In this paper, we investigate the asymptotic crack tip fields in a neo-Hookean sheet reinforced by two families of nonlinear fibers, where the fibers are characterized by the standard reinforcing model. In the asymptotic analysis, the fibers with stronger stiffening compared to the matrix dominate the mechanical behavior at the crack tip, which simplifies the analysis. A hodograph transformation is used to solve for the leading and higher order eigenmodes for the nonlinear eigenvalue problem derived from the model. Asymptotic path-independent J-integrals are constructed to evaluate the leading order parameters separately. The asymptotic crack tip fields agree well with finite element results for different combinations of fiber orientation angles and modulus ratios. We find that the peak value of stress for the case with two families of fibers decreases significantly compared to the case for a single family of fibers.

在本文中，我们研究了由两类非线性纤维增强的新胡克板中的渐近裂纹尖端场，其中纤维由标准增强模型表征。在渐近分析中，与基体相比具有更强刚度的纤维主导了裂纹尖端的力学行为，这简化了分析。hodograph 变换用于求解从模型导出的非线性特征值问题的前导和高阶特征模。渐近路径无关J- 积分被构造为分别评估前导阶参数。对于纤维取向角和模量比的不同组合，渐近裂纹尖端场与有限元结果非常吻合。我们发现，与单族纤维的情况相比，具有两个纤维族的情况的应力峰值显着降低。