58 S. Taguchi et al. Fig. 6.1 Master curves of each material property Fig. 6.2 Poisson’s ratio in the Laplace domain (T =273K, s =γ +iω, γ = 0.142, ω=0.767 rad/s) where k0, ki, G0, Gi, υ0, and υi are the coefficients of the Prony series, Nis the number of terms in the series, and ρi is the relaxation time. Figure 6.1 shows master curves of the material properties at the reference temperature T0 =303. The material is a soft epoxy resin (Epikote 871). ∼εzz(s) is computed using Eq. (6.3). In the equation, s∼υ(s) can be obtained by calculating the Laplace transformation of υ(t) and multiplying s on both sides of the equation as follows: s∼υ(s) =υ0 − M i=1 sρiυi sρi +1 (6.12) Poisson’s ratio in the Laplace domain is obtained by Eq. (6.12). Since the Fourier transformation is used, taking into considering that the variable s =γ +iω, s∼υ(s) is shown in Fig. 6.2. Figure 6.2 shows the Poisson’s ratio in the Laplace domain. The temperature is T =273K. ∼εzz(s) is calculated by using the above property. The input strains is shown in Fig. 6.3. Δt is Δt =0.008, and the number of original input data is 1024. According to the proposed method, the number of original data is increased to 2048 for calculation. Each parameter is γ =0142 and ω=0.767 rad/s. Figure 6.4 shows the calculation results of the through-thickness strains calculated by Eqs. (6.3) and (6.7) using the input values obtained by the proposed method. Calculation results are compared with the values obtained by 3D FEM. There are 1024 calculation results. Calculation results are generally consistent. Next, the stresses are computed from the obtained values, in-plane strains, and material properties by the numerical integration using Eqs. (6.1) and (6.2). Figure 6.5 shows the calculation results of normal stress components.
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