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

<table>Normalized SIFs as a function of <svg height="11.05" id="M446" 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="M447" 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> (Case I) and <svg height="14.7125" id="M448" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 51.375 14.7125" width="51.375" 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">−</tspan>
<tspan style="font-size: 12.50px; " x="20.592442" y="0">1</tspan>
</text>
</g>
</g>
</svg>, <svg height="14.7125" id="M449" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 41.087502 14.7125" width="41.087502" 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">𝜀</tspan>
</text>
<text transform="matrix(1,0,0,-1,-57.47,63.5)">
<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> (Case II).</table>

International Scholarly Research Notices

fig10

Figure 10

Figure 10: Antiplane Shear Crack Normal to and Terminating at the Interface of Two Bonded Piezo-Electro-Magneto-Elastic Materials 