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The purpose of this problem is to show the relationship between material constants typically used in engineering practice. This is useful because you may often have access to measurements of or tabulated values of some constants (e.g., Young's modulus and Poisson's ratio) but need another constant (e.g., shear modulus) for a calculation. Use the expression Cijkl µ(dildjk + dikdjl) + Adijokl to derive = the following: (a) Young's modulus, E = µ(3X+2µ)/(X+μ), from the definition σ11 = E€11 in a unconfined (022 = 0,033 = 0) uniaxial tension test. (b) Poisson's ratio, v = \/(2(X + µ)), from the definition v=-€22/11 in the same test as in (a). (c) Shear modulus, p= G = 012/(2€12) = E/(2(1 + v)). Use the results to show that C can also be written Cijkl Ev/((1+ v)(1 − 2v))dijðkl. = E/(2(1 + v))(dildjk + dikdjl) +

The purpose of this problem is to show the relationship between material constants typically used in engineering practice. This is useful because you may often have access to measurements of or tabulated values of some constants (e.g., Young's modulus and Poisson's ratio) but need another constant (e.g., shear modulus) for a calculation. Use the expression Cijkl µ(dildjk + dikdjl) + Adijokl to derive = the following: (a) Young's modulus, E = µ(3X+2µ)/(X+μ), from the definition σ11 = E€11 in a unconfined (022 = 0,033 = 0) uniaxial tension test. (b) Poisson's ratio, v = \/(2(X + µ)), from the definition v=-€22/11 in the same test as in (a). (c) Shear modulus, p= G = 012/(2€12) = E/(2(1 + v)). Use the results to show that C can also be written Cijkl Ev/((1+ v)(1 − 2v))dijðkl. = E/(2(1 + v))(dildjk + dikdjl) +

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The purpose of this problem is to show the relationship between material constants typically used in engineering practice. This is useful because you may often have access to measurements of or tabulated values of some constants (e.g., Young's modulus and Poisson's ratio) but need another constant (e.g., shear modulus) for a calculation. Use the expression Cijkl = µ(dildjk + dikdjl) + Ad¿jdkl to derive the following: (a) Young's modulus, E = µ(3X+2µ)/(X+μ), from the definition 11 = Ee11 in a unconfined (022 = 0,033 = 0) uniaxial tension test. (b) Poisson's ratio, v = \/(2(X + μ)), from the definition v = €22/11 in the same test as in (a). (c) Shear modulus, μ = G = 012/(2€12) = E/(2(1 + v)). Use the results to show that C can also be written Cijkl Ev/((1+v)(1 − 2v))dij§kl. = E/(2(1 + v))(duðjk + dikdjl) +
Transcribed Image Text:The purpose of this problem is to show the relationship between material constants typically used in engineering practice. This is useful because you may often have access to measurements of or tabulated values of some constants (e.g., Young's modulus and Poisson's ratio) but need another constant (e.g., shear modulus) for a calculation. Use the expression Cijkl = µ(dildjk + dikdjl) + Ad¿jdkl to derive the following: (a) Young's modulus, E = µ(3X+2µ)/(X+μ), from the definition 11 = Ee11 in a unconfined (022 = 0,033 = 0) uniaxial tension test. (b) Poisson's ratio, v = \/(2(X + μ)), from the definition v = €22/11 in the same test as in (a). (c) Shear modulus, μ = G = 012/(2€12) = E/(2(1 + v)). Use the results to show that C can also be written Cijkl Ev/((1+v)(1 − 2v))dij§kl. = E/(2(1 + v))(duðjk + dikdjl) +
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