Analytical study of a circular inhomogeneity with homogeneously imperfect interface in plane micropolar elasticity

Abstract

In this paper we derive the full analytical solution for the problem of a circular micropolar inhomogeneity in an infinite micropolar plate subjected to a remote uni‐axial tension. The interface between the inhomogeneity and the surrounding matrix is considered to be homogeneously imperfect. This model has been well known in classical elasticity and was validated experimentally and verified analytically . Mathematically it is expressed in the assumption that the stresses are continuous across the interface and proportional to the jumps in the corresponding displacements. This idea was extended to micropolar elasticity , where the additional assumption of continuous couple‐tractions proportional to the jumps in the corresponding microrotations was introduced. In the present work we show the asymptotic derivation of the linear interface model in micropolar elasticity (plane‐strain), based on the expansion of all fields in a thin “interphase” layer between the inhomogeneity and the matrix, , and link the interface parameters to the properties of the interphase layer. The problem is subsequently solved with the use of Eringen's stress functions, which allow to express all stresses/couple stresses and displacements/microrotation as a linear combination of the solutions of two governing equations and reduce the boundary conditions on the interface to a system of algebraic equations for the unknown coefficients. A parametric study is conducted to show that the stress concentration factors are significantly dependent on the micropolar material constants as well as the parameters characterizing the imperfect bonding between the inhomogeneity and the matrix. The solution is given in a ready‐to‐use form, freely downloadable, and can be further used, for example, for the analysis of interface failures or as a reference solution in numerical methods.

An integral representation for the solution of the inclusion problem in the theory of antiplane micropolar elasticity

“…It can be shown that these assumptions are possible if and only if φ 1 = φ 2 =0 everywhere in both the interior and exterior domains so the problem reduces to the classical one considered in the work by Shen et al [16]. The interface condition given by equation (29) with 3 interface parameters is supported by Videla and Atroshchenko [31] where a circular inclusion under the assumptions of plane micropolar elasticity is considered.…”

“…with 3 interface parameters is supported by Videla and Atroshchenko[31] where a circular inclusion under the assumptions of plane micropolar elasticity is considered.Consider an inclusion represented by an ellipse prescribed by the equationsx 1 = a cos θ, x 2 = b sin θin the case of remote loading S 0 under the assumptions of pure anti plane shear and in the absence of any eigenstrain inside the inclusion. By changing the values of the parameters a and b we can consider elliptic inclusions of different sizes and aspect ratios.…”

Effect of imperfect interface on the effective properties of elastic micropolar multilaminated nanostructures

“…This can define the existence of mechanical imperfections, interfacial damages (such as debonding, delamination, sliding, and/or cracking across the interface), thermic isolations, chemical reactions, and so forth. In Videla and Atroshchenko [35], the problem of homogeneously imperfect interface reported by Achenbach and Zhu [36] and Hashin [37,38] is generalized to micropolar elastic media assuming that couple tractions are continuous across the interface and proportional to the jumps of the out-of-plane microrotation. The simulation of the mechanical effects on microstructured Cosserat materials reinforced by inclusions with perfect and imperfect interfaces is developed using the boundary element method in Atroshchenko et al [39].…”

Effective anti-plane moduli of couple stress composites containing elliptic multi-coated nano-fibers with interfacial damage and variational bounds

“…The current work considers an embedded multi-coated elliptic nano-fiber under three different interfacial conditions of pure sliding (completely damaged), imperfect (partially damaged), and perfect (undamaged) in anti-plane couple stress theory. To model interfacial damage in this framework, in addition to what is considered in traditional theory, the couple traction is allowed to be continuous while the components of the microrotation vector are considered to be proportional to the related couple traction along the interfaces; see, for example, Atroshchenko et al (2017), Hashemian et al (2015), Shodja and Hashemian (2019), and Videla and Atroshchenko (2017).…”