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Quasistatic elastoplasticity via Peridynamics: existence and localization

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    0493142 - ÚTIA 2019 RIV DE eng J - Journal Article
    Kružík, Martin - Mora-Corral, C. - Stefanelli, U.
    Quasistatic elastoplasticity via Peridynamics: existence and localization.
    Continuum Mechanics and Thermodynamics. Roč. 30, č. 5 (2018), s. 1155-1184. ISSN 0935-1175. E-ISSN 1432-0959
    R&D Projects: GA MŠMT(CZ) 7AMB16AT015; GA ČR(CZ) GF16-34894L
    Institutional support: RVO:67985556
    Keywords : Peridynamics * Elastoplasticity * Variational formulation
    OECD category: Pure mathematics
    Impact factor: 1.758, year: 2018
    http://library.utia.cas.cz/separaty/2018/MTR/kruzik-0493142.pdf

    Peridynamics is a nonlocal continuum mechanical theory based on minimal regularity on the deformations. Its key trait is that of replacing local constitutive relations featuring spacial differential operators with integrals over differences of displacement fields over a suitable positive interaction range. The advantage of such perspective is that of directly including nonregular situations, in which discontinuities in the displacement field may occur. In the linearized elastic setting, the mechanical foundation of the theory and its mathematical amenability have been thoroughly analyzed in the last years. We present here the extension of Peridynamics to linearized elastoplasticity. This calls for considering the time evolution of elastic and plastic variables, as the effect of a combination of elastic energy storage and plastic energy dissipation mechanisms. The quasistatic evolution problem is variationally reformulated and solved by time discretization. In addition, by a rigorous evolutive Γ -convergence argument we prove that the nonlocal peridynamic model converges to classic local elastoplasticity as the interaction range goes to zero.
    Permanent Link: http://hdl.handle.net/11104/0287000

     
     
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