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).
Highlights
The last figure clearly shows the capability of the model in capturing the strain localization of the two 45–degree oriented stripes that arise from the load application point
This behavior is exclusively due to the multifield nature of the model, since macro displacements plots are free from any localization phenomenon and exhibit the usual smoothness expected in the context of a classical Cauchy continuum
The paper has dealt with the numerical description of microcracked bodies according to the theories introduced in [9, 10] and belonging to the framework of multifield continua [5]
Summary
A wide class of theoretical and technological problems are related to the mechanical description and the practical use of bodies endowed with a large number of microcracks scattered throughout the volume. Since we consider dense populations of microcracks we follow here a multi–field model of microcracked bodies that has been already formulated in a series of papers (see [9] and references therein). This approach seems to predict verifiable non–usual phenomena, namely strain localization that straightforwardly arise from the adopted model notwithstanding the linear elastic regime. The numerical investigations discussed in [9] and [10] refer to displacement–based finite element methods that adopt post–processing techniques to derive the stress fields. Afterwards, the second example allows to discuss the effects of the presence of a single macrocrack within the diffuse microcracks peculiar to the adopted multifield model.
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