Polyurea (PUa) elastomers are extensively used in a wide range of applications spanning from biomedical to defense fields due to their enabling mechanical properties. These materials can be further reinforced through the incorporation of nanoparticles to form nanocomposites. This study focuses on an IPDI-based PUa matrix with exfoliated graphene nanoplatelet (xGnP) fillers. We propose a generalized constitutive model by integrating one Fractional Maxwell Model (FMM) and one Fractional Maxwell Gel (FMG) branch in a parallel configuration via introducing a new dimensionless number to bridge between these branches physically and mathematically. Through systematic local-to-global sensitivity analyses, we investigate the behavior of these nanocomposites to facilitate simulation, design, and performance prediction. Consistently, the constructed models share the same most/least influential model parameters. $\alpha_1$ and $E_{c_1}$, the power exponent and the characteristic modulus of the first branch, are found to be the most influential model parameters, while $\tau_{c_2}$ and $\tau_{c_1}$, the characteristic time-scales of each branch, are recognized as the least influential model parameters. The proposed PU nanocomposite constitutive laws can now make an impact to the design and optimization of coating and shock-absorbing coatings in a range of applications.

翻译：聚脲（PUa）弹性体因其优异的力学性能，在从生物医学到国防领域的广泛应用中得到了广泛使用。通过引入纳米颗粒形成纳米复合材料，可以进一步增强这些材料的性能。本研究聚焦于以异佛尔酮二异氰酸酯（IPDI）为基体的聚脲基质与剥离石墨烯纳米片（xGnP）填料构成的复合材料。我们提出了一种广义本构模型，通过引入一个新的无量纲数，在物理和数学上连接一个分数阶麦克斯韦模型（FMM）分支与一个分数阶麦克斯韦凝胶（FMG）分支，并以并联方式集成这两个分支。通过系统的局部到全局敏感性分析，我们研究了这些纳米复合材料的行为，以促进模拟、设计和性能预测。一致地，所构建的模型共享相同的最具/最不敏感模型参数。研究发现，第一分支的幂指数 $\alpha_1$ 和特征模量 $E_{c_1}$ 是最具影响力的模型参数，而各分支的特征时间尺度 $\tau_{c_2}$ 和 $\tau_{c_1}$ 则被确认为最不具影响力的模型参数。所提出的聚脲纳米复合材料本构定律现可对一系列应用中的涂层和减震涂层的设计与优化产生重要影响。