Keywords: strong discontinuity, material softening, post-critical analysis, strain localisation, statics and dynamics, three-dimensional rotations.

In this paper, we propose a computational framework capable of addressing the challenges of material softening and strain localization in spatial frame-like structures. By following an alternative non-local approach and the method of embedded strong discontinuity within the original velocity-based finite element formulation, we enable the framework to identify critical load levels and critical cross-sections accurately and describe the phenomenon of strain localisation effectively. The strong discontinuity-based approach involves introducing additional jump-like variables at the level of interpolated velocities and angular velocities. These variables are governed by additional equilibrium equations at the critical cross-section, derived using the weighted residual method. Our methodology is effective for both quasi-static and dynamic analysis. The numerical examples demonstrate the effectiveness and robustness of the proposed methodologies while also showing a comparison of results between the two approaches within the same underlying beam formulation.

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