Abstract. In this paper we tackle the simulation of microstructured materials modelled as heterogeneous Cosserat media with both perfect and imperfect interfaces. We formulate a boundary value problem for an inclusion of one plane strain micropolar phase into another micropolar phase and reduce the problem to a system of boundary integral equations, which is subsequently solved by the boundary element method. The inclusion interface condition is assumed to be imperfect, which permits jumps in both displacements/microrotations and tractions/couple tractions, as well as a linear dependence of jumps in displacements/microrotations on continuous across the interface tractions/couple traction (model known in elasticity as homogeneously imperfect interface). These features can be directly incorporated into the boundary element formulation.The BEM-results for a circular inclusion in an infinite plate are shown to be in an excellent agreement with the analytical solutions. The BEM-results for inclusions in finite plates are compared with the FEM-results obtained with FEniCS.

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A new n− noded polygonal plate element is proposed for the analysis of plate structures comprising of thin and thick members. The formulation is based on the discrete Kirchhoff Mindlin theory. On each side of the polygonal element, discrete shear constraints are considered to relate the kinematical and the independent shear strains. The proposed element: (a) has proper rank; (b) passes patch test for both thin and thick plates; (c) is free from shear locking and (d) yields optimal convergence rates in L 2 −norm and H 1 −semi-norm. The accuracy and the convergence properties are demonstrated with a few benchmark examples.

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.