A concentrated couple inside or outside a circular inclusion in finite plane elastostatics

We consider a circular elastic inclusion embedded in an infinite matrix each from a particular class of compressible hyperelastic materials of harmonic type. A concentrated couple is applied either inside the circular inclusion or in the matrix. Closed-form solutions of the corresponding boundary value problems are obtained using complex variable methods, in particular the principle of analytic continuation. Our analysis reveals several interesting conclusions including: the sum σ11+σ22 of the normal stresses inside the inclusion remains constant when the concentrated couple is located in the surrounding matrix; the sum of the normal stresses is zero everywhere in the matrix when the concentrated couple is located inside the inclusion.