1.1. Stress-Strain relation

Try these first

1. 1.

   What are the two independent Lame's constants for isotropic materials?

   Hint

   Think of the constants associated with stress-strain relations.

2. 2.

   Define Young's modulus in simple terms.

   Hint

   Consider how a material's length changes with load.

3. 3.

   What is the range of Poisson's ratio for isotropic materials?

   Hint

   Think about material behavior when under stress.

4. 4.

   Is Young's modulus defined for both elastic and plastic deformation?

   • True
   • False

   Hint

   Consider the definitions and ranges of deformation types in materials.

5. 5.

   A cylindrical rod of material has a Young's modulus of 200 GPa and is subjected to a tensile stress that produces a strain of 0.005. Calculate the elongation of a 2 m long rod. Discuss also the implications of this elongation in real-world applications.

   Hint

   Use the standard elongation formula and explore stress relationships.

6. 6.

   Consider the relationship between E, G, and ν. If the Young's modulus E is given, and you find Poisson’s ratio is 0.3, derive the shear modulus using the known relation.

   Hint

   Employ relationships between moduli and confirm through calculations.