Two-dimensional Green's function of orthotropic three-phase material under a normal line force with application in the design of composite

Green's function of orthotropic three-phase material is an important and basic problem in the study of mechanics of materials. It is also the foundation of further theoretical researches and engineering applications. Most of adhesive structures in engineering can be well simulated by the mechanical model of orthotropic three-phase material, such as composite laminate, integrated circuit (IC) packaging, micro-electro-mechanical systems (MEMS) and biomedical materials, etc. In order to understand the mechanical properties of the adhesive structure, a two-dimensional Green's function of orthotropic three-phase material loaded with a normal line force is presented. Based on the Green's function proposed in this paper, the stress field of adhesive structure under arbitrary normal loadings can be obtained with superposition method. Besides, this Green's function is convenient to be used in further studies, because it is expressed explicitly in form of elementary functions. Numerical examples are proposed to study the mechanical properties of the adhesive structure in five difference aspects: (1) the distribution rule of stress fields of the adhesive structure; (2) the influence from fiber orientation of composite to the stress fields of the adhesive structure; (3) the influence from elastic modulus of adhesive layer to the stress transfer of the adhesive structure; (4) the influence from the thickness of adhesive layer to the stress transfer of the adhesive structure; (5) the reasonability of spring interface model.