16 July 2015GLG510 Advanced Structural Geology Force, Traction, and Stress.

April 22, 2023 GLG510 Advanced Structural Geology

Force, Traction, and Stress

Physical quantities

• Force, F = m a; [=]kg m s-2 = N (newton)

• Stress, s[=](kg m s-2)m-2 = N m-2 = Pa

Force: Newton’s Laws of Motion

• Law I: Every body continues in its state of rest, or in uniform motion in a straight line, unless it is compelled to change its state by forces impressed upon it.

• Law II: The rate of change of momentum is proportional to the impressed force and is made in the direction in which the force is impressed.

m = massv = velocity vectort = timea = acceleration vector

Dimensional analysis: fundamental units

Mass = amount of material in a bodyWeight = Force due to gravity action on a body1 liter of water has a mass of

on earth it weighson the moon it weighs

What does a Newton feel like?

-Davis and Reynolds, p. 101

• Law III: To every action there is always opposed an equal reaction, or the mutual actions of two bodies on each other are always equal in magnitude and opposite in direction

Stress simply

• Simple definition of stress (for the moment) = pressure

Stress and deformation

• Rheology: relationship between stress and deformation

Stress and deformation

• Use your stress and deformation words correctly:

• Stress Deformation (strain)• Tension Extension• Compression Contraction or

shortening-watch out for Art Sylvester!

Tractions and stress

• A more strict definition of stress

• Traction is stress relative to a surface through a point p.

• Stress tensor is the field of tractions acting over a point p.

• Stress field is the entire collection of stress tensors in a body.

• Start with equilibrium (Newton’s 3rd Law):

• Resolve each into its components in the coordinate directions

• Total torque must vanish

Rock quarried from the earth

• Sign Conventions: compression positive

-Fundamentals of Rock Mechanics by Jaeger and Cook (3rd ed., p. 10)

In many engineering situations, we consider tension as positive and compression negative. This is not usually the case in structural geology.

(a) “Traction” or “Stress vector”

(b) Equilibrium“Cauchy’s relationship

(c) Components of the Traction Vector

Stress tensor

3D Stress tensor

Note that the opposite sides have the stress components too!

Stress tensor

Andersonian Faulting Theory

• Key assumptions: – Earth’s surface is a free surface (so it has no

shear tractions acting along it). Therefore, 1, 2, 3 must be either parallel or perpendicular to it.

– A fault will slip in the direction of maximum resolved shear traction

Davis and Reynolds, p. 306

Rowland and Duebendorfer

April 22, 2023 GLG510 Advanced Structural Geology-Engelder, 1993, Stress regimes in the lithosphere, Princeton Univ. Press

World Stress Map

http://www.world-stress-map.org/

April 22, 2023 GLG510 Advanced Structural GeologyNorth America Stress Map

http://www.world-stress-map.org/

16 July 2015GLG510 Advanced Structural Geology Force, Traction, and Stress.

stress field

newtons laws of motionlaw

newtons laws of motionm

equilibrium newtons

impressed force

point p

field of tractions

compression negative

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