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Effective Cohesive Behavior of Layers of Interatomic Planes

Braides, Andrea and Lew, Adrian J. and Ortiz, Michael (2006) Effective Cohesive Behavior of Layers of Interatomic Planes. Archive for Rational Mechanics and Analysis, 180 (2). pp. 151-182. ISSN 0003-9527. https://resolver.caltech.edu/CaltechAUTHORS:20171128-101614160

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Abstract

A simple model of cleavage in brittle crystals consists of a layer of material containing N atomic planes separating in accordance with an interplanar potential under the action of an opening displacement δ prescribed on the boundary of the layer. The problem addressed in this work concerns the characterization of the constrained minima of the energy E_N of the layer as a function of δ as N becomes large. These minima determine the effective or macroscopic cohesive law of the crystal. The main results presented in this communication are: (i) the computation of the Γ limit E_0 of E_N as N → ∞; (ii) the characterization of the minimum values of E_0 as a function of the macroscopic opening displacement; (iii) a proof of uniform convergence of the minima of E_N for the case of nearest-neighbor interactions; and (iv) a proof of uniform convergence of the derivatives of E_N, or tractions, in the same case. The scaling on which the present Γ-convergence analysis is based has the effect of separating the bulk and surface contributions to the energy. It differs crucially from other scalings employed in the past in that it renders both contributions of the same order.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://dx.doi.org/10.1007/s00205-005-0399-9DOIArticle
https://link.springer.com/article/10.1007/s00205-005-0399-9PublisherArticle
http://rdcu.be/zLcFPublisherFree ReadCube access
ORCID:
AuthorORCID
Ortiz, Michael0000-0001-5877-4824
Additional Information:© Springer-Verlag Berlin Heidelberg 2006. Andrea Braicles is grateful to Caltech for the hospitality. Michael Ortiz and Adrian Lew are grateful to the Department of Energy for support provided through Caltech’s ASCI/ASAP Center for the Simulation of the Dynamic Response of Materials.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)UNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20171128-101614160
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20171128-101614160
Official Citation:Braides, A., Lew, A. & Ortiz, M. Arch. Rational Mech. Anal. (2006) 180: 151. https://doi.org/10.1007/s00205-005-0399-9
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83496
Collection:CaltechAUTHORS
Deposited By: Lydia Suarez
Deposited On:28 Nov 2017 18:24
Last Modified:24 Feb 2020 10:30

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