基于互补理论和扩展有限元法的摩擦接触裂纹应力强度因子计算

从虚功方程出发，结合扩展有限元离散技术与接触条件的非线性互补表述，建立了摩擦接触裂纹问题的扩展有限元非线性互补模型，将不等式接触条件转化为非线性互补类的非光滑方程组，并采用基于广义导数的非光滑阻尼牛顿法求解方程组，无需引入任何额外人工变量以及迭代求解。以含中心倾斜裂纹平板和边裂纹平板为例，运用相互作用积分法计算摩擦接触裂纹的应力强度因子，将其结果与理论解进行对比分析，该方法都能给出精确的计算结果；基于扩展有限元方法对单轴压缩作用下倾斜裂纹扩展过程进行了数值模拟，计算结果表明，受压裂纹数值结果与实验结果比较吻合，从而验证了本文方法的有效性与正确性。

Stress Intensity Factor Calculation of Friction Contact Cracks Based on Complementary Theory and Extended Finite Element Method

The extended finite element method is a numerical method for modeling discontinuities within the classical finite element framework. This method can treat arbitrary cracks independent of the mesh and crack growth with minimal remeshing. Based on the principle of virtual work equation, and combined with the nonlinear complementary for contact conditions and the extended finite element discrete technique, a nonlinear complementary model for frictional contact crack problem with the extended finite element method is presented. First, the conditions that describe frictional contact are formulated as a system of non-smooth equations based on variational inequality theory, and the non-smooth damped newton method is given based on the definitions of generalized derivative to directly solve the system of equations without any extra parameters and iteration. Then, take the finite plane with a single inclined crack, edge-cracked plate as examples. The stress intensity factor of finite plane with closed crack was calculated by the interaction integral approach. The numerical solution calculated by the extended finite element method is basically consistent with the theory solution. Finally, the propagation of inclined crack under uniaxial compression is simulated by the extended finite element method. The calculation result shows that the numerical result is agreement with the experimental result and this method can accurately simulate the crack growth under uniaxial compression. Numerical example is presented to demonstrate the correctness and effectiveness of this method.