PERFECT PLASTICITY WITH DAMAGE AND HEALING AT SMALL STRAINS, ITS MODELING, ANALYSIS, AND COMPUTER IMPLEMENTATION

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 su...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 2016-01, Vol.76 (1), p.314-340
Main Authors: ROUBÍČEK, TOMÁŠ, VALDMAN, JAN
Format: Article
Language:English
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Summary: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.
ISSN:0036-1399
1095-712X
DOI:10.1137/15M1019647