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Algorithms 2009, 2(1), 606-622; doi:10.3390/a2010606

Mixed Variational Formulations for Micro-cracked Continua in the Multifield Framework

Department of Structural Mechanics, University of Pavia, via Ferrata 1, Pavia, Italy
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Received: 9 March 2009 / Accepted: 24 March 2009 / Published: 27 March 2009
(This article belongs to the Special Issue Numerical Simulation of Discontinuities in Mechanics)
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Abstract

Within the framework of multifield continua, we move from the model of elastic microcracked body introduced in (Mariano, P.M. and Stazi, F.L., Strain localization in elastic microcracked bodies, Comp. Methods Appl. Mech. Engrg. 2001, 190, 5657–5677) and propose a few novel variational formulations of mixed type along with relevant mixed FEM discretizations. To this goal, suitably extended Hellinger-Reissner principles of primal and dual type are derived. A few numerical studies are presented that include an investigation on the interaction between a single cohesive macrocrack and diffuse microcracks (Mariano, P.M. and Stazi, F.L., Strain localization due to crack–microcrack interactions: X–FEM for a multifield approach, Comp. Methods Appl. Mech. Engrg. 2004, 193, 5035–5062).
Keywords: Multifield theory; mixed FEM; localization; fracture Multifield theory; mixed FEM; localization; fracture
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Bruggi, M.; Venini, P. Mixed Variational Formulations for Micro-cracked Continua in the Multifield Framework. Algorithms 2009, 2, 606-622.

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