Strain Flashcards
Define strain
A measure of the change in size and shape that a body experiences during deformation
Define linear/longitudinal strain
The change in length parallel to a given direction (change in length / original length)
Give four parameters that can be used to specify shear strain
Engineering strain (extension), stretch, quadratic elongation, logarithmic strain (natural strain)
Define shear strain (can also be known as angular shear, ψ)
The change in angle between two lines
When is angular shear positive and when is it negative?
Positive for an anticlockwise (sinistral) rotation and negative for a clockwise (dexral) rotation
What is the difference between displacement, strain, and deformation?
Displacement is the change in position of a given particle, strain is the relative change in positions of particles within the feature, and deformation is displacement that may or may not involve strain
Give the four basic types of displacement?
Rigid body translation, rigid body rotation, distortion, dilation
How are Lagrangian and Eulerian specifications used differently in the deformation gradient matrix?
Lagrangian specification gives the deformed position using the original, Eulerian gives the original position using the deformed
What type of strain cannot be accounted for used the deformation gradient matrix?
Rigid body translation
What can the displacement gradient matrix be split into?
Symmetric (gives strain (distortion and dilation) and antisymmetric parts (gives rotation)
What do 2nd rank tensors do?
Dictate the way that the values of the components in the strain matrix change and the orientation of the coordiante frame is changed.
Define tensor
A mathetical quantity that describes the physical state of a material
Wheh is strain not a single number?
At a single point
How is strain in 2d visualised?
Strain ellipse (represents deformed shape of originally round object)
What does the strain ellipse show?
How linear strain and angular shear vary with direction
Where is there zero angular shear on a strain ellipse?
On the minor and major axes, where the extensions are at maximum and minimum values, these are the principal strains
How is strain in 3d visualised?
Strain ellipsoid (represents deformed shape of an originally spherical object)
What do the three semi-axes of the strain ellipsoid represent?
The three principal strains, these are orthongonal, parallel to them, the shear strain is zero
Define plane strain in 3d
Where there is no stretching or shortning in one principal direction (Y direction), the strain can be regarded as 2d
Define axially symmetric extension or compression in 3d
An irrotational deformation in which the length changes along two principle directions are equal
What are Flinn diagrams used for?
Distinguishing the shapes of strain ellipsoids
When is strain homogeneous?
If changes in size and shape for each small part of a body are proportionately identical to that for the body as a whole
When is strain inhomogeneous?
Of changes in size and shape vary from place to place in the body
Describe how the incremental strain ellipse is used
It splits up the deformation in a series of small strain increments because calculating strain says nothing about the deformation path
