Incremental elastic compliance and electric resistance of a cylinder with partial loss in the cross-sectional area

Motivated by material science applications, the paper focuses on quantitative characterization and comparison of two microstructural elements typical for lamellar materials – crack and contacting area – in the context of their effect on macroscopic elastic and conductive (thermal or electrical) properties of a body of finite size. The problem is solved in axisymmetric formulation – axial load or axial heat flux is applied to a circular cylinder containing a centered crack, either internal or external. The latter case corresponds to the welding of two halves of the cylinder at the center. The changes in the elastic and conductive properties of the cylinder due to these types of cracks are obtained in explicit analytical form. It is shown that the contributions of internal and external cracks into elastic and conductive properties are similar if the relative loss in the cross-sectional between two parts of the cylinder is up to 70% for elasticity problem and up to 85% for conductivity problem. We also show that the changes in elastic compliance and conductive properties generated by both microstructural elements are interrelated by cross-property connection identical to one obtained for an unbounded material.