基于SIR模型的工程材料统一单轴本构关系研究  

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

作　　者：何浩祥[1] 闫维明[1] 李晓飞[2] 

机构地区：[1]北京工业大学工程抗震与结构诊治北京市重点实验室,北京100022 [2]大连海事大学道路与桥梁工程研究所,大连116026

出　　处：《计算力学学报》2014年第1期84-90,共7页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(51108009;50878010);高等学校博士学科点专项科研基金(20111103120022)资助项目

摘　　要：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。The uniaxial stress-strain curve of engineering but the research on the uniform constitutive relation for material reflects the basic constitutive relation, 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 repre- sented 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 solu- tion of the SIR model can fully and accurately show the change of the mechanical performance and the in- fluence of the size effect and the strain rate.

关 键 词：本构关系 尺寸效应 应变率 同伦分析方法 传染病模型 

分 类 号：TU973[建筑科学—结构工程]