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Modeling Deformable Bodies Using Discrete Systems with Centroid-Based Propagating Interaction: Fracture and Crack Evolution

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Mathematical Modelling in Solid Mechanics

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 69))

Abstract

We use a simple discrete system in order to model deformation and fracture within the same theoretical and numerical framework. The model displays a rich behavior, accounting for different fracture phenomena, and in particular for crack formation and growth. A comparison with standard Finite Element simulations and with the basic Griffith theory of fracture is provided. Moreover, an ‘almost steady’ state, i.e. a long apparent equilibrium followed by an abrupt crack growth, is obtained by suitably parameterizing the system. The model can be easily generalized to higher order interactions corresponding, in the homogenized limit, to higher gradient continuum theories.

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Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Università di Roma La Sapienza, Via Eudossiana 18, 00184, Rome, Italy

    Alessandro Della Corte

  2. Laboratory of Science for Environmental Engineering, Université de la Rochelle, La Rochelle, France

    Antonio Battista

  3. MeMoCS, International Research Center for the Mathematics & Mechanics of Complex Systems, Università dell’Aquila, L’Aquila, Italy

    Francesco dell’Isola & Ivan Giorgio

Authors
  1. Alessandro Della Corte
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  2. Antonio Battista
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  3. Francesco dell’Isola
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  4. Ivan Giorgio
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Corresponding author

Correspondence to Francesco dell’Isola .

Editor information

Editors and Affiliations

  1. Università di Roma "La Sapienza" , Roma, Italy

    Francesco dell'Isola

  2. Université de Perpignan Via Domitia, LAboratoire de Mathématiques et PhySique Université de Perpignan Via Domitia, Perpignan, France

    Mircea Sofonea

  3. Dept Mechanical Engineering, UC Berkeley Dept Mechanical Engineering, Berkeley, California, USA

    David Steigmann

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Della Corte, A., Battista, A., dell’Isola, F., Giorgio, I. (2017). Modeling Deformable Bodies Using Discrete Systems with Centroid-Based Propagating Interaction: Fracture and Crack Evolution. In: dell'Isola, F., Sofonea, M., Steigmann, D. (eds) Mathematical Modelling in Solid Mechanics. Advanced Structured Materials, vol 69. Springer, Singapore. https://doi.org/10.1007/978-981-10-3764-1_5

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  • DOI: https://doi.org/10.1007/978-981-10-3764-1_5

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