Question 2 of 4: Definitions

Question B — Definitions (4 marks each: 20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(1) Pure shear vs. Simple shear. Pure shear is a coaxial, non-rotational homogeneous strain: material lines parallel to the principal strain axes do not rotate relative to a fixed external frame, and the incremental and finite strain axes stay coincident throughout — it is a symmetrical flattening/extension (e.g. a brick squashed from top and bottom while free to widen sideways). Simple shear is a non-coaxial, rotational homogeneous strain produced by displacement parallel to a single shear plane, with no change in the perpendicular dimension (constant-volume, one set of parallel material lines never rotates — the shear-plane-parallel lines — while every other line both stretches and rotates progressively toward the shear plane). Both can produce an identical FINITE strain ellipse for a given episode, but only simple shear leaves the finite strain axes rotated away from the instantaneous (45°) stretching axes, which is the diagnostic difference.

(2) Anticline vs. Antiform. Both describe a fold that is convex-upward (arches upward), but anticline is defined by STRATIGRAPHIC age: the core of the fold contains the OLDEST beds, with progressively younger beds outward on both limbs — a purely age-based, way-up-dependent term. Antiform is defined purely by GEOMETRY: a fold that is convex-upward regardless of the relative age of the beds in its core. In overturned or unknown-facing terrane the two are not interchangeable — a geometrically convex-upward fold with the core beds facing (younging) downward is an antiform but a SYNCLINE (an overturned syncline), not an anticline; "anticline"/"syncline" should only be applied once younging direction is established.

(3) Stress traction vs. Stress tensor. Traction is the stress VECTOR resolved on ONE specific plane through a point — a force per unit area with a magnitude and direction tied to that single surface. The stress tensor is the complete, plane-independent description of stress AT A POINT: the full set of six independent components (three normal, three shear) from which the traction on any arbitrarily-oriented plane through that point can be computed via Cauchy's relation \(t_i=\sigma_{ij}n_j\). A traction is one projection of the tensor; the tensor is the complete field from which every possible traction can be recovered.

(4) Incremental strain ellipse vs. Finite strain ellipse. The incremental (or instantaneous) strain ellipse describes the strain accrued during one small INCREMENT of the deformation history — its axes show the instantaneous stretching directions AT THAT MOMENT. The finite strain ellipse is the TOTAL, integrated strain accumulated from the undeformed state to the CURRENT state, obtained by compounding every increment together. For coaxial (pure shear) deformation the incremental and finite ellipses share the same principal directions at every stage; for non-coaxial (simple shear) deformation the incremental axes stay fixed at 45° to the shear plane while the finite axes progressively rotate toward the shear plane as strain accumulates — so the two ellipses diverge in orientation as deformation proceeds.

(5) Plastic vs. Viscous deformation. Plastic deformation has a YIELD STRESS (or yield criterion): the material behaves rigidly (no permanent strain) until stress reaches a threshold, after which it flows, ideally at that same constant stress regardless of strain rate (rate-independent). Viscous deformation has NO yield stress: the material deforms permanently under ANY applied stress, however small, with strain RATE proportional to the applied stress (Newtonian) or a power-law function of it — i.e. viscous flow is fundamentally rate-dependent while ideal plastic flow is not. Rocks at depth commonly approximate a combined visco-plastic (or power-law creep) rheology that grades between these two end-members depending on temperature, strain rate and stress magnitude.