Download Encyclopedia of Physics (Principles of Classical Mechanics by S. Flugge (edited) PDF
By S. Flugge (edited)
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Additional info for Encyclopedia of Physics (Principles of Classical Mechanics and Field Theory) - Volume III 1
Example text
BlatzÀKo ¼ ! ! Gel f 1 À 2ν À2ν Gel ðf À 1Þ I 2 1 À 2ν 2ν I1 À 3 þ J J À 3 þ À1 þ À 1 2 ν 1 À 2ν 2 ν 1 À 2ν J2 ! 1 ∂ F 2 ψ ¼ FT σ BlatzÀKo ij J ∂C BlatzÀKo ð3:3Þ ð3:4Þ The viscoelastic stress modeled by Li and Lau [Eq. 5)] was selected as it has shown to produce reasonable results for polymers under high-rate loadings [1, 3]: σ visco 8t 9 " # ð < = 6 X 1 ÀðtÀτÞ=T _ ðτÞdτ FT i E ¼ F ½ A1 þ A 2 ð I 2 À 3Þ Gi e ; J : i¼1 ð3:5Þ 0 The convolution integral was solved either through direct numerical integration or a state variables approach [2, 10, 11].
5] numerical results. 38 R. Hall et al. Fig. 4 Fluid and solid kinematic and force quantities along the domain at the end of 100 h. (a) Solid density along the domain, (b) fluid density along the domain, (c) fluid stress along the domain, (d) interactive force along the domain Tandon et al. [5] studied the oxidation layer growth via diffusion reaction equation assuming an ideal fluid permeating through a rigid solid. Accordingly, in their model the deformation of the solid and viscous effects in the fluid are neglected.
In this section, we present numerical results for the oxidation behavior of polyimide PMR15 resin based on the oxidation reaction model developed in the works of Tandon et al. [5]. For the sake of completeness, we provide a brief description of the oxidation process in polymer. However, for a detailed description of the oxidation process and the reaction kinetics model, refer to [5, 12]. Oxidation front in polymer materials advances through a combination of diffusion and reaction mechanism. The exposed surface reacts with the diffusing air, depleting the amount of polymer 4 Diffusion of Chemically Reacting Fluids through Nonlinear Elastic Solids and 1D Stabilized Solutions 37 Fig.