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Table 1 Summary of adopted parameters and information for the two metamaterials

From: Enriched homogenized model for viscoelastic plane wave propagation in periodic layered composites

Meta-mat

D\(^{{\mathbf{a}}}\)

Matrix

Compliant layer

Stiff inclusion

\({\varvec{E}}_{\mathbf {1}}^{{\mathbf{b}}}\)

\({\varvec{\rho }_{\mathbf 1}}^{{\mathbf{c}}}\)

f

\({{\varvec{E}}_{\mathbf 2}^{\mathbf {0}}}^{{\mathbf{b}}}\)

\({{\varvec{E}}_{\mathbf {2}}^{\varvec{\infty }}}^{{\mathbf{b}}}\)

\({\varvec{\rho }_{\mathbf 2}}^{{\mathbf{c}}}\)

\({\varvec{g}}\)

\({{\varvec{E}}_{\mathbf {3}}}^{{\mathbf{b}}}\)

\({\varvec{\rho }_{\mathbf 3}}^{{\mathbf{c}}}\)

\({\varvec{h}}\)

  

Epoxy

Silicon rubber

Lead\({}^{\mathrm{d}}\)

1

21

4.35

1180

\(\displaystyle {\frac{6}{21}}\)

\(1.175 \times 10^{-4}\)

\(0.47 \times 10^{-4}\)

1300

\(\displaystyle {\frac{5}{21}}\)

40.8

11600

\(\displaystyle {\frac{10}{21}}\)

  

Mortar

Natural rubber

Lead\({}^{\mathrm{e}}\)

2

30

30

2500

\(\displaystyle {\frac{6}{30}}\)

0.01

0.004

900

\(\displaystyle {\frac{2}{30}}\)

16

11400

\(\displaystyle {\frac{22}{30}}\)

  1. \({}^{\mathrm{a}}\) Units in \(\mathrm {mm}\)
  2. \({}^{\mathrm{b}}\) Units in GPa
  3. \({}^{\mathrm{c}}\) Units in \(\mathrm {kg/m^3}\)
  4. \({}^{\mathrm{d}}\) Typical of lead alloys
  5. \({}^{\mathrm{e}}\) Typical of pure lead