On advanced solution strategies to overcome locking effects in strong discontinuity approaches

This paper is concerned with the analysis of locking effects resulting from different orientations of micro-defects and those of the corresponding macro-defects. Based on a mixed-mode material model embedded within the framework of the strong discontinuity approach (SDA), the described locking effect is illustrated by means of a crack analysis of a notched concrete beam. To overcome the deficiency of the proposed finite element model, the original SDA is modified and extended. For that purpose, two different advanced numerical formulations are developed: a rotating crack approach and a multiple crack approach. Restricting the governing equations to the material point level, a standard return-mapping procedure is applied to the algorithmic formulations of both models. The applicability and the performance of the proposed numerical implementations are investigated by means of a re-analysis of the two-dimensional notched concrete beam