A model for the mechanics of a hyperelastic material reinforced with unidirectional and bidirectional fibers is presented in finite plane elastostatics. This includes the refinement/development of a series of continuum-based prediction models to accommodate the nonlinear responses of both the matrix material and the reinforcing fibers. The kinematics of the embedded fibers, including the torsional kinematics between two adjoining fibers, are formulated via the first and second gradient of continuum deformations. Within the framework of variational principles and a virtual work statement, the Euler equation and the admissible boundary conditions are derived. To this end, a set of inhouse experiments are performed for the purpose of cross-examination and model implementation. The obtained models successfully predict the strain-stiffening responses of the elastomer – polyester fiber composites together with other key design considerations such as, deformation profiles, shear strain distributions, and the deformed configurations of a local unit fiber mesh. The Euler – Almansi strain integrate model is also proposed through which the strain-softening behaviors of a certain type of polyurethane fiber composites are predicted, yet further implementation of the obtained Euler – Almansi model remains to be determined due to the paucity of available data. The practical utility of the proposed models may be expected in the design and analysis of hyperelastic composites exhibiting strain-stiffening/softening responses by providing instant estimations of the resultant properties of intended composites.

在有限平面弹性静力学中提出了一种用单向和双向纤维增强的超弹性材料的力学模型。这包括改进/开发一系列基于连续介质的预测模型，以适应基体材料和增强纤维的非线性响应。嵌入纤维的运动学，包括两个相邻纤维之间的扭转运动学，是通过连续变形的第一和第二梯度制定的。在变分原理和虚拟工作陈述的框架内，导出了欧拉方程和容许边界条件。为此，为了交叉检验和模型实现的目的，进行了一组内部实验。获得的模型成功地预测了弹性体 - 聚酯纤维复合材料的应变硬化响应以及其他关键设计考虑因素，例如变形剖面、剪切应变分布和局部单元纤维网格的变形配置。还提出了 Euler-Almansi 应变积分模型，通过该模型可以预测某种类型的聚氨酯纤维复合材料的应变软化行为，但由于可用数据的缺乏，所获得的 Euler-Almansi 模型的进一步实施仍有待确定。通过提供对预期复合材料的合成特性的即时估计，可以预期所提出的模型在设计和分析显示应变硬化/软化响应的超弹性复合材料中具有实际效用。