The purpose of this problem is to show the relationship between material constants typically used in...

 

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 + dikdjt) + Adijoki to derive the following: (a) Young's modulus, E = (3x+2)/(A+), from the definition o11 = Ee11 in a unconfined (022=0,033 = 0) uniaxial tension test. (b) Poisson's ratio, v= A/(2(A+)), from the definition v=-622/11 in the same test as in (a). (c) Shear modulus, p=G=012/(2612) = E/(2(1+1)). Use the results to show that C can also be written Cijkt = E/(2(1+v)) (dijk + dikdjl) + Ev/((1+v)(1-2v))dijkt. 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 + dikdjt) + Adijoki to derive the following: (a) Young's modulus, E = (3x+2)/(A+), from the definition o11 = Ee11 in a unconfined (022=0,033 = 0) uniaxial tension test. (b) Poisson's ratio, v= A/(2(A+)), from the definition v=-622/11 in the same test as in (a). (c) Shear modulus, p=G=012/(2612) = E/(2(1+1)). Use the results to show that C can also be written Cijkt = E/(2(1+v)) (dijk + dikdjl) + Ev/((1+v)(1-2v))dijkt.

Answer rating: 100% (QA)

ANSWER a To derive Youngs modulus E from the definition of o11 Ee11 in a unconfined 022 00330 uniaxial tension test we can start with the expression for Cijkt Cijkt did jk dikdjt Adijoki Substituting ... View the full answer