CaltechAUTHORS
  A Caltech Library Service

Symmetry-preserving return mapping algorithms and incrementally extremal paths: A unification of concepts

Ortiz, Michael and Martin, John B. (1989) Symmetry-preserving return mapping algorithms and incrementally extremal paths: A unification of concepts. International Journal for Numerical Methods in Engineering, 28 (8). pp. 1839-1853. ISSN 0029-5981. https://resolver.caltech.edu/CaltechAUTHORS:20180104-144352841

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20180104-144352841

Abstract

In this work we seek to characterize the conditions under which an elastic–plastic stress update algorithm preserves the symmetries inherent to the material response. From a numerical standpoint, the aim is to determine under what conditions a stress update algorithm produces symmetric consistent tangents when applied to materials obeying normality. For the ideally plastic solid we show that only the fully implicit or closest point return mapping algorithm is symmetry preserving. For hardening plasticity, symmetry cannot be preserved in general unless suitable restrictions are imposed on the constitutive equations. We show that these restrictions amount to the existence of a pseudo-internal energy function acting as a joint potential for both the direction of plastic flow and the hardening moduli. In view of the fact that holonomic methods based on incrementally extremal paths also result in update rules possessing a potential structure and, hence, in symmetric tangents, we address the question of whether any connections exist between the two approaches. We show that holonomic methods and the fully implicit algorithm may indeed be brought into correspondence.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://dx.doi.org/10.1002/nme.1620280810DOIArticle
http://onlinelibrary.wiley.com/doi/10.1002/nme.1620280810/fullPublisherArticle
ORCID:
AuthorORCID
Ortiz, Michael0000-0001-5877-4824
Additional Information:© 1989 John Wiley & Sons. Received 13 June 1988. Revised 28 December 1988.
Group:GALCIT
Issue or Number:8
Record Number:CaltechAUTHORS:20180104-144352841
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180104-144352841
Official Citation:Ortiz, M. and Martin, J. B. (1989), Symmetry-preserving return mapping algorithms and incrementally extremal paths: A unification of concepts. Int. J. Numer. Meth. Engng., 28: 1839–1853. doi:10.1002/nme.1620280810
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84091
Collection:CaltechAUTHORS
Deposited By: Lydia Suarez
Deposited On:05 Jan 2018 18:10
Last Modified:24 Feb 2020 10:30

Repository Staff Only: item control page