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  3. 3 you are given that where is the stress...

Question: 3 you are given that where is the stress...

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3 You are given that where σ¡¡ is the stress tensor. Eij is the (symmetric) strain tensor, and Cijk, is a fourth order tensor of constant coefficients. In the following, δί, is the Kronecker delta tensor (a) Given that for constants λ and 14. show that Show that the mean normal stress ơak is 3 (b) Given that λ satisfies ει,--0.3014 x 10-2, ε22 0.5315 x 10-2 ε33 0.4353 x 10-2. ε12-0.3124 x 10-2, ε23-0.7518 x 10-2, and ε31--0.5416 x 10-2. find the stress tensor 0.6391 Pa and μ-09068 Pa, and that the strain tensor Hence find the stress force on a unit area element in the direction n (0.5774, -0.5774,0.5774)

Relation between different parameters: A number of relationships between E. v. K, λ and μ hold and are summarized in Table 1 μ ( G) is the elastic shear modulus. K the elastic bulk modulus, E the elastic stiffness or Youngs Modulus) and Poissons ratio Ev 3(1-21-22(1 ) 3KE E, K 6K 9uK 3K + μ 3K-2μ | 2(3K + μ) 2μ 3 κ.μ Table 1: The relations between the properties of elastic bodies

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