Question

1. For an isotropic material, E and v are often chosen as the two independent engineering constants. There are other elastic constants that we have introduced in Lecture 5: the shear modulus G, the bulk modulus K, and the Lames, constants, μ and λ·Suppose that Prove that μ and λ, and K, satisfy the following relations: 2vG 2 3(1- 2v) To prove it, apply pure shear stress t, and connect it to pure shear strain γ by G, ie. τ_Gy. Then in the 45° orientation, consider its normal stresses σ, and σ: are related to its normal strains ε, and e, through E and vin Hooke's law. We can easily establish this relation.

Answer 1

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