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Earth and Space Sciences · পরিভাষা

Pure shear, simple shear কী?

অন্য নাম: pure shear · simple shear

Definition 16.10 University Earth and Space Sciences — Year 1 · অধ্যায় 16 — Stress, Strain and Rheology

A pure shear is a homogeneous strain that keeps the area and keeps its principal directions fixed in the rock: F=(k001/k)F = \begin{pmatrix} k & 0 \\ 0 & 1/k\end{pmatrix} in those axes, with k>1k > 1. A simple shear moves every point parallel to one direction, the shear direction, by γ\gamma times its distance from a fixed plane parallel to it: F=(1γ01)F = \begin{pmatrix} 1 & \gamma \\ 0 & 1\end{pmatrix}.

A square of rock with its inscribed circle (a), deformed by a pure shear with k = 1.618 (b) and by a simple shear with = 1 (c), which has the same principal stretches, 1.618 and 0.618. Dashed blue: the axes of the strain ellipse; dashed grey: the square before. In pure shear the axes stay on the same lines of material; in simple shear the long axis lies at 31.7 to the shear direction, and the diagonal that was the direction of fastest stretching at the start (red) has already turned past it, to 26.6. The shapes are exact images of the square and the circle under the two matrices.
A square of rock with its inscribed circle (a), deformed by a pure shear with k=1.618k = 1.618 (b) and by a simple shear with γ=1\gamma = 1 (c), which has the same principal stretches, 1.618 and 0.618. Dashed blue: the axes of the strain ellipse; dashed grey: the square before. In pure shear the axes stay on the same lines of material; in simple shear the long axis lies at 31.7∘31.7{}^{\circ} to the shear direction, and the diagonal that was the direction of fastest stretching at the start (red) has already turned past it, to 26.6∘26.6{}^{\circ}. The shapes are exact images of the square and the circle under the two matrices.
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