Mohr circles for strain, simplified

Abstract

AbstractThe Mohr circle is a well known representation of two‐dimensional strain. It is commonly used to illustrate strain algebra, or derive a strain ellipse from particular strain data. The established sign convention is positive (anticlockwise) shear strain on the upward ordinate, after Brace. However, in practice, confusion may easily arise from inconsistent conventions in standard text books.A Mohr‐circle convention is proposed here which represents clockwise shear strain on the upward γ ordinate (i.e. upside‐down). It simplifies the Mohr circle by representing both single and double angles in their natural sense. Single angles may be traced from rock to Mohr circle directly which is not the case for the Brace circle. Deformed brachiopods and stretched belemnites are used to illustrate this simplified Mohr circle.The pole to the Mohr circle is a useful addition which allows strain data to be represented in their true orientation. The pole method only works on the γ clockwise‐up Mohr circle.The Mohr circle is useful to demonstrate simple‐shear geometry and algebra. Successive Mohr circles with poles may be used to map strain across a heterogeneous simple‐shear zone.