MECHANICAL BEHAVIOUR QUESTIONS
AND ANSWERS UPDATED 2026
# Term Definition
1 Describe the application of forces on a
body. In most applications a body is subject to numerous
forces however these can not just be simply added. In
many cases the vector sum of the forces is 0. So a body
is imagined to be made up of infinitesimally small
cubes on the surface of which the forces are projected.
2 Define a stress tensor.
It is a 9 component matrix needed to define a vector.
See written notes for general tensors.
3 Define strain.
The ratio of the change in length. See written notes for
equations. See written notes for matrix form.
4
How are normal strains represented Components along the diagonal are called direct or
by a matrix? How are shear strains normal strains. Components off the diagonal are shear
represented by a matrix? strains. The strain tensor must be symmetric.
5 How are normal stresses represented
Components along the diagonal are called normal
by a matrix? How are shear stresses
stresses and are perpendicular to the plane.
represented by a matrix?
Components off the diagonal are shear stresses and are
parallel to the surface. The strain tensor must be
symmetric.
6 What is pure shear? When there are no normal stresses or strains.
7 Define equibiaxial tension.
The normal strains are all equal. The tensile and the
shear strain equal 0.
8 Describe a hydrostatic stress and
volumetric strain.. By decompressing the stress and strain tensors into
their normal and shear components they can be
simplified. They are simplified to the hydrostatic stress
and volumetric strain (mean normal components). See
written notes for equations.
, 9 Describe deviatoric stresses and strains.
The invariant nature of the mean normal components
means that they can be used to obtain the shear related
components from any strain and shear tensor. This
means that deviatoric stress and strain tensors can be
used with its hydrostatic components to express any
stress or strain tensor. See written notes for tensor
equations.
# Term Definition
10 Define Hooke's law.
F=kx K is the elastic constant that determines the
stiffness of the spring.
11 Describe elasticity.
There are loads of tensors and equations for this.
Including relations: with the Poisson ratio, with the
shear modulus, with the strain, with the stress and with
elastic strain energy. So definitely see written notes.
12 Describe a tensile test.
A sample is gripped at both ends and extended using a
testing machine. During the test both the force and the
extension are recorded. These can be converted into
engineering stress and strain by normalising the load
values by the sample geometry. See notes for
normalising equations.
13 Describe the elastic region.
Strains are small and increase linearly with stress. In a
tensile test only the load is uni-axial and the strain is not
0 perpendicular to the applied load.
14 Describe yielding.
The onset of the plastic region is determined by the yield
point. The stress at which it starts is known as the yield
stress. A proof stress is used as a measure of yield
strength.
15 Describe how to calculate a proof
Fit the linear elastic region. Shift it along the strain axis
stress.
until the desired proof level. Where the fit intercepts the
curve is the proof stress.
, 16 Describe true strain.
In the plastic regions strains can be very large and can
no longer be represented using the small strain
approximations. As the strain increases so does the
gauge length. See written notes for equations.
17 Describe true stress.
As a metal deforms the cross sectional area decreases.
The ratio of the instant area and the
initial area during straining is inversely proportional to
the ratio of instant length and initial length of the gauge.
For equations see written notes.
# Term Definition
18 Describe work/strain hardening.
It occurs in the plastic region and can be described by
several equations. For these expressions see written
notes.
19 Describe necking.
The reduction in cross sectional area that occurs at the
ultimate tensile strength. Necking will occur when the
stress of the material equals the work hardening rate.
For equations see written notes.
20 Describe compression testing.
During a compression test a sample is deformed uni-
axial in compression between parallel platters. For true
stress and strain expressions see written notes.
21 Describe plastic deformation as a
localised shear event. Yield in tension usually takes place as a localised shear
event at 45° to the loading direction. The yield strength
can be thought of as the materials resistance to shear.
See written notes for shear equations.
22 Define the maximum shear stress or
Tresca yield criterion. For a bi-axial state the maximum shear stress at a point
in a material is given by 1/2 of the absolute difference of
the principle stresses. In 3D, all of these differences in
the principle stresses must be evaluated. For derivation
see written notes.
