Use the \(E / ho\) chart of Fig. 3.3 to identify materials with both \(E>100 \mathrm{GPa}\) and \(E^{1 / 3} / ho>0.003(\mathrm{GPa})^{1 / 3} /\left(\mathrm{kg} / \mathrm{m}^{3}\right)\). Remember that, on taking logs, the index \(M=E^{1 / 3} / ho\) becomes

\[\log (E)=3 \log (ho)+3 \log (M)\]

and that this plots as a line of slope 3 on the chart, passing through the point \(E=27\) when \(ho=1000\) in the units on the chart.

Fig.3.3

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oungs modulusE GPa Coungos modulus density 1000 100 110 10-2 Longitudinal wave speed 10 ms 3x103 Foams 10 ms- Rigid polymer foams 10-33x102 10-4 10 10 ms 100 Diamond Al2Os Steels SIC Ti alloys Technical ceramics SigNa B.C. Al alloys Composites CFRP Glass Bamboo Mg alloys- GFRP -Wood grain Natural PMMA- materials PA- Ni alloys WC O-W alloy's Cu alloys Metals Polyester Lead alloys Concrete Zinc alloys PEEK PS Wood 1 grain Nontechnical Epoxies ceramics PC PP Leat RET PE PTFE Polymers EVA Cork Isoprene Flexible polymer foams Butyl rubber 1000 Density pkgom "Silicone elastomers Polyuret ane. Neoprene Elastomers Guidelines for minimum mass design 100000 MFA 1