Table 2

Laws providing the elastic constants in MPa as a function of ρ, the density of the plate: left column for spruce, with ρ0s=450 kg·m-3$ {\rho }_0^s=450\mathrm{\enspace }\mathrm{kg}\middot {\mathrm{m}}^{-3}$; right column for maple, with ρ0m=640 kg·m-3$ {\rho }_0^m=640\enspace {\mathrm{kg}\middot \mathrm{m}}^{-3}$.

Spruce Maple
[MPa] [MPa]
E L s = 13000 + 45 ( ρ - ρ 0 s ) $ {E}_L^s=13000+45(\rho -{\rho }_0^s)$ E L m = 12210 × ( ρ ρ 0 m ) 1.30 $ {E}_L^m=12210\times {\left(\frac{\rho }{{\rho }_0^m}\right)}^{1.30}$
E R s = 1000 + 5.5 ( ρ - ρ 0 s ) $ {E}_R^s=1000+5.5(\rho -{\rho }_0^s)$ E R m = 1820 × ( ρ ρ 0 m ) 1.03 $ {E}_R^m=1820\times {\left(\frac{\rho }{{\rho }_0^m}\right)}^{1.03}$
G LR s = 840 + 1.32 ( ρ - ρ 0 s ) $ {G}_{{LR}}^s=840+1.32(\rho -{\rho }_0^s)$ G LR m = 1375 × ( ρ ρ 0 m ) 1.14 $ {G}_{{LR}}^m=1375\times {\left(\frac{\rho }{{\rho }_0^m}\right)}^{1.14}$
G RT s = 48 + 0.018 ( ρ - ρ 0 s ) $ {G}_{{RT}}^s=48+0.018(\rho -{\rho }_0^s)$ G RT m = 430 × ( ρ ρ 0 m ) 1.74 $ {G}_{{RT}}^m=430\times {\left(\frac{\rho }{{\rho }_0^m}\right)}^{1.74}$
G TL s = 840 + 1.93 ( ρ - ρ 0 s ) $ {G}_{{TL}}^s=840+1.93(\rho -{\rho }_0^s)$ G TL m = 1010 × ( ρ ρ 0 m ) 1.26 $ {G}_{{TL}}^m=1010\times {\left(\frac{\rho }{{\rho }_0^m}\right)}^{1.26}$

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