Poisson's Ratio & Elastic Relations
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- 1.
Poisson's ratio of cork is approximately:
- 2.
Poisson's ratio of rubber is approximately:
- 3.
If Y = 2G(1 + nu) and Y = 3B(1 - 2nu), for nu = 0.25, the ratio Y:G:B is:
- 4.
For a material with nu = 0.5, the bulk modulus is:
- 5.
Poisson's ratio is the ratio of: <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 400 140" style="max-width:400px;width:100%;height:auto;background:#faf9f5;border-radius:12px;border:1px solid rgba(20,20,19,0.10)"> <title>Poisson's ratio — lateral contraction under longitudinal stretch</title> <defs> <marker id="ah-q051-08a" markerWidth="8" markerHeight="6" refX="8" refY="3" orient="auto"><polygon points="0,0 8,3 0,6" fill="#c6613f"/></marker> <marker id="ah-q051-08b" markerWidth="8" markerHeight="6" refX="0" refY="3" orient="auto"><polygon points="8,0 0,3 8,6" fill="#788c5d"/></marker> </defs> <!-- Original rod (dashed) --> <rect x="100" y="35" width="180" height="40" rx="3" fill="none" stroke="#14140f" stroke-width="1" stroke-dasharray="4,3" opacity="0.35"/> <!-- Stretched rod (narrower, longer) --> <rect x="80" y="40" width="220" height="30" rx="3" fill="#c6613f" fill-opacity="0.08" stroke="#14140f" stroke-width="1.5"/> <!-- Longitudinal arrows --> <line x1="300" y1="55" x2="345" y2="55" stroke="#c6613f" stroke-width="2" marker-end="url(#ah-q051-08a)"/> <line x1="80" y1="55" x2="40" y2="55" stroke="#c6613f" stroke-width="2" marker-end="url(#ah-q051-08a)"/> <text x="355" y="59" font-size="9" fill="#c6613f" font-family="sans-serif">F</text> <text x="30" y="59" font-size="9" fill="#c6613f" font-family="sans-serif">F</text> <!-- Lateral contraction arrows (inward) --> <line x1="190" y1="35" x2="190" y2="42" stroke="#788c5d" stroke-width="1.5" marker-end="url(#ah-q051-08b)"/> <line x1="190" y1="75" x2="190" y2="68" stroke="#788c5d" stroke-width="1.5" marker-end="url(#ah-q051-08b)"/> <!-- Labels --> <text x="190" y="25" text-anchor="middle" font-size="9" fill="#788c5d" font-family="sans-serif">lateral contraction</text> <text x="190" y="95" text-anchor="middle" font-size="12" font-weight="700" fill="#14140f" font-family="sans-serif">ν = |ε_lateral / ε_longitudinal|</text> <text x="190" y="115" text-anchor="middle" font-size="10" fill="#788c5d" font-family="sans-serif">stretches longer → gets thinner</text> </svg>
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