Contact and crack problems in generalized materials and their relationships

Abstract

A new term of generalized material is introduced here. This definition covers all anisotropic magneto-electro-elastic materials and one-, two- and tree-dimensional generally anisotropic quasi-crystals and hopefully, some new not yet discovered materials. We consider a half-space $x_{3}\ge 0$, made of generalized material and subjected to arbitrary point sources or point dislocations, which can be interpreted also as electric and/or magnetic influence. General solution was obtained by using two-dimensional Fourier transform. The final results are presented as single integrals over a unit circle. Some components of the surface Green’s functions were computed in a finite form, no computation of any integral is needed. The theory of generalized functions was used. This result allows us to derive the governing integral equations for the normal and tangential contact and crack problems. We also establish certain relationships between the Fourier transforms of the kernels of the relevant integral equations. As a bonus, some interesting properties of the determinants, which might be new, were established.