b and c

Engineering Materials Lab HW1 2/21/2022 1. For isotropic and homogeneous materials, two independent material constants are required, such as E (Young's modulus) and G (shear modulus), or G and v(Poisson's ratio). Elastic moduli, such as E or G, are in units of Pa (N/m). Poisson's ratio is dimensionless. It is known that G=E/[2(1+ v)]. (a) Why the valid range of Poisson's ratio is between-1 and 0.5? (b) Please show the longitudinal wave speed in terms of the following pairs: (8,6), (E,G), (Ev),(G, v),(B.v). (c) Please write down the equation of Poisson's ratio in terms of , where 1 = (C/C)? The shear and longitudinal wave speed are denoted by C, and C, respectively. Find out the value of for v=0.5, 0.33, 0, and -1. What is the valid range of A