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A finite element method for analyzing localization in rate dependent solids at finite strains

Nacar, A. and Needleman, A. and Ortiz, M. (1989) A finite element method for analyzing localization in rate dependent solids at finite strains. Computer Methods in Applied Mechanics and Engineering, 73 (3). pp. 235-258. ISSN 0045-7825. https://resolver.caltech.edu/CaltechAUTHORS:20180104-144547414

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Abstract

The finite element method for localization analysis of Ortiz et al. [Comp. Methods Appl. Mech. Engrg. 61] is generalized to account for finite deformations and for material rate dependence. Special shape functions are added to the finite element basis to reproduce band-like localized deformation modes. The amplitudes of these additional modes are eliminated locally by static condensation. The performance of the enhanced element is illustrated in a problem involving shear localization in a plane strain tensile bar. Solutions based on the enhanced element are compared with corresponding results obtained from the underlying compatible isoparametric quadrilateral element and from crossed-triangular and uniformly reduced integration elements. In the finite deformation context, the enhanced element solution is not very sensitive to the precise specification of initial orientation of the additional band-like modes. The enhanced element formulation described here can be used for a broad range of rate independent and rate dependent material behaviors in two dimensional and three dimensional problems.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/0045-7825(89)90067-4DOIArticle
https://www.sciencedirect.com/science/article/pii/0045782589900674PublisherArticle
ORCID:
AuthorORCID
Ortiz, M.0000-0001-5877-4824
Additional Information:© 1989 Elsevier. Received 25 August 1987. Revised manuscript received 21 December 1988. The support provided by the Office of Naval Research through grants N0001485-K-0720 and N0001486-K-0262 is gratefully acknowledged. The computations were carried out at the John von Neumann Center for Scientific Computing.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N0001485-K-0720
Office of Naval Research (ONR)N0001486-K-0262
Issue or Number:3
Record Number:CaltechAUTHORS:20180104-144547414
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180104-144547414
Official Citation:A. Nacar, A. Needleman, M. Ortiz, A finite element method for analyzing localization in rate dependent solids at finite strains, In Computer Methods in Applied Mechanics and Engineering, Volume 73, Issue 3, 1989, Pages 235-258, ISSN 0045-7825, https://doi.org/10.1016/0045-7825(89)90067-4. (http://www.sciencedirect.com/science/article/pii/0045782589900674)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84092
Collection:CaltechAUTHORS
Deposited By: Lydia Suarez
Deposited On:05 Jan 2018 17:54
Last Modified:24 Feb 2020 10:30

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