Kirsch equations

The Kirsch equations describe the elastic stresses around a hole in an infinite plate under one directional tension.

They are named after Ernst Gustav Kirsch.

Loading an infinite plate with a circular hole of radius a with stress σ, the resulting stress field is (the angle is with respect to the direction of application of the stress):

σ

σ 2

σ 2

cos ⁡ 2 θ

σ

σ 2

σ 2

cos ⁡ 2 θ

σ

σ 2

sin ⁡ 2 θ