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A posteriori error estimation for the non-associated plasticity Drucker-Prager model with hardening. (English) Zbl 1378.74014

Shehata, Hany (ed.) et al., Numerical analysis of nonlinear coupled problems. Proceedings of the 1st GeoMEast international congress and exhibition, Egypt 2017 on sustainable civil infrastructures. Cham: Springer (ISBN 978-3-319-61904-0/pbk; 978-3-319-61905-7/ebook). Sustainable Civil Infrastructures, 98-109 (2018).
Summary: The numerical solution of non-associated elastoplasticity is still a key aspect of research and development in computational plasticity. Approximate solution procedures are based, in the context of a displacement method, on a weak form of the equilibrium and reply upon two main ingredients: the numerical integration of the rate constitutive relations over a generic time step (local stage) and the iterative algorithm exploited to solve the nonlinear equilibrium equations (global stage). The fully discrete problem is the obtained by performing a spatial discretization of the field equations and a time-integration of the evolution rule. The interest is here given to the discretization errors, which are caused by the numerical discretization of the continuous mathematical model in order to define an adaptive strategy.
The aim of this paper is to extend the concept of error in the constitutive equations to non-associated plasticity Drucker-Prager model to handle non-associative rate-independent plasticity problems solved by employing the incremental displacement conforming finite element method.
Numerical examples by PLSAER2D (a Matlab program) for both the associated and the non-associated cases for Drucker-Prager model with hardening are also presented.
For the entire collection see [Zbl 1401.65003].

MSC:

74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)

Software:

PLSAER2D; Matlab
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