##
**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].

For the entire collection see [Zbl 1277.65003].

Reviewer: Jan Chleboun (Praha)

### 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 |

### Keywords:

damage plasticity model; nonlocal tangent operator; hardening; return mapping; finite element code### Software:

OOFEM
PDF
BibTeX
XML
Cite

\textit{M. Horák} et al., in: 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. 89--94 (2010; Zbl 1340.74083)

Full Text:
Link