Mechanics of materials

Question 1

What are the tensor notation of stresses?

Answer 1

Question 2

Why are the 9 componens of engineering stress reduced to 6?

Answer 2

In the context of static equilibrium, the body is not accelerating, and the sum of forces and moments in any direction must be zero. This leads to simplifications in the stress tensor.

Question 3

What are the tensor notation of strains?

Answer 3

Question 4

Explain the tensor notation (τ_ij)

Answer 4

• i = direction of the normal to the plane on which the stress acts
• j = direction of the stress

Question 5

Define: orthotropic materials

Answer 5

They have different mechanical properties along three mutually perpendicular symmetry planes and have 9 idndependent elastic constants.

Question 6

What are the hookes law by matrix form for an orthotropic material?

Answer 6

Question 7

What are principal stresses, and how are they calculated?

Answer 7

• Principal stresses are the maximum and minimum normal stresses acting on specific planes where shear stress is zero.
• They are found by solving the eigenvalue problem for the stress tensor.

Question 8

Why is the Von Mises stress criterion not useful for composites?

Answer 8

• It assumes isotropy, so it does not ccount for different strenghts and stiffnesses in different directions.
• It is based on the concept of yielding, and composites are mostly brittle.

Question 9

What is engineering strain?

Answer 9

A measure of deformation and includes both normal strain (changes in length) and shear strain (changes in angle)

Question 10

What is the hookes law for an anisotropic material by matrix form?

Answer 10

Question 11

For an orthotropic material: what are the the independent elastic constants expressed by the engineering constants?

Answer 11

Question 12

Why does an orthotropic material have fewer independent elastic constants?

Answer 12

Due to symmetry, there are no coupling between normal stresses and shear strains, between shear stresses and normal strains, or between a shear stresses and a shear strains on different planes.

Question 13

What is a transversly isotropic material, and how many independent elastic constants do they have?

Answer 13

A material with properties that are symmetric about an axis that is normal to a plane of isotropy. This transverse plane has infinite planes of symmetry and thus, within this plane, the material properties are the same in all directions.
They have 5 independent elastic constants.

Question 14

For an transversly isotropic material: what are the the independent elastic constants expressed by the engineering constants? (Assuming the plane 2-3 is a plane of isotropy)

Answer 14

Question 15

How does an anisotropic material behave during elastic deformation?

Answer 15

• Direction dependent stiffness and strength
• Coupling between normal and shear stresses

Question 16

What are the independent elastic constants for isotropic materials?

Answer 16

Question 17

What is the plane stress assumption?

Answer 17

The assumption is that stress components perpendicular to a given plane (typically the z-plane) are negligible, allowing analysis to be simplified to two dimensions.

Question 18

What is the hookes law for plane stress?

Answer 18

Question 19

What is the transformation of the stiffness matrix Q from material to global coordinate system?

Answer 19

Question 20

Define Creep in viscoelastic context

Answer 20

Time dependent increase in strain/deformation under a constant applied stress

Question 21

What are the transformation matrices for plane stress?

Answer 21