AND ANSWERS UPDATED 2026
# Term Definition
1 Describe the application of forces on a
body. In most applications a body is subject to numerous
forces however these can not just be simply added. In
many cases the vector sum of the forces is 0. So a body
is imagined to be made up of infinitesimally small
cubes on the surface of which the forces are projected.
2 Define a stress tensor.
It is a 9 component matrix needed to define a vector.
See written notes for general tensors.
3 Define strain.
The ratio of the change in length. See written notes for
equations. See written notes for matrix form.
4
How are normal strains represented Components along the diagonal are called direct or
by a matrix? How are shear strains normal strains. Components off the diagonal are shear
represented by a matrix? strains. The strain tensor must be symmetric.
5 How are normal stresses represented
Components along the diagonal are called normal
by a matrix? How are shear stresses
stresses and are perpendicular to the plane.
represented by a matrix?
Components off the diagonal are shear stresses and are
parallel to the surface. The strain tensor must be
symmetric.
6 What is pure shear? When there are no normal stresses or strains.
7 Define equibiaxial tension.
The normal strains are all equal. The tensile and the
shear strain equal 0.
8 Describe a hydrostatic stress and
volumetric strain.. By decompressing the stress and strain tensors into
their normal and shear components they can be
simplified. They are simplified to the hydrostatic stress
and volumetric strain (mean normal components). See
written notes for equations.
, 9 Describe deviatoric stresses and strains.
The invariant nature of the mean normal components
means that they can be used to obtain the shear related
components from any strain and shear tensor. This
means that deviatoric stress and strain tensors can be
used with its hydrostatic components to express any
stress or strain tensor. See written notes for tensor
equations.
# Term Definition
10 Define Hooke's law.
F=kx K is the elastic constant that determines the
stiffness of the spring.
11 Describe elasticity.
There are loads of tensors and equations for this.
Including relations: with the Poisson ratio, with the
shear modulus, with the strain, with the stress and with
elastic strain energy. So definitely see written notes.
12 Describe a tensile test.
A sample is gripped at both ends and extended using a
testing machine. During the test both the force and the
extension are recorded. These can be converted into
engineering stress and strain by normalising the load
values by the sample geometry. See notes for
normalising equations.
13 Describe the elastic region.
Strains are small and increase linearly with stress. In a
tensile test only the load is uni-axial and the strain is not
0 perpendicular to the applied load.
14 Describe yielding.
The onset of the plastic region is determined by the yield
point. The stress at which it starts is known as the yield
stress. A proof stress is used as a measure of yield
strength.
15 Describe how to calculate a proof
Fit the linear elastic region. Shift it along the strain axis
stress.
until the desired proof level. Where the fit intercepts the
curve is the proof stress.
, 16 Describe true strain.
In the plastic regions strains can be very large and can
no longer be represented using the small strain
approximations. As the strain increases so does the
gauge length. See written notes for equations.
17 Describe true stress.
As a metal deforms the cross sectional area decreases.
The ratio of the instant area and the
initial area during straining is inversely proportional to
the ratio of instant length and initial length of the gauge.
For equations see written notes.
# Term Definition
18 Describe work/strain hardening.
It occurs in the plastic region and can be described by
several equations. For these expressions see written
notes.
19 Describe necking.
The reduction in cross sectional area that occurs at the
ultimate tensile strength. Necking will occur when the
stress of the material equals the work hardening rate.
For equations see written notes.
20 Describe compression testing.
During a compression test a sample is deformed uni-
axial in compression between parallel platters. For true
stress and strain expressions see written notes.
21 Describe plastic deformation as a
localised shear event. Yield in tension usually takes place as a localised shear
event at 45° to the loading direction. The yield strength
can be thought of as the materials resistance to shear.
See written notes for shear equations.
22 Define the maximum shear stress or
Tresca yield criterion. For a bi-axial state the maximum shear stress at a point
in a material is given by 1/2 of the absolute difference of
the principle stresses. In 3D, all of these differences in
the principle stresses must be evaluated. For derivation
see written notes.
