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Nonlocal tangent operator for damage plasticity model. (English) Zbl 1340.74083

Vejchodský, T. (ed.) et al., Programs and algorithms of numerical mathematics 15. Proceedings of the 15th seminar (PANM), Dolní Maxov, Czech Republic, June 6–11, 2010. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-57-8). 89-94 (2010).
A model combining anisotropic elasticity and anisotropic plasticity coupled with isotropic damage is described. The yield function depends on the effective stress tensor and cumulated plastic strain; it also includes a hardening law. To avoid a pathological sensitivity of numerical results obtained via the finite element method to the underlying mesh, a combination of local and nonlocal cumulated plastic strain is introduced. The nonlocal cumulated plastic strain is defined through the integration of the weighted local cumulated plastic strain over a neighborhood of the investigated point. Next, a stress return algorithm is proposed. It is based on an elastic-plastic operator split that consists of a trial elastic predictor followed by a return mapping algorithm. The entire procedure is summarized in a brief algorithmic way. Finally, the concept of a consistent tangent stiffness operator is presented. The proposed method is illustrated by a numerical example showing a quadratic rate of convergence.
For the entire collection see [Zbl 1277.65003].

MSC:

74R05 Brittle damage
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74E10 Anisotropy in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74R20 Anelastic fracture and damage

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