Hutsaylyuk Volodymyr, Piskozub Yosyf, Piskozub Liubov, Sulym Heorhiy
Institute of Robots and Machine Design, Military University of Technology, Gen. S. Kaliskiego str. 2, 00-908 Warsaw, Poland.
Department of Applied Mathematics and Physics, Ukrainian Academy of Printing, Pidgolosko 19, 79020 L'viv, Ukraine.
Materials (Basel). 2022 Feb 15;15(4):1435. doi: 10.3390/ma15041435.
Within the framework of the concept of deformable solid mechanics, an analytical-numerical method to the problem of determining the mechanical fields in the composite structures with interphase ribbon-like deformable multilayered inhomogeneities under combined force and dislocation loading has been proposed. Based on the general relations of linear elasticity theory, a mathematical model of thin multilayered inclusion of finite width is constructed. The possibility of nonperfect contact along a part of the interface between the inclusion and the matrix, and between the layers of inclusion where surface energy or sliding with dry friction occurs, is envisaged. Based on the application of the theory of functions of a complex variable and the jump function method, the stress-strain field in the vicinity of the inclusion during its interaction with the concentrated forces and screw dislocations was calculated. The values of generalized stress intensity factors for the asymptotics of stress-strain fields in the vicinity of the ends of thin inhomogeneities are calculated, using which the stress concentration and local strength of the structure can be calculated. Several effects have been identified which can be used in designing the structure of layers and operation modes of such composites. The proposed method has shown its effectiveness for solving a whole class of problems of deformation and fracture of bodies with thin deformable inclusions of finite length and can be used for mathematical modeling of the mechanical effects of thin FGM heterogeneities in composites.
在可变形固体力学概念的框架内，提出了一种解析数值方法，用于解决在力和位错联合作用下，具有相间带状可变形多层不均匀性的复合结构中机械场的确定问题。基于线性弹性理论的一般关系，构建了有限宽度的薄多层夹杂的数学模型。考虑了夹杂与基体之间以及夹杂层之间部分界面处存在非理想接触的可能性，这种非理想接触会产生表面能或干摩擦滑动。基于复变函数理论和跳跃函数法的应用，计算了夹杂与集中力和螺旋位错相互作用时夹杂附近的应力应变场。计算了薄不均匀性端部附近应力应变场渐近线的广义应力强度因子值，利用这些值可以计算结构的应力集中和局部强度。已识别出几种效应，可用于设计此类复合材料的层结构和运行模式。所提出的方法在解决一类具有有限长度的薄可变形夹杂的物体的变形和断裂问题方面已显示出有效性，可用于复合材料中薄功能梯度材料不均匀性力学效应的数学建模。
