PSI - Issue 39

Fabrizio Greco et al. / Procedia Structural Integrity 39 (2022) 638–648 Author name / Structural Integrity Procedia 00 (2019) 000–000

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The effectiveness of the strategy presented in Section 2.2 is now assessed. Figure 5-a reports stress vs elongation curves gained through the proposed DIM considering several values of Weibull parameter m . For completeness, the perfectly stable and metastable solutions are reported in the graph. Figure 5-b shows snapshots of the deformed shapes of the couplet corresponding to elongation values marked by Roman numerals. The results show that the imperfections of cohesive properties ensure a numerical solution with physical sense because, regardless of the m values adopted, the stress-elongation curves have a softening behavior close to the one predicted by the stable model ( i.e. , SIM 1). However, the m parameter affects the stress peak, as one can see in the zoomed view. For m =10, the peak stress is 2.5% lower than the stable one. Contrarily, for larger values of m ( i.e., m =10000 and m =100000), the solution remarks the metastable one soon after post-peak, as highlighted by observing the overlap of the softening branches of the DIM and metastable models. Therefore, such results possess less physical meaning. The solutions are close to the metastable one because the effect of material imperfections is rather limited. Finally, for 100< m <1000, the structural response is quite close to the stable one, thus highlighted that selecting values within such range represents a suitable compromise. The snapshots of Figure 5-b confirm that the predictions of the proposed DIM with randomized cohesive strengths (assuming m =100) and those of the auxiliary model SIM 1 are quite comparable.

Figure 5. (a) Stress vs elongation curves achieved using the proposed DIM model with imperfections (for increasing values of the Weibull parameter m), without imperfection (gray line), and the auxiliary model SIM 1; (b) Snapshots of the deformed configurations of the brick masonry couplets relative to the elongation values marked by Roman numerals concerning the proposed DIM (with m=100) and the auxiliary SIM 1.

4. Conclusions This work has presented an effective Diffusive Interface Modeling (DIM) approach for the analysis of tensile cracking behavior of quasi-brittle materials. In particular, the work proposes a useful strategy that avoids bifurcation and localization instabilities that may affect the numerical model when several interface elements manifest softening behavior simultaneously. Under such circumstances, the model can suffer from uniqueness-solution issues, whose major consequence is an incorrect evaluation of the dissipated energy. The proposed strategy consists of introducing imperceptible variations in the cohesive strengths of the embedded interfaces according to a Weibull distribution. As a result, there is no probability that multiple interfaces reach the minimum strength value within the same embedded package, thereby ensuring the uniqueness of the solution. The proposed model has been applied for simulating the direct tensile test of a brick masonry couplet. In particular, the failure mode involving the damage of the couplet because of the crisis of brick-mortar interfaces is investigated.