Fundamental solutions for chiral solids in gradient elasticity

• Deformation of chiral solids in gradient elasticity.
• We establish a counterpart of the Cauchy–Kowalewski–Somigliana solution in the dynamic theory of classical elasticity.
• A general solution of the field equations in the gradient elastostatics is presented.
• Fundamental solutions of the displacement equations in the equilibrium theory and in the case of steady vibrations.

This paper is concerned with the linear theory of gradient elasticity. The deformation of homogeneous and isotropic chiral materials subjected to concentrated body forces is investigated. First, a counterpart of the Cauchy–Kowalewski–Somigliana solution in the dynamic theory of classical elasticity is established. Then, a general solution of the field equations that is analogous to the Boussinesq–Somigliana–Galerkin solution in the classical elastostatics is presented. The results are used to derive the fundamental solutions of the displacement equations in the equilibrium theory and in the case of steady vibrations.