PSI - Issue 79

Lorenzo Leonetti et al. / Procedia Structural Integrity 79 (2026) 485–492

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4.1. Validation under proportional loading-unloading paths A first validation of the proposed data-driven multiscale strategy has been conducted with reference to different loading-unloading histories, being characterized by combined shear/biaxial macrostrains for fixed 22.5  =  and the following values of  : 0°, 45°, 90°, 135°. For each direction, the loading branch has an increasing loading factor  from 0 to 0.4. Fig. 4 reports the comparison between the present data-driven approach and the (reference) micromechanical approach, in terms of overall stress-strain curves, for all the considered loading-unloading paths.

Fig. 4. Comparison between present data-driven and reference micromechanical homogenization for proportional loading-unloading paths: (a) 0  =  ; (b) 45  =  ; (c) 90  =  ; (d) 135  =  .

4.2. Validation under nonproportional unloading paths Finally, the following nonproportional macrostrain paths have been considered for further validation: • Path 1. The first step is purely tensile along the 1 x direction, with effective macrostrain increasing from 0 to 0.025. The second step is purely shear, with the effective macrostrain increasing up to 0.0354. • Path 2. This path has the same steps as Path 1 with a reversed order of application. • Path 3. The first step is purely shear, with effective macrostrain increasing from 0 to 0.025. The second step is purely compressive along the 1 x direction, with the effective macrostrain increasing up to 0.0354. • Path 4. This path has the same steps as Path 3 with a reversed order of application. Fig. 5 reports the comparison between the present data-driven approach and the (reference) micromechanical approach, in terms of overall stress-strain curves, for all the considered nonproportional loading paths.