Shear is a stress that results from the opposition of forces that are not aligned (F/A).
Strain is defined as deflection divided by the original dimension, and is a measure of deformation, that is, the differential change in size, shape, or volume of a material. Strain is dimensionless.
The modulus of elasticity is stress divided by strain.
Lithostatic stress or confining pressure is uniform stress that operates equally in all directions in rocks. Confining pressure is due to the burden of overlying rock, just as seawater exerts equal pressure from all directions at depth.
Differential or divertorial stress results from compressional or extensional tectonic stresses that are not equal from all directions: tensional stress (stretching), compressional stress (squeezing), or shearing stress (side to side shearing). Compressional stresses act along the direction of maximum principal stress, whereas extensional stresses act along the direction of minimum principal stress.
For the mutually orthogonal directions along which stress is applied, the
▪ maximum principal stress direction is designated σ1 ,
▪ minimum principal stress direction is σ3 , and
▪ intermediate principal stress direction is designated σ2 .
▪ normal stress, directed perpendicular to a given plane is designated, ση
▪ shear stress, directed parallel to a given plane is designated, στ
▪ vector components of stress can be expressed according to Cartesian coordinate system as 9 components (x,y, z combinations) relative to the 3 mutually perpendicular x-y-z axes
Materials differ in their responses to stress, depending upon composition, conditions of temperature and confining pressure, and strain rate. However, regardless of intrinsic degrees of brittle or ductile qualities, all strained materials pass through 3 successive stages of deformation: elastic, ductile, and fracture (failure, or brittle deformation). Provided that the strain rate is sufficiently slow to allow minerals to accommodate structurally, minerals can adjust to applied stresses by a variety of mechanisms.
In elastic deformation, rock changes shape by a very small amount and the deformation is not permanent. Elastic deformation occurs only with small differential stresses, which are less than the rock's yield strength. Rock adjacent to failed rock in earthquakes propagates seismic waves by elastic deformation, then springs back to its original shape in elastic rebound. For this reason, structural damage to rocks and formations provides the only evidence of passage of past seismic waves.
In ductile deformation, rock deeper than 10-20 km is subjected to enormous lithostatic stress, and the high temperatures of burial render the hot rock softer and more malleable. At these depths, in the lower continental crust and mantle, rock undergoes plastic deformation and flows in response to application of a differential stress that is stronger than its yield strength. Rock undergoes ductile deformation by gradual creep along crystal grain boundaries and planes within crystal lattices. Ductile deformation in generates folding and ductile shear zone features, such the dynamic metamorphic mineralogical and textural changes seen in foliated schistose, banded, lineated, and augen-structured dynamic metamorphic rocks, mylonites, distorted porphyroclasts and mica fish, phyllonites.
In brittle deformation close to the Earth's surface, where rocks are comparatively cool, rock behaves in a brittle fashion, fracturing in response to differential stress greater than the rock's yield strength. Rock failure and fracture generates faulting, brecciation, pseudotachlites, cataclasis, and slickenside striations. Rock adjacent to the failed rock springs back to its original shape in the elastic rebound that is responsible for earthquakes.