3D modelling of strong discontinuities in elastoplastic solids: Fixed and rotating localization formulations.

*(English)*Zbl 1062.74623Summary: This paper is concerned with the incorporation of displacement discontinuities into a continuum theory of elastoplasticity for the modelling of localization processes such as cracking in brittle materials. Based on the strong discontinuity approach (SDA) (Computational Mechanics 1993; 12:277-296) mesh objective 2D and 3D finite element formulations are developed using linear and quadratic 2D elements as well as 8-noded 3D elements. In the formulation of the finite-element model proposed in the paper, the analogy with standard formulations is emphasized. The parameter defining the amplitude of the displacement jump within the finite element is condensed out at the material level without employing the standard static condensation technique. This approach results in linearized constitutive equations formally identical to continuum models. Therefore, the standard return mapping algorithm is used to solve the non-linear equations. In analogy to concepts used in continuum smeared crack models, a rotating formulation of the SDA is proposed in addition to the standard concept of fixed discontinuities. It is shown that the rotating localization approach reduces locking effects observed in analyses based on fixed localization directions. The applicability of the proposed SDA finite-element model as well as its numerical performance is investigated by means of a three-dimensional ultimate load analysis of a steel anchor embedded in a concrete block subjected to a shear force.

##### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74R20 | Anelastic fracture and damage |

##### Keywords:

finite-element method; plasticity; localization; discontinuous displacements; cracks; brittle materials
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\textit{J. Mosler} and \textit{G. Meschke}, Int. J. Numer. Methods Eng. 57, No. 11, 1553--1576 (2003; Zbl 1062.74623)

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