Strain localization in elastic micro-cracked bodies

Mariano, Paolo Maria; Stazi, Furio Lorenzo

doi:10.1016/s0045-7825(01)00200-6

Cited by 20 publications

(15 citation statements)

References 7 publications

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“…Concerning the constitutive model, the purpose of this section is to present the basic equations governing micro-fractured media modeled within the framework of multifield continua. Reference is made to [8] for an exhaustive treatment on this subject and to [9] for the micro-fractured model investigated herein. For simplicity sake, we adopt the hypothesis of small displacements and strains.…”

Section: The Constitutive Modelmentioning

confidence: 99%

“…Details of the implementation are discussed in Section 2.3., while two numerical examples are illustrated in Section 3.. The first is devoted to assess the capabilities of the proposed method to predict localization phenomena not only in the micro displacement field, as already shown in [9], but also in the micro stress one. 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.…”

Section: Introductory Remarksmentioning

confidence: 99%

“…The basic aim of the paper is to represent in some way sub-structural interactions due to microcrack changes in a scattered sense. 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.…”

Section: Introductory Remarksmentioning

confidence: 99%

“…The constitutive relationships described in Section 1.2. allow to link their gradients to the relevant macro and micro stress fields. 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. The present paper proposes instead ad hoc mixed formulations that interpolate independently stresses and displacements.…”

Section: Introductory Remarksmentioning

confidence: 99%

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

Bruggi

Venini

2009

Algorithms

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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)

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Section: The Constitutive Modelmentioning

confidence: 99%

Section: Introductory Remarksmentioning

confidence: 99%

Section: Introductory Remarksmentioning

confidence: 99%

Section: Introductory Remarksmentioning

confidence: 99%

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

Bruggi

Venini

2009

Algorithms

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“…As a consequence strain localization phenomena appear even if constitutive relations are linear and microcracks are in the elastic phase without growth (numerical results concerning the localization of deformation are contained in Mariano and Stazi (2001) and Mariano et al (2002)). …”

Section: Introductionmentioning

confidence: 99%

Uniqueness and minimum theorems for a multifield model of brittle solids

Mosconi

2006

International Journal of Solids and Structures

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Micro‐to‐macro interactions in complex bodies: Wavelet‐based post‐processing detection

Bosi¹,

Mariano

Salvatori

2021

Math Methods in App Sciences

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We propose to couple finite element simulations and wavelet‐based post‐processing analysis to explore deeply the interaction degree of microscopic events on the gross behavior of complex bodies (which class includes metamaterials), above all around material or load discontinuities. After summarizing the theoretical structures our procedure refers to, as a sample case we select a special class of complex materials, namely, quasicrystals, and show how the proposed scheme works. As a result, we point out the effects of atomic rearrangements characterizing the quasicrystal structure on the stress field around a crack tip in static and dynamical setting. Our procedure can be also used for the analysis of dynamic experimental data. In this case, it allows us to detect discontinuities at least along directions selected within the body. In turn, our procedure can be used for monitoring purposes.

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Strain localization in elastic micro-cracked bodies

Cited by 20 publications

References 7 publications

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

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

Uniqueness and minimum theorems for a multifield model of brittle solids

Micro‐to‐macro interactions in complex bodies: Wavelet‐based post‐processing detection

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