3 Ways!

1) Line Length - basically look at the difference

2) Volume (which may increase of decrease based on the material and the amount of strain)

3) Angular Sheer strength - the angular difference between two perp. lines

* when we measure strain, we assume the material is homogeonous

General Strain = L1>L2>L3

Axially Symmetric Extention = L1>L2=L3

Axially Symmetric Shortnening = L1=L2>L3

Plane Strain = L1>L2=1>L3

L1 is perp to L2+L3

L2 is perp to L1+L3

L3 is perp to L1+L2

L1 is parallel to max extension

L2 is parallel to max shortnening

Pure shear = no shear

Ls are at the same lengths!

coaxial deformation

at undeformed states, L3=L2

L2 remains unchanged

lines parallel to L1 and L2 don't rotate

lines @ a low angle to L1 + L3 rotate slowly

max rotation for lines 45 to L1+L3

two directions of rotation

Simple shear is simply that there IS ROTATION

no coaxial deformation

L2 is remained unchanged

we care about SS because we get different structures.

all lines rotate except those parallel to the shear plane

maximum rotation rate for lines perp. to shear plane

all lines rotate in the same direction

Snce structures are not always completely exposed, we rely on the concept of structural compablity to fill in missing gaps.

The concept is a code for assessing whether the kinematic displacement are in harmony for a given area.

Strain compares two states: "undeformed and deformed"

rock memory: give info on strain path, track the path (tracking)

Kinematics = Motion history

Mechanics = the forces involved

interaction between motion and forces

- the relation between stress(mechanics) and strain (kinematics)

we study rheology (material behavior) to explain dynamics.

Intensity of a force (push or pull)

USE SIGMA

S = F/A

the more stress, the smaller the area

that which change or tends to change that state. rest or state of motions of a body

e.g. push or pull

F=ma or F=mg

F=(kg)(m2/s2)=Newton

acts on all volume elements of an object

1) gravitational

2)inertial (meteors) - travel faster than the speed on earth

1) traction = force on a vector; F/A = S on a plane

2) Stress on a surface

3) Stress on a "point"

- pair of equal and opposite traction on a surface

- each traction can be broken up into components; normal and shear

normal stress is perp to surface and shear stress

shear stress is parallel to surface

force distribution is not equal

on any surface, the distribution of forces may not be uniform, need to examine a smaller area.

i.e "point", where the surface is uniform to stress

point is often represented as a cube

Pascal (Pa) = N/m2

kilopascal, mega, and giga all go up by 3

remember: F/A = Stress

head to head

infinite number of surfaces that pass through a point

stress ellipsoids, unlike ellipsodes Don't represent the the shape of the deformed object.

all have normal stress

principle plane is defined by stresses

(S1S2, S1S3, S2S3)

S1 = max compressive stress

S2 = intermediate

S3 = minimum

Ammonton's law

f(normal stress) = shear stress

-friction acts parallel to pre-existing surface and acts in a direction opposite to the surface tending to produce slip (shear stress)

so...F/A=shear stress

however, normal force is also present becase 2 surfaces must stay in contact so F/A = norml stress

shear stress/normal stress = f(sliding force)

f=tanO

O = angle of sliding force

Ammonton's law w/ real values for f and theda (determined emperically)

-irrespective of material.

-sliding takes place 41 degrees to max compress

tan theda = f= 0.85

-measures how much normal and shear stress is needed to form a fracture in what orientation that fracture forms

-this is when there is no pre-existing weakness in the rock

shear stress = f(normal stress)

-stress measures the intensity of the forces applied to a "point" at one "instant"

we know this by comparing natural rxs to experimental results

1) size: same size is very small and typically homogeneous so strength of rx might not compare to nature

2) strain history - is it completely reserved in nature?

3) time - compensate for short period of time by intensifying w/ high temperatures

4) analog materials - materials that behave like rocks dont necessarily represent natural rxs.

deformation and flow of matter

- experiments helps define rheology

material behavior

created w/ some sort of fluid, so same around the entire sample

more pressure = greater define deth of deformation

1) axial compression = S1 -> vertical position; S2=S3 -> confining pressure

2) axial tension= S3 -> vertical; S1=S2 -> confining pressure

3) TWIST SAMPLE

BRITTLE

ex: spring

no permanent deformation

no linear relationship between strain and stress

equivalent to hooke's law - stress = (young's modulus E) (strain)

if stress is applied that is greater than the strength of the material, then it could break = yield strength

DUCTILE

ex: fingerprint in clay

permanent deformation after yield strength and non before

deals with fluids

if stress is applied to a fluid, it flows immediately when stress stops, it stops

no yield strength

measures by stress vs. rate of strain

aka visco-elastic

ex: silly putty

represents material behavior in earth

-rocks can behave viscously over long periods of time -> creep

follow coloumb's law

has dip angle of 60 degrees from surface

follow coulomb's criteria

has dip angle of 30 degrees from surface

layering

primary foliation = bedding

surface of layering

primary structure and secondary structures

-forms surface perp. to maximum shortnening and parallel to max extension

-not discontinuous surfaces. ie not a break in the rock when they form

-after cleavage forms, it may act as a fracture. ie there might be sliding along a cleavage

-material gets dissolved away and the insoluble material forms cleavage.

are always perp to cleavage.

fractures w/o motion parallel to fracture surface

may form alone or in groups (ie swarms)

can identify opening (ie propagation)

cleavage and joints ideally form at 45 degrees to the shear zone

-because rotation of 45 degrees happen, new joints form on the previous joint to keep the 45 degrees and form SIGMOIDAL VIENS

push from upward to form fold

"Drape Folds"

1) flexural slip - slickenlines perp to fold hinge (LIMBS)

2) tangential longitudinal strain (HINGES)

outer arc may have joints, normal faults, extension..

inner arc may have trust faults, shortening, cleavage, small scale folds