拉胀蜂窝材料循环变形行为及本构模型研究

Auxetic materials (including auxetic honeycomb lattices) are newly structural-functional cellular materials performing a negative Poisson’s ratio and have great application potential in load-bearing areas. To overcome the shortcomings in the study on the cyclic deformation and constitutive modeling of auxetic materials, this project intends to use two classical auxetic honeycomb lattices as the research objects, performing detailed experimental and theoretical research on such topics. Firstly, based on finite element (FE) homogenization, investigate the effect of the orientation and size of the unit-cell on the negative Poisson’s ratio and cyclic deformation of auxetic honeycomb lattices as well as the deformation characteristic of the micro-structures of unit-cell. Choose several representative orientations and sizes of unit-cell in view of the FE analysis, and manufacture experimental specimens by 3D printing. Then, perform systematic experimental tests of the specimens under cyclic loading conditions to investigate the cyclic deformation evolutions of the materials and further reveal the deformation mechanism of the micro-structures of unit-cell. Finally, based on the FE and experimental results, establish a cyclic constitutive model in the framework of micro-polar elasto-plasticity considering the micro-deformation of the unit-cell, and implement it into a finite element code (e.g., ABAQUS). The research achievements are an important development of cyclic constitutive relations of functional-structural materials. Moreover, the established cyclic constitutive model can be directly used in the prediction of fatigue life and assessment of safety and reliability of auxetic structure components, promote the application of auxetic honeycomb lattices to the lightweight structures.

拉胀材料（包括拉胀蜂窝材料）是具有负泊松比效应的新型功能和结构一体化的多孔材料，在承载领域具有广阔的应用前景。本项目针对拉胀材料循环变形为和本构描述方面的不足，拟以两种典型拉胀蜂窝材料为研究对象，开展如下系统的实验和理论研究：首先，通过基于有限元的均匀化方法，系统考察元胞微结构取向和尺寸对负泊松比和循环变形行为的影响以及元胞微结构变形特征，并选取几组典型元胞取向和尺寸,通过3D打印制备实验所需试样；然后，开展系统的循环变形行为研究，考察拉胀蜂窝材料循环变形行为的演化规律并进一步揭示其微结构变形机理；最后，基于有限元和实验分析，在大变形微极弹塑性理论框架下建立可考虑元胞微结构变形的循环本构模型，并进行有限元实现。研究成果是对功能性结构材料本构关系的重要拓展；同时，研究成果可用于复杂加载条件下拉胀结构的疲劳寿命预测和可靠性评估中，并可促进拉胀蜂窝材料在轻量化结构中的应用。

具有规则微结构形状的拉胀蜂窝材料有诸多优越的力学性能，且易于设计和制备，具有广阔的工程应用前景。本课题针对拉胀蜂窝材料的优化设计、循环变形行为及其本构描述开展了实验、仿真和理论研究，取得了如下研究成果：1）系统考察了基体材料的循环变形行为，并发展了可合理描述应力-应变滞回环的基于反双曲正弦函数的循环本构模型和改进的Ohno-Kaim循环本构模型；2）系统揭示了手性拉胀结构和缺失支柱结构的变形机理，并基于此发展了拉胀和吸能效果更好的屈臂手性拉胀结构及在超大变形范围内具有可调、恒定负泊松比的增强缺失支柱结构并基于拉-扭变形机理进行了三维拓展；3）基于等几何分析将拉胀，设计了拉胀和强度俱佳花瓣形拉胀结构；4）对增强缺失支柱结构开展了系统的循环变形行为研究（数值仿真为主，并辅以实验），考察了其循环变形及泊松比演化特征；5）基于卡氏原理，推导了小变形下增强缺失支柱结构的弹性模量和泊松比，并进一步推导了其本构关系；6）构建了基于微态理论的循环本构框架。另外，本课题还考察了高速列车车轮钢在偏轴和预弹性应变加载下疲劳行为，建立了适用于生物软骨的循环本构模型，为后续新型拉胀工程构件的可控构筑奠定了基础。