Mechanics of fiber composites with fibers resistant to extension and flexure

A model of elastic solids reinforced with fibers resistant to extension and bending is formulated in finite-plane elastostatics. The linear theory of the proposed model is also derived through which a complete analytical solution is obtained. The presented model can serve as an alternative two-dimensional Cosserat theory of non-linear elasticity.

The Stress Field Due to an Edge Dislocation Interacting With Two Circular Inclusions

A general series solution to the problem of interacting circular inclusions in plane elastostatics is presented in this paper. The analysis is based on the use of the complex stress potentials of Muskhelishvili and the theorem of analytical continuation. The general forms of the complex potentials are derived explicitly for the circular inhomogeneities under arbitrary plane loading. Using the alternation technique, these general expressions were subsequently employed to treat the problem of an infinitely extended matrix containing two arbitrarily located inhomogeneities. The major contribution of the present proposed method is shown to be capable of yielding approximate closed-form solutions for multiple inclusions, thus providing the explicit dependence of the solution on the pertinent parameters. The result shows that the dislocation has a stable equilibrium position at a certain combination of material constants. The case of an inhomogeneity interacting with a circular hole under a remote uniform load is also investigated.

A circular inclusion with inhomogeneous non-slip imperfect interface in harmonic materials

In this work, a rigorous study is presented for the problem associated with a circular inclusion embedded in an infinite matrix in finite plane elastostatics where both the inclusion and matrix are comprised a harmonic material. The inclusion/matrix boundary is treated as a circumferentially inhomogeneous imperfect interface that is described by a linear spring-type imperfect interface model where in the tangential direction, the interface parameter is infinite in magnitude and in the normal direction, the interface parameter is finite in magnitude (the so-called non-slip interface condition). Through the repeated use of the technique of analytic continuation, the boundary value problem for four analytic functions is reduced to solve a single first-order linear ordinary differential equation with variable coefficients for a single analytic function defined within the inclusion. The unknown coefficients of said function are then found via various analyticity requirements. The method is illustrated, using a specific example of a particular class of inhomogeneous non-slip imperfect interface. The results from these calculations are then contrasted with the results from the homogeneous imperfect interface. These comparisons indicate that the circumferential variation of interface damage has a pronounced effect on the average boundary stress.