PSI - Issue 33

Andrea Pranno et al. / Procedia Structural Integrity 33 (2021) 1103–1114 Author name / Structural Integrity Procedia 00 (2019) 000–000

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cell along the X 2 direction and 1 along the X 1 direction). In Table 1, the microscopic critical stretch ratios for k = 20 have been reported at increasing RVE size, together with the percentage changes between the critical stretch ratios leading to the onset of microscopic and macroscopic instability. The results show that the prediction of the microscopic instability approaches to the macroscopic one by increasing the number of unit cells along the X 1 direction. It is assumed that the convergence between the macroscopic and the microscopic instability occurs when the relative percentage change is less than 1% (if the convergence is achieved the related microscopic critical load factor is reported in bold in the table). A slight inaccuracy of the microscopic critical load factors is related to the FE discretization and the linear interpolation method adopted to evaluate the critical stretch ratio, in fact, once the convergence of the predictions is reached, the values of the percentage change, by increasing the unit cell assembly, can oscillate around the zero value often changing their sign. Table 1. Comparison between the macroscopic and microscopic critical stretch ratios for different unit cell assembly in nacre-like composites with k = 20. The “ref.value” is referred to the macroscopic critical stretch ratio and the “% change” denotes the percentage changes between the macroscopic critical stretch ratio and the microscopic one.

Unit cell assembly

v f = 0.1 v f = 0.5 v f = 0.9 v f = 0.1 v f = 0.5 v f = 0.9 v f = 0.1 v f = 0.5 v f = 0.9

k = 20

1 × 1 0.361

2 × 1 0.361

4 × 1 0.425

8 × 1 0.612

16 × 1 0.660

32 × 1 0.672

64 × 1 0.674

ref. value 0.670 % change -46.18% -46.18% -36.64% -8.68%

0.22% 0.62%

-1.55%

0.848

0.518

0.520

0.564

0.670

0.779

0.832

ref. value 0.855 % change -39.42% -39.17% -34.01% -21.58% -8.90%

w = 0.1

-2.72% -0.77%

0.392

0.546

0.564

0.564

0.564

0.591

0.637

ref. value 0.685 % change -42.83% -20.26% -17.67% -17.71% -17.60% -13.66% -7.08%

0.585

0.585

0.414

0.546

0.574

-

-

ref. value 0.585 % change -29.29% -6.80%

-0.02% -0.03%

-1.97%

- -

- -

0.874

0.515

0.750

0.828

0.865

ref. value 0.876 % change -41.18% -14.37% -5.41%

w = 1

-0.14%

-1.27%

- -

- -

0.829

0.535

0.628

0.744

0.810

ref. value 0.835 % change -35.93% -24.84% -10.86% -3.02%

-0.77%

- -

- -

0.756

0.758

0.758

0.758

0.758

ref. value 0.755 % change 0.11%

0.35%

0.35%

0.35%

0.35%

- -

- -

0.925

0.930

0.930

0.930

0.913

ref. value 0.93002 % change -1.84%

w = 10

-0.51%

0.02%

0.02%

0.02%

- -

- -

0.871

0.876

0.878

0.878

0.851

ref. value 0.87508 % change -2.75%

-0.46%

0.11%

0.30%

0.33%

-

-