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

<table>Variation of <svg height="18.700001" id="M464" style="vertical-align:-4.87915pt" version="1.1" viewbox="0 0 25.075001 18.700001" width="25.075001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.7)">
<g transform="translate(72,-57.04)">
<text transform="matrix(1,0,0,-1,-71.95,61.95)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑘</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.17,68.09)">
<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>
</g>
</g>
</svg>, <svg height="18.975" id="M465" 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">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="M466" 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="M467" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 13.675 11.05" width="13.675" 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">𝑐</tspan>
</text>
</g>
</g>
</svg> with <svg height="14.7125" id="M468" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 73.8125 14.7125" width="73.8125" 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">𝑒</tspan>
</text>
<text transform="matrix(1,0,0,-1,-57.81,63.5)">
<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,-39.49,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝜀</tspan>
</text>
<text transform="matrix(1,0,0,-1,-31.29,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">1</tspan>
</text>
</g>
</g>
</svg>.</table>

International Scholarly Research Notices

fig12

Figure 12

Figure 12: Antiplane Shear Crack Normal to and Terminating at the Interface of Two Bonded Piezo-Electro-Magneto-Elastic Materials 