基于SIR模型的工程材料统一单轴本构关系研究

工程材料的单轴应力-应变全曲线反映了材料最基本的本构关系，但目前对适用于多种材料的统一本构关系研究尚不够深入。本文基于传染病传播动力学SIR模型，建立了反映材料单元动态变化的应力-应变模型。根据同伦分析方法提出了模型的解析解和近似解，并讨论了模型反映材料尺寸效应和应变率的能力。结果表明，本文提出的单轴应力-应变模型中的参数可以与实际材料的力学特性相对应，模型解能够统一、全面、准确地反映多种材料力学性能的变化规律以及尺寸效应和应变率等因素的影响。

Uniform uniaxial constitutive relation for engineering material based on SIR epidemic model

The uniaxial stress-strain curve of engineering material reflects the basic constitutive relation,but the research on the uniform constitutive relation for various materials is still not deep enough.A new dynamic stress-strain model is established based on the SIR model for the transmission dynamics of infectious diseases.The analytical solution and the approximate solution for the proposed model is represented according to the homotopy analysis method,and the relationship of the solution and the size effect and strain rate is discussed.The results show that the mechanical mechanism of the parameters in the uniaxial stress-strain model proposed in this paper reflects the actual materials characteristics.The solution of the SIR model can fully and accurately show the change of the mechanical performance and the influence of the size effect and the strain rate.