Computation of Energy Release Rates for a Nearly Circular Crack

<table>The energy release rate, <svg height="13.55" id="M290" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 32.412498 13.55" width="32.412498" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="0" y="0">𝐺</tspan>
<tspan style="font-size: 12.50px; " x="9.1772022" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="13.340701" y="0">𝜑</tspan>
<tspan style="font-size: 12.50px; " x="21.6677" y="0">)</tspan>
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</svg> for <svg height="16.775" id="M291" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 106.9625 16.775" width="106.9625" xmlns="http://www.w3.org/2000/svg">
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<tspan style="font-size: 12.50px; " x="0" y="0">𝑓</tspan>
<tspan style="font-size: 12.50px; " x="6.9391651" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="11.102664" y="0">𝜁</tspan>
<tspan style="font-size: 12.50px; " x="17.779266" y="0">)</tspan>
<tspan style="font-size: 12.50px; " x="25.418598" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="37.458988" y="0">𝜁</tspan>
<tspan style="font-size: 12.50px; " x="46.923759" y="0">+</tspan>
<tspan style="font-size: 12.50px; " x="58.263981" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="64.51548" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="67.641228" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="73.892731" y="0">𝜁</tspan>
</text>
<text transform="matrix(1,0,0,-1,8.64,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">3</tspan>
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</svg> at various choices of <svg height="7.2375002" id="M292" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 7.9749999 7.2375002" width="7.9749999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.2375)">
<g transform="translate(72,-66.21)">
<text transform="matrix(1,0,0,-1,-71.95,66.37)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜈</tspan>
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</svg> with <svg height="13.55" id="M293" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 36.849998 13.55" width="36.849998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜇</tspan>
<tspan style="font-size: 12.50px; " x="11.077658" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="23.118048" y="0">1</tspan>
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</svg>.</table>

Mathematical Problems in Engineering

Computation of Energy Release Rates for a Nearly Circular Crack

Figure 8