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Perfect plasticity with damage and healing at small strains, its modeling, analysis, and computer implementation

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    0458557 - ÚTIA 2017 RIV US eng J - Journal Article
    Roubíček, Tomáš - Valdman, Jan
    Perfect plasticity with damage and healing at small strains, its modeling, analysis, and computer implementation.
    Siam Journal on Applied Mathematics. Roč. 76, č. 1 (2016), s. 314-340. ISSN 0036-1399. E-ISSN 1095-712X
    R&D Projects: GA ČR GA13-18652S; GA ČR GA14-15264S
    Institutional support: RVO:67985556 ; RVO:61388998
    Keywords : Prandtl-Reuss perfect plasticity * bounded-deformation space * incomplete damage
    Subject RIV: BA - General Mathematics
    Impact factor: 1.670, year: 2016
    http://library.utia.cas.cz/separaty/2016/MTR/valdman-0458557.pdf

    The quasistatic, Prandtl-Reuss perfect plasticity at small strains is combined with a gradient, reversible (i.e., admitting healing) damage which influences both the elastic moduli and the yield stress. Existence of weak solutions of the resulting system of variational inequalities is proved by a suitable fractional-step discretization in time with guaranteed numerical stability and convergence. After finite-element approximation, this scheme is computationally implemented and illustrative two-dimensional simulations are performed. The model allows, e.g., for application in geophysical modeling of reoccurring rupture of lithospheric faults. Resulting incremental problems are solved in MATLAB by quasi-Newton method to resolve the elastoplasticity component of the solution, while the damage component is obtained by solving a quadratic programming problem.
    Permanent Link: http://hdl.handle.net/11104/0258816

     
     
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