Chapter 2 Flashcards
It is the transformation from an initial to
a final geometry by means of rigid body translation, rigid body rotation, strain (distortion) and/or volume change
Deformation
This do not tell us how the
particles moved during the deformation history – they merely link the undeformed and deformed states.
the positions of points before and after deformation (can be connected with vectors.)
Displacement Vectors
moves every particle in the rock in the same direction and the same distance, and its displacement
field consists of parallel vectors of equal length.
Translation
The term refers to the distortion (strain) that is expressed in a (deformed) rock.
A change in form or shape.
Deformation
Rigid body deformation
Rotation and Translation
Non-rigid body deformation
Strain or Distortion
are the field of displacement vectors.
Displacements field
________trace the actual motion of individual particles in the deforming rock. while __________ simply connect the initial and final positions.
Particle path, Displacement Vector
The actual path that each particle follows during the deformation history.
Particle Path
referring to the progressive changes that take place during deformation
deformation History
is here taken to mean rigid rotation of the entire deformed rock volume that is being studied. It should not be confused with the rotation of the (imaginary) axes of the strain ellipse during progressive deformation.
Rotation
is non-rigid deformation and relatively simple to define:
Strain
also referred to as dilation, is commonly considered to be a special type of strain, called volumetric strain.
Volume Change
Where the deformation applied to a rock volume is identical throughout that volume, the deformation is
homogeneous.
Homogeneous: Rigid rotation and translation
Heterogeneous: Strain and volume or area change
originally straight and parallel lines will be straight and parallel also after the deformation. Further, the strain and volume/area change will be constant throughout the volume of rock under consideration.
homogenous deformation
ratio between the long and short axes of the ellipse.
Ellipticity
Homogeneous deformation can therefore be described by a set of first-order equations (three in three dimensions) or, more simply, by a transformation matrix referred to as the
deformation matrix
called the deformation matrix or the position gradient tensor, and the equation describes a linear transformation or a homogeneous deformation.
Matrix D
takes the deformed rock back to its undeformed state.
reciprocal or inverse deformation
(a single direction), strain is about stretching and shortening (negative stretching) of lines or approximately linear (straight) objects.
one-dimension
of a line is defined as e= (l-l0)/l0 where l0 and l are the lengths of the line before and after deformation.
Elongation
a line is identical to elongation (e) and is used in the analysis of extensional basins where the elongation of a horizontal line
Extension
Negative extension is called
Contraction
which describes the change in angle between two originally perpendicular lines in a deformed medium.
Angular shear
can be found where objects of known initial angular relations occur. Where a number of such objects occur within a homogeneously strained area, the strain ellipse can be found
Shear strain
the ellipse that describes the amount of elongation in any direction in a plane of homogeneous deformation.
strain ellipse
Having constant volume or area.
Isochoric
An arbitrary section through a deformed rock contains a strain ellipse that is called
sectional strain ellipse.
is a state of strain were stretching in X is compensated for by equal shortening in the plane orthogonal
Uniform Extension
is the opposite, with shortening in a direction Z compensated for by identical stretching in all directions perpendicular to Z.
Uniform flattening
where stretching in one direction is perfectly compensated by shortening in a single perpendicular direction.
plane strain
- is the deformed shape of an imaginary sphere with unit radius that is deformed along with the rock volume under consideration.
strain ellipsoid
The strain ellipsoid has three mutually orthogonal planes of symmetry, the principal planes of strain, which intersect along three orthogonal axes that are referred to as the principal strain axes. Their lengths (values) are called the principal stretches.
important
the eigenvectors and eigenvalues will always be identical for any given state of strain. Another way of saying the same thing is that they are
strain invariants
example of strain invariants.
Shear strain, volumetric strain, and kinematic vorticity number (Wk)
Any strain ellipsoid contains
two surfaces of no finite strain.
For constant volume deformations
isochoric deformations
The radial lines in this diagram indicate equal amounts of strain, based on the natural octahedral unit shear.
Hsu Diagram
Volume and area changes do not involve any internal rotation, meaning that lines parallel to the principal strain axes have the same orientations that they had in the undeformed state. Such deformation is called
coaxial
is real volume change where the object is equally shortened or extended in all directions.
Isotropic Volume Change
involves not only a volume (area) change but also a change in shape because its effect on the rock is different in different directions
Anisotropic volume change
implies expansion in one direction. This may occur by the formation of tensile fractures or veins or during metamorphic reactions.
Uniaxial extension
where the rock shortens or extends in one direction, is another example of coaxial deformation.
Uniaxial strain
implies that lines along the principal strain axes have the same orientation as they had in the undeformed state.
Coaxial deformation
is a special type of constant volume plane strain deformation. There is no stretching or shortening of lines or movement of particles in the third direction.
Simple shear
Between pure shear and simple shear is a spectrum of planar deformations
subsimple shear
is the sum of particle paths in a deforming medium.
flow pattern
Parameters that act instantaneously during the deformation history
flow parameters
are the three perpendicular axes (two for plane deformations) that describe the directions of maximum and minimum stretching at any time during deformation.
Instantaneous Stretching Axes (ISA)
separate different domains of particle paths.
flow apophyses
describes how fast a particle rotates in a soft medium during the deformation.
Vorticity
describes the velocity of the particles at any instance during the deformation history.
velocity field
is a measure of the internal rotation during the deformation. The term comes from the field of fluid dynamics.
Vorticity
If the flow pattern and the flow parameters remain constant throughout the deformation history, then we have
steady state flow
If, on the other hand, the ISA rotates, Wk changes value or the particle paths change during the course of deformation, then we have
non-steady-state flow.
which is the result of the entire deformation history.
Finite deformation
which concerns only a portion of the deformation history
Incremental deformation
progressive volume change
dilating
