a) T =TF 10 kPa F 0 0 So S 0 # Tu T Ta To Atge A SFT Q D S-1 0 Isotropic Hookean elastic Solid Tij = ^ Sij Ckk + Buki M 0 0 0 +9 T = (nts w) (S-1) T T = (a+aw)(s,-1) T T = T = 10kPa + AKT ++ || to 10 = (1+24) (S - 1) + (0xk 10 = (1 + 2) (S -1) + OAK JA 20 S+s+42 10 7 1 10 kPa b) (3)+24) E= P = D+M 2(x+4) substituting (1), 20$3 E P= 35 +5,-21 (35, +52) 53-253 2(35, +S, +24) (5,+S) S3-21) $3 + 3/4 $3 E 1 = 2053 3(Sits)+8x42 (35, +S) (S+S+4k)-40 (2 (S+s) (S+52 +4X, K)-40 c) E = 21=0.01 AV = +0.5=5%. AV = 4x + 44 + 42 0.5 100 = 0.01+0.01 +42 0.005 = 0.02 + 4 = -0.015 1+22 e1 = 3=0.01 E = 4y = 0.01 - 633 = S3 = -0.015 =) 0.01 = S+S +11 + 1/1 | (S-S) + (kitk)", Similary 0.01=- S +S = 1/1 15-5.5+ (14 + k) = 2 0.02=8,+S, S = S, K = -K2 S = 0.01, S = 0.01, S3 = -0,015, K = -K Given the following homogeneous biaxial deformation: x = 8+, x2 = 82+ K2X1, x3 = 83X3 where x and x are the position of the material particles in the reference and deformed states, respectively, and s; and ki are the stretch ratios and in-plane shear components. a) For the equibiaxial test, T = T22 = 10 kPa. Assuming an isotropic Hookean elastic solid, what are the Lame constants A, ? b) What are the technical constants E, v? (c) Assuming equal biaxial test with 11 = 22 = 0.01 and volume increases by 0.5%, determine 81, 82, 83, K1, K2.