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Assignment 1, MSE 362

Due Date 04-14-2023, 10:30AM (beginning of the lecture)

Q 1) Assuming that bulk modulus (K) and Young’s modulus (E) are known, derive expressions for Poisson’s ratio (v) and shear modulus (G) as a function of these known variables, and show your  calculations.

Q 2) Assume a linear-elastic isotropic material with known material properties:

K = 200 GPa,         E = 190 GPa

a)    Use equations in previous question, and calculate the compliance matrix of the material

b)   Assume a load of ax  = 100 MPa, ay  = 100 MPa, T = 50 MPa  is applied on the material. Calculate strains.

Q 3) Assume a perfectly plastic material with the given engineering stress-strain curve below:

a)   Calculate true stress-strain curve and plot both engineering and true curves in the same graph.

b)   Calculate Young’s modulus, Secant Modulus at strain=0. 15, and Tangential modulus at strain=0.05, using both engineering and true stress-strain curves. Comment on the differences.

c)    Based on previous calculation, what is the true failure stress? what is the true failure strain?

Q 4) A polymer cube with Young’s modulus of 10 MPa and Poisson’s ratio of 0.33 is a critical component on a moon lander. The volume of the cube is measured precisely in a lab before the space mission. What is the percentage of volume expansion of cube while landing on the moon, considering the zero atmospheric pressure on the moon? How does this percentage change for a polymer with Young’s modulus of 10 GPa and Poisson’s ratio of 0.33?