation for isotropic perfectly plastic materials given a dissipation potential dependent on three cylindrical invariants and involving the Ottosen shape function is proposed and illustrated by examples. The main goal is to provide instructions on how to perform the Legendre transformation used when passing from a dissipation potential to its conjugate yield condition and offer some suggestions regarding calibration for particular potentials dependent on the trace of the strain rate tensor and the product of the norm of its deviator and the Ottosen shape function, which covers a wide class of engineering materials. The classic framework for constitutive modelling of thermodynamically consistent materials within the small deformation theory is used. First, general formulae connecting a dissipation potential dependent on three invariants of the strain rate tensor to the coupled yield condition are derived. Then, they are narrowed down for the aforementioned case of dissipation functions dependent on the Lode angle in a way proposed by Ottosen. Finally, three examples are given involving classical potentials: Beltrami’s, Drucker–Prager’s and Mises–Schleicher’s generalised potential using the shape function. Detailed calculations exposing the introduced technique are performed. Also, a method of the calibration of such potentials leading to explicit mathematical formulae is demonstrated, based on the typical tests located on the tension and compression meridians.
- Record ID
- WUT62bbfb4f48314dcbb5b79aedfc2e2971
- Author
- Journal series
- Acta Mechanica, ISSN 0001-5970, e-ISSN 1619-6937
- Issue year
- 2021
- No
- 232
- Pages
- 1087–1111
- ASJC Classification
- ;
- DOI
- DOI:10.1007/s00707-020-02876-4 Opening in a new tab
- Language
- (en) English
- File
-
- File: 1
- Szwed-Kamińska2021_Article_ExplicitFormOfYieldConditionsD(1).pdf
-
- Score (nominal)
- 100
- Score source
- journalList
- Score
- = 100.0, 19-05-2022, ArticleFromJournal
- Publication indicators
- = 2; = 2; = 2; : 2018 = 1.109; : 2020 (2 years) = 2.698 - 2020 (5 years) =2.505
- Citation count
- 2
- Uniform Resource Identifier
- https://repo.pw.edu.pl/info/article/WUT62bbfb4f48314dcbb5b79aedfc2e2971/
- URN
urn:pw-repo:WUT62bbfb4f48314dcbb5b79aedfc2e2971
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or PerishOpening in a new tab system.