Antiplane Shear Crack Normal to and Terminating at the Interface of Two Bonded Piezo-Electro-Magneto-Elastic Materials

<table>Variation of <svg height="19.6875" id="M469" style="vertical-align:-4.87915pt" version="1.1" viewbox="0 0 61.75 19.6875" width="61.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.6875)">
<g transform="translate(72,-56.25)">
<text transform="matrix(1,0,0,-1,-71.95,61.17)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑘</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.17,67.3)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝛾</tspan>
<tspan style="font-size: 8.75px; " x="0" y="10.91">i</tspan>
<tspan style="font-size: 8.75px; " x="2.4330561" y="10.91">n</tspan>
<tspan style="font-size: 8.75px; " x="6.8090558" y="10.91">t</tspan>
</text>
<text transform="matrix(1,0,0,-1,-51.99,61.17)">
<tspan style="font-size: 12.50px; " x="0" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="9.364747" y="0">𝑘</tspan>
</text>
<text transform="matrix(1,0,0,-1,-35.84,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐷</tspan>
<tspan style="font-size: 8.75px; " x="0" y="9.2799997">i</tspan>
<tspan style="font-size: 8.75px; " x="2.4330561" y="9.2799997">n</tspan>
<tspan style="font-size: 8.75px; " x="6.8090558" y="9.2799997">t</tspan>
</text>
</g>
</g>
</svg> (in C/m<sup>2</sup>) and <svg height="18.975" id="M470" style="vertical-align:-4.30869pt" version="1.1" viewbox="0 0 25.075001 18.975" width="25.075001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.975)">
<g transform="translate(72,-56.82)">
<text transform="matrix(1,0,0,-1,-71.95,61.17)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑘</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.17,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝐸</tspan>
<tspan style="font-size: 8.75px; " x="0" y="9.2799997">i</tspan>
<tspan style="font-size: 8.75px; " x="2.4330561" y="9.2799997">n</tspan>
<tspan style="font-size: 8.75px; " x="6.8090558" y="9.2799997">t</tspan>
</text>
</g>
</g>
</svg> (in 10<sup>6</sup> kV/m) against <svg height="11.05" id="M471" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 13.4625 11.05" width="13.4625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.05)">
<g transform="translate(72,-63.16)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜌</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.67,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑒</tspan>
</text>
</g>
</g>
</svg> with <svg height="14.7125" id="M472" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 74.037498 14.7125" width="74.037498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.7125)">
<g transform="translate(72,-60.23)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜌</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.67,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑐</tspan>
</text>
<text transform="matrix(1,0,0,-1,-57.63,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">𝜌</tspan>
</text>
<text transform="matrix(1,0,0,-1,-39.32,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝜀</tspan>
</text>
<text transform="matrix(1,0,0,-1,-31.11,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">1</tspan>
</text>
</g>
</g>
</svg>.</table>

International Scholarly Research Notices

fig13

Figure 13

Figure 13: Antiplane Shear Crack Normal to and Terminating at the Interface of Two Bonded Piezo-Electro-Magneto-Elastic Materials 