The fracture behavior of three cracks originating from a circular hole in a
thermoelectric material is studied. The basic theory of thermoelectric materials is
given under the condition of the impermeable boundary of the heat flux and electric
current. By introducing the conformal mapping function, the infinite plane on the
physical plane is mapped into the inner unit circle on the mathematical plane. The
formulas of the relevant temperature and stress fields are derived, and the analytical
solutions of the complex stress functions are obtained by the complex variable
function method. According to Cauchy integral formula, the analytical expressions of
the electric current intensity factor and the stress intensity factor for three cracks
originating from a circular hole are obtained. The effects of the hole radius and the
crack lengths on the electric current intensity factor and stress intensity factors were
investigated.
