有限变形下粘弹性纤维增强复合材料的本构建模

Due to the intrinsic difficulties resulted from the coupling of geometric nonlinearity, material nonlinearity and dependency of deformation history, the research on the mechanical properties of the viscoelastic fiber-reinforced composites at finite deformations is still at its infant stage. Their effective properties have not been well understood because of the lack of accurate constitutive models. The goal of this proposed project is to develop an accurate constitutive model for the finite-strain viscoelastic fiber-reinforced composites, which aims at predicting the “overall” mechanical responses of the composites based on the mechanical properties of the constituents, as well as the microstructures of the composites. A specific multiplicative decomposition will be utilized to decouple a general deformation to several simple deformations. The mechanical responses of the viscoelastic fiber-reinforced composites at the corresponding simple deformations will then be derived based on micromechanics. Hence the constitutive model can be obtained by the sum of all the free energy components. After that, the representative volume element (RVE) samples of the composites with different microstructures will be created and numerical simulations will be performed to validate the constitutive model. The 3D printing technology will also be utilized to fabricate viscoelastic fiber-reinforced composite specimens with various microstructures and a number of experiments, including uniaxial tension, simple shear, and relaxation, will be carried out to further verify the proposed model. The research will not only pave the way for better understanding of the mechanics of composites in finite deformation, but also promote the design optimization and applications of the advanced composite materials in industry.

由于几何非线性、材料非线性以及变形历史相关性耦合造成的困难，对于粘弹性纤维增强复合材料在有限变形下力学性质的研究尚处于起步阶段。本项目的研究旨在根据基体和纤维的材料参数和复合材料的微观结构，预测复合材料的“整体”力学行为，推导复合材料在有限变形下的本构关系。首先利用变形梯度的乘法分解，将一般有限变形解耦为若干步简单变形，建立简单有限变形下粘弹性纤维增强复合材料的本构模型，通过自由能叠加，得到一般有限变形下粘弹性纤维增强复合材料的本构模型。随后建立具有不同微观结构的粘弹性纤维增强复合材料代表体积单元模型，通过数值方法验证本构模型的精确性。同时利用3D打印技术制备粘弹性纤维增强复合材料实验试件，通过实验方法验证本构模型的精确性。本项目的研究成果将促进粘弹性纤维增强复合材料在工程上的设计优化及应用。

广泛应用于各类工程结构中的高分子基复合材料大多具有粘弹性特性，建立该类复合材料基于细观力学理论的本构模型可实现复合材料粘弹性力学性能的精确预测，提升复合材料多尺度分析的效率和精度。本项目首先基于复合材料细观力学理论，提出了一种有限变形下粘弹性复合材料的均匀化方法。通过该均匀化方法，将粘弹性复合材料的等效Helmholtz自由能密度函数解耦为弹性储能部分与粘性耗散部分，因此复合材料的等效应力解耦为相对应的平衡应力（弹性、时间无关）与非平衡应力（粘性、时间相关）部分。随后，通过细观力学方法，分别推导出纤维和颗粒增强复合材料平衡应力和非平衡应力的表达式，从而建立了这两类粘弹性复合材料在有限变形下的本构模型。在此基础上，本项目将建立的有限变形均匀化理论进行扩展，建立了线性粘弹性纤维和颗粒增强复合材料的本构模型，并分别针对复合材料的界面层效应和热-力耦合效应进行了系统地研究。最后，本项目分别建立了粘弹性纤维和颗粒增强复合材料的代表体积单元模型，通过数值模拟方法对本构模型的预测精度进行验证。同时，本项目还选取了典型工况下的实验数据，对本构模型的预测精度进行进一步的验证。研究结果表明：本项目建立的所有本构模型可以精确地预测粘弹性复合材料在典型载荷作用下的力学行为。本项目建立的本构模型表达式简单、预测精度高，可有效提升复合材料的多尺度分析效率和精度，具有重要工程应用价值。