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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Fig. 4. Nacre-like composite material exhibiting a local instability with v f = 0.1, w = 10 and k = 20 at increasing RVE size in the X 1 direction .

Table 2. Comparison between the macroscopic and microscopic critical stretch ratios for different unit cell assembly in nacre-like composites with k = 1000. 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 = 1000

1 × 1 0.747

2 × 1 0.745

4 × 1 0.745

8 × 1 0.758

16 × 1 0.768

32 × 1

64 × 1

-

-

ref. value 0.765 % change -2.30% -2.59%

-0.97%

0.39%

-2.60%

- -

- -

0.970

0.938

0.935

0.935

0.940

ref. value 0.975 % change -3.77% -4.07%

w = 0.1

-0.55%

-4.07%

-3.57%

-

-

0.977

0.975

0.975

0.975

0.975

0.975

0.975

ref. value 0.986 % change -1.12% -1.12%

-1.12% -0.92%

-1.12%

-1.12%

-1.12%

0.645

0.648

0.616

0.618

0.633

-

-

ref. value 0.640 % change -3.77% -3.51%

0.79%

1.16%

-1.13%

- -

- -

0.931

0.932

0.908

0.906

0.913

ref. value 0.936 % change -2.97% -3.12%

w = 1

-0.54% -0.43%

-2.46%

-

-

0.982

0.987

0.989

0.960

0.960

0.960

0.964

ref. value 0.986 % change -2.58% -2.58%

-0.40%

0.11%

0.29%

-2.58%

-2.22%

0.821

0.822

0.824

0.809

0.812

-

-

ref. value 0.820 % change -1.35%

0.12%

0.29%

0.52%

-1.03%

-

- -

0.981

0.983

0.984

0.957

0.962

0.962

ref. value 0.980 % change -2.40% -1.87%

w = 10

0.08%

0.31%

0.36%

-1.87%

- -

0.987

0.994

0.995

0.996

-

0.965

ref. value 0.995 % change -2.97%

-0.77% -0.15%

0.01%

0.05%

-

-

In Table 1 the microscopic critical stretch ratios c  for nacre-like composite materials with k = 20 clearly shows that the microscopic critical stretch ratios are strongly underestimated by the microscopic stability analysis compared with the macroscopic one. The highest percentage change reached is 46.18% for a unit cell assembly 1 × 1 with w =