Lecture 1 - Stress and Strain

Question 1

What is meant by ‘stress at a point’?

Answer 1

All tractions that act on a plane with all possible orientations.

Question 2

What term is used to define the force per area?

Answer 2

Traction

Question 3

A force (F) acting on a plane results in which two forms of force?

Answer 3

Normal (Fn) and Shear force (Fs)

Question 4

Define the term scalar

Answer 4

Only have one component (magnitude) invariant of the number of coordinates e.g. density, pressure

Question 5

Define the term vector

Answer 5

Number of components equal to the number of coordinates (magnitude and direction), not invariant under change of coordinates, e.g. velocity, force, traction

Question 6

Define the term tensor

Answer 6

Tensor components obey specific transformation laws under changechange of coordinates. Certain combinations of components can be invariant in a coordinate system. Fundamental rheological quantities stress, strain and strain rate) are all rank two tensors.

Question 7

What are the generic coordinates on the stress tensor?

Answer 7

Question 8

Which compoonents indicate shear stress and which components indicate normal stress in this diagram?

Answer 8

Shear Stress = σ12, σ13 + σ23

Normal Stress = σ11, σ22 + σ33

Question 9

Name 4 important stress components

Answer 9

Principle Stresses, Mean Stress, Differential Stresses + Deviatoric Stresses

Question 10

What is meant by principle stresses? (σ1>σ2>σ3)

Answer 10

Principle stresses act on planes that contain no shear stresses. These stresses are always have a direction and are always orientated perpindicular to each other.

Question 11

What is meant by mean stress? (σm=(σ11+σ22+σ33)/3)

Answer 11

The mean stress is an invariant of the stress tensor, it has no direction.

Question 12

What is meant by differential stresses? (σ_diff=σ₁-σ₃ or σ₂-σ₃ or σ₁-σ_2⁾

Answer 12

The differential stresses demonstrate the difference between the principle stresses, they are also “invariant“.

Question 13

What is deviatoric stress? (σdev = σ1 - σm or σ2 - σm or σ3 - σm)

Answer 13

The deviatoric stresses show the difference between the principle stresses and the mean stress, they are also “invariant“.

Question 14

What is the difference between stress and strain?

Answer 14

basic dynamic quantity: stress -> forces on body
basic kinematic quantity: strain -> deformation of body

Question 15

What is the difference between strain and deformation?

Answer 15

Strain is only change in volume or shape (something that we can see), deformation includes strain rotataion and translation.

Question 16

What is the difference between longidual stain and shear strain?

Answer 16

Longidual strain is the change in length whereas shear strain is the change in angle

Question 17

A circle deforms into an ellipse, how do we describe the shape of our elipse?

Answer 17

We use the longest axis (x) and the shortest axis (z) and work out a ratio between them. R=X/Z