Quasistatic elastoplasticity via Peridynamics: existence and localization

0493142 - ÚTIA 2019 RIV DE eng J - Článek v odborném periodiku
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
Grant CEP: GA MŠMT(CZ) 7AMB16AT015; GA ČR(CZ) GF16-34894L
Institucionální podpora: RVO:67985556
Klíčová slova: Peridynamics * Elastoplasticity * Variational formulation
Obor OECD: Pure mathematics
Impakt faktor: 1.758, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0287000