This paper deals with an elastic orthotropic inhomogeneity problem due to non-uniform eigenstrains. The specific form of the distribution of eigenstrains is assumed to be a linear function in Cartesian coordinates of the points of the inhomogeneity. Based on the polynomial conservation theorem, the induced stress field inside the inhomogeneity which is also linear, is determined by the evaluation of 10 unknown real coefficients. These coefficients are derived analytically based on the principle of minimum potential energy of the elastic inhomogeneity/matrix system together with the complex function method and conformal transformation. The resulting stress field in the inhomogeneity is verified using the continuity conditions for the normal and shear stresses on the boundary. In addition, the present analytic solution can be reduced to known results for the case of uniform eigenstrain.

In this article, a decoupled modified characteristic finite element method is proposed for the time-dependent Navier-Stokes/Biot problem. In the numerical scheme, the implicit backward Euler scheme is used for the time discretization, whereas the coupling terms are treated explicitly. At each time step, we only need to solve two decoupled problems, one is the Navier-Stokes equations solved by the modified characteristic finite element method, and the other is Biot equations. The stability and the error estimates are established for the proposed fully discrete scheme. Numerical experiments are provided to illustrate the theory.

To study the effect of phase on the microstructure and mechanical properties of nitride coatings, three films of TiN, TiAlN, and TiSiN were prepared on the surface of high-speed steel using hollow cathode assisted multi-arc ion plating technique. The XRD lines of the three films were analyzed and calculated by linear analysis. The element and phase of the film were observed and analyzed by x-ray Diffraction (XRD), Transmission Electron Microscope (TEM), energy dispersive x-ray analysis (EDS). The microstructure and film thickness of the coating were characterized by scanning electron microscopy (SEM). The surface roughness of the film was observed by Confocal laser scanning microscope (CLSM). The hardness, friction coefficient, and coating/substrate adhesion of the film were tested by the G200 nanometer hardness tester and CETR UNMT-1 surface micro-nano mechanical test system. We discovered two different reinforcement mechanisms. The high microscopic strain value (1.309×10 −3 ) in the TiAlN film was related to the formation of Ti 3 AlN substitutional solid solution in the film formed a large lattice distortion,however, the coating/substrate adhesion (33.5 N) was lowered. The result of independent nucleation and growth of the Si 3 N 4 phase in the TiSiN film refines the structure of the film, alleviating the increase of microscopic strain. At this time, the coating/ substrate adhesion reaches the highest value of 40 N and the film surface roughness reaches the minimum value of 0.451 μm. The results also show that the TiSiN coating can obtain good coating/ substrate adhesion without pre-plating. OPEN ACCESS RECEIVED

A closed-form solution for elastic field of an elliptical inhomogeneity with polynomial eigenstrains in orthotropic media having complex roots is presented. The distribution of eigenstrains is assumed to be in the form of quadratic functions in Cartesian coordinates of the points of the inhomogeneity. Elastic energy of inhomogeneity-matrix system is expressed in terms of 18 real unknown coefficients that are analytically evaluated by means of the principle of minimum potential energy and the corresponding elastic field in the inhomogeneity is obtained. Results indicate that quadratic terms in the eigenstrains induce zeroth-order elastic strain components, which reflect the coupling effect of the zeroth-and second-order terms in the polynomial expressions on the elastic field. In contrast, the first-order terms in the eigenstrains only produce corresponding elastic fields in the form of the first-order terms. Numerical examples are given to demonstrate the normal and shear stresses at the interface between the inhomogeneity and the matrix. Furthermore, the solution reduces to known results for the special cases.

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