Part I. True or False?

(Answers at the end of this section)

1. The principal stress axes are always the same as the principal strain axes in an isotropic material.

2. The principal stress axes are always the same as the principal strain axes in an orthotropic material.

3. The equations of compability derived in this text, such as εxx,yy + εyy,xx = γxy,xy, are valid for large strains as well as small strains. (Recall that small strains are linear expressions involving the derivatives of displacements, while large strains further include quadratic expressions involving derivatives of the displacements.)

4. The coordinate rotation equation for stresses, that is, [σ*]= [c][σ][c]t, is valid for any material, not just an isotropic material.

5. The equations of equilibrium apply to a material undergoing plastic deformations as well as a material undergoing purely elastic deformations.

6. The line paralleling the linear portion of the stress–strain curve that defines an offset yield stress originates at a strain value of 0.01 in/in.

7. Not counting the coefficient of thermal expansion, there are three independent material constants that require specification for the linearly elastic, isotropic material model.

8. Young's modulus is the same as the modulus of rigidity.

9. The Cauchy equations are a set of algebraic equations that relate the tractions to the internal stresses, but do not include the body forces.

10. Both the constitutive and strain–displacement equations for an isotropic material are different from those for an orthotropic material.

11. The Cauchy equations can be viewed as an application of Newton's second law; that is, they are based upon a summation of forces.

12. The material stiffness matrix [E] is the matrix transpose of the material compliance matrix [S].

13. […]