Simplified model within coupled linear anisotropic strain gradient elasticity and its applications to the solution of various boundary value problems

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The objectives of the proposed research are to develop simplified anisotropic constitutive relations within coupled strain gradient elasticity, to determine correspondent scale parameters, to apply such modeling to the solution of some boundary value problems where classical elasticity has the limitations, to demonstrate the natural elimination of these limitations. More specifically: - Homogenization problems accounting for the size effect will be considered. In particular, bounds like Voigt and Reuss, and like Hashin–Shtrikman for particulate composites will be obtained using principles of a minimum of potential and complementary energies, effective properties of fiber-reinforced and particulate composites will be evaluated within the coupled anisotropic strain gradient elasticity. - Plane-strain crack problems, namely, mode I, mode II and mode III crack problems, and problem on an edge crack will be studied. - Concentrated force problems, in particular, half-plane loaded at its surface, a force applied on interior and on the free boundary of the plate will be analyzed in the context of the theory. For all problems, the influence of the coupling term and the anisotropy of material properties on the solutions, departure of solutions from predictions of classical elasticity, and from uncoupled strain gradient elasticity will be studied. Results will be compared and analyzed in the context of those available in the literature.