等方性粘弾性体の非線形構成方程式 : 分散系のレオロジー,その他

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Based upon the phenomenological theory of non-linear responses of many variably systems (K. Okano and O. Nakada, J. Phys. Soc. Japan, 16, 2071 (1961)) the non-linear constitutive equations for isotropic viscoelastic materials are presented. Let σ(t) denote the stress tensor at an instant of time t, and D(t) be the displacement gradient ∇S (S being the displacement vector) or velocity gradient ∇V (V being the velocity vector) according as the material concerned is a viscoelastic solid or a viscoelastic liquid, then we have (K. Okono, Japanese J. Appl. Phys., 1, 302 (1961)) the following non-linear constitutive equation (up to the second order terms in D) for an isotropic viscoelastic material: σ(t)=∫^t_<-∞>[a^<(1)>(t-τ)D^<(0)>(τ)+b^<(1)>(t-τ)D^<(2)>(τ)]dτ+∫^t_<-∞>∫^t_<-∞>[a^<(2)>(t-τ_1, t-τ_2)D^<(0)>(τ_1) : D^<(0)>(τ_2)l+b^<(2)>(t-τ_1, t-τ_2)D^<(2)>(τ_1) : D^<(2)>(τ_2)I+c^<(2)>(t-τ_1, t-τ_2)D^<(0)>(τ_1)・D^<(2)>(τ_2)+d^<(2)>(t-τ_1, t-τ_2){1/2D^<(2)>(τ_1)・D^<(2)>(τ_2)+1/2D^<(2)>(τ_2)・D^<(2)>(τ_1)-1/3D^<(2)>(τ_1) : D^<(2)>(τ_2)I}+e^<(2)>(t-τ_1, t-τ_2){1/2D^<(1)>(τ_1)・D^<(2)>(τ_2)-1/2D^<(2)>(τ_2)・D^<(1)>(τ_1)}]dτ_1dτ_2+higher order terms. In the above equation I is the unit tensor and D^<(0)>≡1/3∇・SI or 1/3∇・VI D^<(1)>≡1/2(D-D^^~) D^<(2)>≡1/2(D+D^^~)-D^<(0)> and a^<(0)>(t), b^<(1)>(t), a^<(2)>(t_1, t_2), ect. are the scalar material functions characterizing the viscoelastic response of the system concerned. The third order terms in D are given in the text. (eq. 2.5). If the material concerned is incompressible the terms on the right hand of the above constitutive equation which are connected with a dilatation deformation (he terms containing a^<(1)>, a^<(2)>, b^<(2)>, c^<(2)>) should be replaced by and indeterminate hydrostatic pressure : -pI
社団法人日本材料学会の論文
1963-05-15

著者

岡野光治
理化学研究所

等方性粘弾性体の非線形構成方程式 : 分散系のレオロジー,その他

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