On the uniform stress state inside an inclusion of arbitrary shape in a three-phase composite
The paper studies a uniform hydrostatic stress state inside a 2D arbitrary-shape (non-elliptical) inclusion bonded to uniformly loaded infinite elastic matrix through an interphase layer subjected to remote uniform in-plane stresses. The uniform hydrostatic stress state under in-plane loading is investigated by using a conformal mapping function and the analytic continuation method from the complex variable theory. The possible non-elliptical inclusion shapes that allow such uniform hydrostatic stress state are classified into three groups: (i) for the design of harmonic shapes under non-uniform loading, (ii) for approximation a rectangle (centered at origin with its sides parallel to the coordinate axes), and (iii) for description of hypotrochoid. For each group, two conditions that ensure a uniform hydrostatic stress state are analytically obtained. The first condition links the interphase layer thickness to elastic properties of the composite phases, and the second one relates the remote stresses to geometrical and material parameters of the three-phase composite. Besides the general case of elastic properties of three-phase composites, the authors consider a special case of three phases with the same shear modulus. Finally, a uniform stress state is studied in the inclusion under remote uniform anti-plane shear stresses. As a result, the authors obtain the possible inclusion shapes and conditions for generating uniform stress fields in the inclusions. This identified inclusion shape is in agreement with known Antipov-Schiavone solution for uniform stress state inside an inclusion bonded to a surrounding matrix through a ``spring-layer type'' imperfect interface with vanishing thickness.
scientific article; zbMATH DE number 5996244
scientific article