Analyzing material softening and strain localisation through embedded strong discontinuity approach within velocity-based beam formulation.

In this paper, we propose a novel computational formulation capable of solving the problem of material softening and the emerging localisation of strains in spatial frame-like structure, a common phenomenon for brittle heterogeneous materials. This study adopts the embedded strong discontinuity approach within our original velocity-based framework. The velocity-based formulation is thus enhanced with additional capabilities of detection of critical load level and critical cross-section and introduction of the jump-like variables at the level of velocities and angular velocities to enable more realistic description of strain localisation. A modified consistency condition is derived using the method of weighted residuals in complete accordance with the theoretical concept of strong discontinuity. One of the key advantages of the proposed method is its computational efficiency, which is preserved even after detecting cross-sectional singularities and handling post-critical localised strains. The numerical examples show the effectiveness and robustness of the proposed approach. • The problem of material softening and strain localization is addressed. • The primary unknowns are velocities and angular velocities. • The field of unknowns is enriched with additional shape functions. • The solution procedure enables possible discontinuities and localisms. • The updated strains are obtained using kinematic compatibility equations. • We surpass the singularity of cross-sectional constitutive equations. [ABSTRACT FROM AUTHOR]