Cycle IV Geology
John Dewey High School
Mr. Klimetz
Principles of Structural Geology III:
Concepts of Stress and Strain
Introduction. Every particle of matter of which the Earth is comprised is experiencing stress. This stress is not of one type but of many which collaboratively act upon every body of matter continuously, perpetually, and without respite. By definition, stress is defined as the ratio of the amount of force acting on an object to the area across which the force is acting. Stress is reasonably equivalent to pressure and both are expressed in the same units of measurement. Stresses are of many types, such as mechanical (the stresses exerted by the mass of one body in direct contact with and onto the mass of another body), thermal (the stresses exerted internally within a body as a consequence of the gain [or loss] of heat energy), and hydrostatic (the internal stresses possessed by bodies of fluid) to name a few. One of the ways that bodies of matter respond to stresses is by deforming, that is, by changing shape. The deformation a body experiences in response to an applied stress is more commonly referred to as strain. By definition, strain is the ratio of the change in length of a linear feature possessed by a body between the undeformed and deformed states to its original undeformed length. Strain is therefore a number with no units of measurement. The larger the strain number, the greater the amount of deformation (or change in shape) a body has experienced. Bear in mind that bodies are rarely stressed (and consequently strained) in one single direction or orientation.. Stresses and strains occur in all three space-dimensions and as such can become very complex to model, quantify, and interpret. Rocks experience stress and respond by straining in some very unique and fascinating ways. It is the responsibility of the structural geologist to attempt to determine the stress and strain history of a sequence of deformed rocks for the purpose of identifying the geologic phenomena responsible for producing the observed rock features.

Stress. Stresses are classified on the basis of the directions in which they act on a particular object. Stresses which act outwards from a body are referred to as tensile. As the name implies, tensile stresses result in a body experiencing tension, that is, being pulled apart. Stresses which act inwards towards a body are referred to as compressive. Similarly, compressive stresses result in a body experiencing compression, that is, being pushed (or squeezed) together. Coaxial stresses are those which are colinear, that is, they are oriented along a straight line. Stresses always occur in pairs, that is, a pushing force in one direction is always accompanied by a pushing force acting along the same line but in the opposite direction. There are three possible pairs of mutually perpendicular axial stresses, with each pair referenced to one of the three dimensional axes (one pair oriented vertically and two pairs oriented horizontally). When a single pair, a double pair, or all three pairs of stresses are acting simultaneously on an object we refer to the stresses as uniaxial, biaxial, and triaxial respectively. Non-coaxial stresses are those which are oppositional but not colinear and tend to cause the rotation of the body upon which they act. These stresses are collectively referred to as shear stresses. Only solid objects, that is, those which possess internal rigidity can sustain shear stress. On the other hand, all other states of matter can sustain compressive and tensile stresses. Compressive stresses cause the shortening of objects parallel to the net compressive stress direction, whereas tensile stresses cause the lengthening of objects parallel to the net tensile stress direction. Like pressure, stress is expressed in units of force per unit area. The two most frequently used stress units are pounds per square inch (psi) and pascals (Pa). (The stress [or pressure] exerted by the weight of Earth's atmosphere across a horizontal surface at sea level is equal to 14.7 psi or 1.01 x 10exp5 Pa.). The symbol for stress is the lower-case Greek letter sigma [s].
John Ramsay,  the most influential and gifted structural geologist of our time, explaining the geometry of extreme deformation in polydeformed metamorphic rocks uplifted and exposed as the erosional remnants of an ancient orogenic core.
Otto Mohr
Nineteenth-century German engineer Otto Mohr is credited with the development of the Mohr Circle, an ingenious graphical method of analysis of the states of stress and strain of a stressed and deformed body. It is widely applied in problem-solving in both modern engineering and geology.
Strain. Strains are the physical responses of objects to stresses and are referred to as deformation. They are classified on the basis of the changes in lengths of objects measured with respect to the directions of the stresses which caused them. An increase in the length of an object in a particular direction is referred to as extension. The object is therefore said to have experienced extensional strain. A decrease in the length of an object on the other hand is referred to as shortening. This object is said to have experienced shortening strain. Similarly, a object which has been rotationally deformed is said to have experienced shear strain. Obviously, net tensional stresses result in extensional strains, net compressional stresses result in shortening strains, and shear stresses result in shear strains. Strain is expressed as the ratio of the net change in length of an object (measured in a particular direction) to the original (or undeformed) length (measured in the same direction). The symbol for strain is the lower-case Greek letter epsilon. The equation for strain is

Strain = (Deformed Length - Undeformed Length)/Undeformed Length

Strain is a unitless number whose sign indicates the type of deformation. Negative strains indicate shortening strains, positive numbers indicate extensional strains. Undeformed objects possess a strain of zero. The larger the number, the greater the amount of deformation. Objects with a strain of +1.0 have doubled their length whereas objects with a strain of -0.5 have been shortened to one-half of their original length.

Questions

1.   Briefly define the term stress. Which other, more frequently used term is equivalent to stress? Name the three basic types of stress.

2.   Briefly define the term strain. Which other, more frequently used term is equivalent to strain? How is strain related to stress?

3.   How does tensile stress differ from compressive stress?

4.   How does extensional strain differ from shortening strain?

5.   How does shear stress differ from shear strain?

6.   Calculate the amount of strain experienced by an object whose original (undeformed) length of 1.0 centimeters is now 0.50 centimeters. Which type of strain has the body experienced? How do you know this from your calculations?