Fig. 1

(a) The schematic of the multi-crack HSs exposed to asymmetrical thermal shock, where $ H $ represents the thickness of HSs, $ b $ and $ d $ denote the two crack tips, 2$ a $ is the crack length, and $ 2c $ is the crack spacing; (b) microstructure of the auxetic and non-auxetic HSs; (c) auxetic and non-auxetic honeycomb units, where $ l $ and $ h $ are honeycomb unit lengths, $ o $ is the honeycomb unit thickness, and $ \theta $ is the internal cell angle (color online)"

Fig. 2

The normalized non-Fourier and Fourier temperature fields in the auxetic HS with $ \theta=-30^{\circ} $, computed for (a) $ t=2 $ s, (b) $ t=4 $ s, (c) $ t=6 $ s, and (d) $ t=8 $ s (color online)"

Fig. 3

The normalized non-Fourier and Fourier temperatures at different positions of the auxetic HS with $ \theta=-30^{\circ} $ as a function of thermal shock time, computed for (a) $ y/H=0.2 $, (b) $ y/H=0.4 $, (c) $ y/H=0.6 $, and (d) $ y/H=0.8 $ (color online)"

Fig. 4

(a) The influence of the internal position of the auxetic HS with $ \theta=-30^{\circ} $ on the critical thermal shock time; (b) the influence of the internal cell angle of the HSs on the critical thermal shock time when $ y/H=0.2 $ (color online)"

Fig. 5

The normalized non-Fourier and Fourier stresses in the auxetic HS with $ \theta=-30^{\circ} $, computed for (a) $ t=2 $ s, (b) $ t=4 $ s, (c) $ t=6 $ s, and (d) $ t=8 $ s (color online)"

Fig. 6

The normalized non-Fourier and Fourier stresses at different positions of the auxetic HS with $ \theta=-30^{\circ} $ as a function of thermal shock time, computed for (a) $ y/H=0.2 $, (b) $ y/H=0.4 $, (c) $ y/H=0.6 $, and (d) $ y/H=0.8 $ (color online)"

Fig. 7

(a) The influence of the internal position of the auxetic HS with $ \theta=-30^{\circ} $ on the normalized maximum thermal stress; (b) the influence of the internal cell angle of HS on the normalized maximum thermal stress when $ y/H=0.2 $ (color online)"

Fig. 8

The variation of normalized multi-crack TSIF of auxetic HS with $ \theta=-30^{\circ} $ at (a) crack tip $ b $ and (b) crack tip $ d $ with thermal shock time for different values of thermal relaxation time when $ a/H=0.1 $ and $ c/H=0.5 $ (color online)"

Fig. 9

The variation of normalized maximum multi-crack TSIF of auxetic HS with $ \theta=-30^{\circ} $ at (a) crack tip $ b $ and (b) crack tip $ d $ with the crack position for different values of thermal relaxation time when $ a/H=0.1 $ and $ c/H=0.5 $ (color online)"

Fig. 10

The variation of normalized maximum TSIF of (a) auxetic HS with $ \theta=-30^{\circ} $ and (b) non-auxetic HS with $ \theta=30^{\circ} $ with crack spacing for different values of thermal relaxation time when $ a/H=0.1 $ and $ c/H=0.5 $ (color online)"

Fig. 11

(a) The influence of thermal relaxation time on the normalized maximum TSIF when $ a/H=0.1 $ and $ c/H=0.5 $; (b) the variation of normalized maximum TSIF with internal cell angle for different values of thermal relaxation time when $ a/H=0.1 $ and $ c/H=0.5 $ (color online)"

Fig. 12

(a) The influence of thermal relaxation time on the critical temperature of the auxetic HS with $ \theta=-30^{\circ} $ for different values of crack spacing when $ a/H=0.1 $; (b) the variation of the critical temperature of HS with internal cell angle for different values of thermal relaxation time when $ a/H=0.1 $ and $ c/H=0.5 $ (color online)"

Table A1

Thermal and mechanical parameters of alumina ceramic[42]"