23.8 : 用莫尔圆分析平面应变

Mohr's circle analyzes plane strain by plotting points with the abscissa equal to the normal strain and the ordinate equal to half the shearing strain.

The center O of Mohr's circle is defined, with the abscissa of O and the radius equal to the average strain and the radius equation, respectively.

The direction of rotation of the sides associated with the strain components indicates where the corresponding points on Mohr's circle are plotted.

The intersections of Mohr's circle with the horizontal axis correspond to the maximum and minimum principal strains, calculated as the sum and difference of the average strain and the radius, respectively.

During elastic deformation in homogeneous, isotropic materials, the principal strain axes coincide with the stress axes following the application of Hooke's law for shearing stress and strain.

The maximum in-plane shearing strain equals the diameter of Mohr's circle. The components of strain corresponding to a rotation of the coordinate axes through an angle θ are obtained by rotating the diameter of Mohr's circle through an angle 2θ.