1. Math
  2. Advanced Math
  3. 2 i the elastic constitutive matrix for an isotropic material...

Question: 2 i the elastic constitutive matrix for an isotropic material...

Question details

2 (i) The elastic constitutive matrix for an isotropic material is given by 2) X A (A+2u) A A+2H) 00 0 0 0 0 0 0 0 0 where = (1 + v)(1-2), μ 2(1 + v) Given further that E 3.32 GPa, 0.178, and that a state of strain defined by Exx-0.7013, Eyyー-0.31Exx, Ezz--0.19exx , Exy-0.2274, Eyz-: 0.6413 and εΖΧ 0.8273 exists at a point in a given isotropic material, calculate the corresponding state of stress at the point. Work correct to four decimal places (ii) Using the results in the first part, evaluate the following quantities . The stress force on ait area element in the direction n (0.7071,-0.7071,0) The mean stress ơkk/3; Note that ε11 Exx,E12 Exy, etc (ii) The deviatoric stress is defined by where δ¡¡ is the Kronecker delta tensor. Show that S,,-0, and that What is the order of S as a tensor expression?

Solution by an expert tutor
Blurred Solution
This question has been solved
Subscribe to see this solution