A non-circular Eshelby inclusion near a non-parabolic inhomogeneity admitting internal uniform stresses

With the aid of conformal mapping and analytic continuation, we prove that within the framework of anti-plane elasticity, a non-parabolic open elastic inhomogeneity can still admit an internal uniform stress field despite the presence of a nearby non-circular Eshelby inclusion undergoing uniform anti-plane eigenstrains when the surrounding elastic matrix is subjected to uniform remote stresses. The non-circular inclusion can take the form of a Booth’s lemniscate inclusion, a generalized Booth’s lemniscate inclusion or a cardioid inclusion. Our analysis indicates that the uniform stress field within the non-parabolic inhomogeneity is independent of the specific open shape of the inhomogeneity and is also unaffected by the existence of the nearby non-circular inclusion. On the other hand, the non-parabolic shape of the inhomogeneity is caused solely by the presence of the non-circular inclusion.

A hole of irregular shape interacting with a non-parabolic open inhomogeneity with internal uniform anti-plane stresses

We use conformal mapping techniques together with analytic continuation to show that a non-parabolic open elastic inhomogeneity continues to admit a state of uniform internal stress when a hole with closed curvilinear traction-free boundary is placed in its vicinity and the surrounding matrix is subjected to uniform remote anti-plane stresses. The internal uniform stress field inside the inhomogeneity is found to be independent of the existence of the nearby hole and the specific non-parabolic shape of the inhomogeneity. In contrast, the non-parabolic shape of the inhomogeneity is influenced solely by the existence of the nearby hole.

DYNAMICAL MODEL OF THE ASYMMETRIC ACTUATOR OF DIRECTIONAL MOTION BASED ON POWER-LAW GRADED MATERIALS

We consider an actuator whose driving bodies are made of Power-Law graded materials. The directional motion is generated by an asymmetric mechanism producing simultaneously vertical and horizontal oscillations of the indenter. The dynamic contact of gradient materials is described and the equation of motion for the drive is written down and analyzed. It is shown that the exponent of the elastic inhomogeneity significantly affects the average velocity of motion of the cargo, which can be dragged by the drive.

Neutral Inhomogeneity in Circular Cylinder Subjected to Axial Load on its Lateral Boundary

In this paper we consider the problem of single circular elastic inhomogeneity embedded within a circular cylinder whose curved boundary surface is subjected to surface traction acting on axial direction. We investigate the displacement neutrality of the coupled system of host body and inclusion. Neutral inhomogeneity (inclusion) does not disturb the displacement, strain and stress fields in the host body. The deformation of the considered inhomogenneous cylinder is antiplane shear deformation.

Thermal Expansion Induced Neutrality of a Circular and an Annular Elastic Inhomogeneity

An elastic inhomogeneity is termed neutral if its introduction does not disturb the original stress field in the initially uncut elastic body. Neutrality in this sense is often achieved by appropriate design criteria such as a careful choice of the shape of the inhomogeneity and the properties of the interfacial layer between the inhomogeneity and its surrounding matrix. Unfortunately, mismatched stress and strain fields in the resulting composite structure make it difficult to simultaneously control both the shape of the inhomogeneity and its interfacial properties to achieve the desired neutrality property. We assert that the associated temperature field can be used to adjust the stress and strain fields within the inhomogeneity via thermal expansion, thus allowing us to control the properties of the interfacial layer for a given shape of inhomogeneity. Our theoretical results show that the design of a neutral circular or annular elastic inhomogeneity requires an accompanying internal uniform temperature field when the elastic body is in equi-biaxial tension and an internal temperature field which is quadratic if the body is subjected to uniaxial tension or shear force. More importantly, in contrast to the well-established result in the literature for a purely elastic inhomogeneity, under certain conditions, a neutral elastic inhomogeneity can be designed via thermal expansion despite the assumption of a perfectly bonded interface between the inhomogeneity and the surrounding matrix.