PSI - Issue 80

Roman Vodička et al. / Procedia Structural Integrity 80 (2026) 501 – 508 R. Vodicˇka / Structural Integrity Procedia 00 (2025) 000–000

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Fig. 3. Reaction force caused by the prescribed increasing displacement g .

(a)

(b)

Fig. 4. Distributions of the plastic strain π (its norm) (a), and of the phase-field variable α (b) in the beam at the instants for g = 0 . 225 , 0 . 625 , 0 . 875 , 0 . 9 , 0 . 95 , 1 . 0 mm. Displacements are magnified 20 times.

beam’s deformation. The highest curvature of the deflected beam can be observed at the plastic zones and close to the cracks after their formation. The first instant pertains to reaching the yield surface. The plastic deformation is initialised when the magnitude of the deviatoric stress approached the yield level in Fig. 5(a). Due to hardening, the stress increases afterwards. Anyhow, after initiation of cracks, the values of the stress decrease which is accompanied by ceased increase of plastic strain in a few last instants. The initialisation of phase-field damage can be observed in the third used instant. It also corresponds to reaching the critical stress (trace) in Fig. 5(b). This initialisation changes to crack nucleation and propagation, which is visible in the last two instants. After rupture, the stress vanishes close to the crack. Nevertheless, at the crack tip, there remains a stress concentration which is however blocked from propagation due to compressive stress appearing in the bent beam.