复合材料桥连的断裂动力学模型

复合材料产生裂纹后，其纤维处形成“桥连”，这是一个不可避免的现象。由于桥连问题很复杂．在数学方法的处理上有很大困难，至今人们研究大多是桥连的静力学问题．而对其动力学问题研究得很少。为了便于分析复合材料的问题，将桥连处用载荷代替，当裂纹高速扩展时．其纤维也连续地断裂。只有建立复合材料的桥连动力学模型，才能更好地研究复合材料的断裂动力学问题。通过复变函数论的方法，将所讨论的问题转化为Riemann—Hilbert问题。利用建立的动态模型和自相似方法，得到了正交异性体中扩展裂纹受运动的集中力P及阶跃载荷作用下位移、应力和动态应力强度因子的解析解，并通过叠加原理，最终求得了该模型的解。

A Fracture Dynamics Model on Bridge of Composite Materials

After a composite material appears a crack, its fibrous position forms bridge, and this is an inevitable phenomenon. Because problems on bridge are complex, there is much difficult to treat with them in mathematical methods. A bridging fiber crack has nearly been studied on its statics up to now, and studies on its dynamics problem are less. In order to analyze the problems of composite materials easily, bridging fiber section was substituted for loads. When a crack extends, its fiber continues to crack. Only, a dynamics model of bridging fiber is built, fracture dynamics problems of composite materials are solved very well. By the theory of complex functions, their problems dealt with can be transformed into Riemann-Hilbert problems. Utilizing the built dynamic models and the self-similar methods, an analytical study on the displacements, stresses and dynamic stress intensity factors of crack propagation under a moving concentrated force P and a unit step load was firstly attained in orthotropic body and it is utilized to obtain the concrete solution of the model by the method of superposition.