Method of complex potentials in linear microstretch elasticity

The paper is concerned with the plane strain of homogeneous and isotropic microstretch elastic bodies. We give a new representation of the solution in terms of complex potentials. The method is useful for the treatment of the constitutive equations established by Eringen in [A.C. Eringen, Microcontinuum Field Theories. I. Foundations and Solids, Springer-Verlag, New York, 1999], where the introduction of stress functions leads to difficulties. The complex variable technique is used to study Kirsch problem in the context of the theory presented in [A.C. Eringen, Microcontinuum Field Theories. I. Foundations and Solids, Springer-Verlag, New York, 1999].