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

提出的研究的目标是发展简化的各向异性本构关系耦合应变梯度弹性，以确定相应的尺度参数，应用这种建模的一些边界值问题的解决方案，经典弹性有局限性，以证明这些限制的自然消除。更具体地说：-均匀化的问题占的大小效应将被考虑。特别是，像Voigt和Reuss，和像Hashin-Shtrikman颗粒复合材料的边界将获得使用最小势能和余能的原则，纤维增强和颗粒复合材料的有效性能将在耦合各向异性应变梯度弹性内进行评估。- 平面应变裂纹问题，即模式I，模式II和模式III裂纹问题，和问题的边缘裂纹将被研究。- 集中力问题，特别是，在其表面加载的半平面，施加在内部和板的自由边界上的力将在理论的范围内进行分析。对于所有的问题，耦合项和各向异性的材料性能的解决方案，偏离经典弹性预测的解决方案，并从非耦合应变梯度弹性的影响将进行研究。将在文献中提供的背景下对结果进行比较和分析。

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.