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Kinematics of elasto-plasticity: Validity and limits of applicability of F = F^eF^p for general three-dimensional deformations

Reina, Celia and Fokoua Djodom, Landry and Ortiz, Michael and Conti, Sergio (2018) Kinematics of elasto-plasticity: Validity and limits of applicability of F = F^eF^p for general three-dimensional deformations. Journal of the Mechanics and Physics of Solids, 121 . pp. 99-113. ISSN 0022-5096. http://resolver.caltech.edu/CaltechAUTHORS:20180806-110927280

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Abstract

This article provides a multiscale justification of the multiplicative decomposition F=F^eF^p for three-dimensional elasto-plastic deformations, and sets its limits of applicability via a careful examination of the assumptions involved in the derivation. The analysis starts from the mesoscopic characterization of the kinematics at the level of discrete dislocations, where F_ϵ, F_ϵ^e and F_ϵ^p are uniquely defined, and the relationships F_ϵ≃F_ϵ^eF_ϵ^p and det F_ϵ^p≃1 are well-justified almost everywhere in the domain. The upscaling to the macroscale (i.e., F=F^eF^p and det F^p=1, with F, F^e and F^p defined as the limits of the analogous quantities at the mesoscale) is then rigorously derived on the basis of the following assumptions: sup_ϵ∥F_ϵ^e∥L^g(Ω)<∞ with 1 < g < ∞, sup_ϵ∥F_ϵ^p∥L∞(Ω)<∞,sup_ϵ|Curl F_ϵ^p|(Ω)<∞, and det F_ϵ^p=1. These may be interpreted, in suitable scenarios, as bounded local energy density and dissipation, finite density of dislocations and incompressibility of the plastic deformation, respectively. Although these assumptions are expected to hold in many single crystal elasto-plastic deformations, they may be violated in certain cases of physical relevance. Illustrative examples where each of the individual assumptions fails in turn are presented and their implications regarding finite multiplicative elasto-plasticity at the macroscale are examined in detail.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.jmps.2018.07.006DOIArticle
ORCID:
AuthorORCID
Conti, Sergio0000-0001-7987-9174
Alternate Title:Kinematics of elasto-plasticity: Validity and limits of applicability of F = FeFp for general three-dimensional deformations
Additional Information:© 2018 Elsevier Ltd. Received 26 February 2018, Revised 3 July 2018, Accepted 9 July 2018, Available online 4 August 2018. C. Reina acknowledges the NSF grant CMMI-1401537. S. Conti and M. Ortiz acknowledge support by the Deutsche Forschungsgemeinschaft through the Sonderforschungsbereich 1060 “The mathematics of emergent effects”.
Group:GALCIT
Funders:
Funding AgencyGrant Number
NSFCMMI-1401537
Deutsche Forschungsgemeinschaft (DFG)Sonderforschungsbereich 1060
Subject Keywords:Crystal plasticity; Finite deformations; Multiplicative decomposition; Homogenization
Record Number:CaltechAUTHORS:20180806-110927280
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180806-110927280
Official Citation:Celia Reina, Landry Fokoua Djodom, Michael Ortiz, Sergio Conti, Kinematics of elasto-plasticity: Validity and limits of applicability of F=FeFp for general three-dimensional deformations, Journal of the Mechanics and Physics of Solids, Volume 121, 2018, Pages 99-113, ISSN 0022-5096, https://doi.org/10.1016/j.jmps.2018.07.006. (http://www.sciencedirect.com/science/article/pii/S0022509618301844)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88599
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:06 Aug 2018 18:19
Last Modified:08 Aug 2018 21:02

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