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Operator split methods in the numerical solution of the finite deformation elastoplastic dynamic problem

Pinsky, Peter M. and Ortiz, Miguel and Taylor, Robert L. (1983) Operator split methods in the numerical solution of the finite deformation elastoplastic dynamic problem. Computers and Structures, 17 (3). pp. 345-359. ISSN 0045-7949. https://resolver.caltech.edu/CaltechAUTHORS:20180105-152230031

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Abstract

The spatial formulation of the elastoplastic dynamic problem for finite deformations is considered. A thermodynamic argument leads to an additive decomposition of the spatial rate of deformation tensor and allows an operator split of the evolutionary equations of the problem into “elastic” and “plastic” parts. This operator split is taken as the basis for the definition of a global product algorithm. In the context of finite element discretization the product algorithm entails, for every time step, the solution of a nonlinear elastodynamic problem followed by the application of plastic algorithms that operate on the stresses and internal variables at the integration points and bring in the plastic constitutive equations. Suitable plastic algorithms are discussed for the cases of perfect and hardening plasticity and viscoplasticity. The proposed formalism does not depend on any notion of smoothness of the yield surface and is applicable to arbitrary convex elastic regions, with or without corners. The stability properties of the global product algorithm are shown to be identical to those of the algorithm used for the integration of the nonlinear elastodynamic problem. Numerical examples illustrate the accuracy of the method.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/0045-7949(83)90126-8DOIArticle
http://www.sciencedirect.com/science/article/pii/0045794983901268PublisherArticle
ORCID:
AuthorORCID
Ortiz, Miguel0000-0001-5877-4824
Additional Information:© 1983 Elsevier. Received 1 April 1982. Revised manuscript received 18 February 1983.
Group:GALCIT
Issue or Number:3
Record Number:CaltechAUTHORS:20180105-152230031
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180105-152230031
Official Citation:Peter M. Pinsky, Miguel Ortiz, Robert L. Taylor, Operator split methods in the numerical solution of the finite deformation elastoplastic dynamic problem, In Computers & Structures, Volume 17, Issue 3, 1983, Pages 345-359, ISSN 0045-7949, https://doi.org/10.1016/0045-7949(83)90126-8. (http://www.sciencedirect.com/science/article/pii/0045794983901268)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84148
Collection:CaltechAUTHORS
Deposited By: Lydia Suarez
Deposited On:08 Jan 2018 19:37
Last Modified:24 Feb 2020 10:30

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