黏弹性理论中广义Maxwell模型的教学法及其在非晶态固体中的应用  

TEACHING METHOD OF GENERALIZED MAXWELL MODEL IN VISCOELASTIC THEORY AND ITS APPLICATION IN AMORPHOUS SOLIDS

作　　者：乔吉超 邢光辉 郝奇 QIAO Jichao;XING Guanghui;HAO Qi(School of Mechanics and Civil Engineering&Architecture,Northwestern Polytechnical University,Xi'an 710072,China)

机构地区：[1]西北工业大学力学与土木建筑学院,西安710072

出　　处：《力学与实践》2023年第6期1403-1408,共6页Mechanics in Engineering

基　　金：国家自然科学基金项目(51971178和52271153);陕西省杰出青年基金项目(2021JC-12);2023年度西北工业大学本科专业建设项目资助(KCJS23GX07)。

摘　　要：黏弹性力学是固体力学研究的重要组成部分,如何开展黏弹性力学教学对于学生理解相关知识至关重要。本文以黏弹性力学最为经典的Maxwell模型为例展示整个教学过程:首先从基本黏弹性元件出发,推导Maxwell模型及其广义表达式,然后结合非晶固体应力松弛实验曲线,从变形单元激活特征时间角度出发,将经典Maxwell模型应用于非晶固体变形,结合实际案例和计算练习来加深学生对于该模型的理解和应用。相比于传统黏弹性力学课程,本文考虑广义Maxwell模型中多个并联单元特征时间在对数时间尺度的Gauss分布形式,这对于非晶态固体的变形研究以及黏弹性理论的课程教学过程具有重要借鉴价值。Viscoelastic mechanics is an important research field in solid mechanics.The proper teaching of viscoelastic mechanics is crucial for students to grasp the related concepts.This paper uses the basic and classical Maxwell model in viscoelastic mechanics to illustrate the teaching process.Initially,the Maxwell model and its generalized expressions are introduced and derived from the basic viscoelastic components.Then,the classical Maxwell model is applied to the deformation of disordered solids by considering the characteristic time of activation of the deformation unit from the perspective of stress relaxation experimental curves of amorphous alloys.To deepen students’understanding and application of the model,the classical Maxwell model is further applied to practical cases and calculation exercises.This paper considers the Gauss distribution of the characteristic time of multiple parallel units in the generalized Maxwell model on a logarithmic time scale,which is highly valuable for studying the deformation of amorphous solids and teaching viscoelasticity theory.Compared to traditional viscoelasticity courses,this approach offers a comprehensive and practical learning experience for students.

关 键 词：黏弹性理论 Maxwell模型 应力松弛 课程教学 

分 类 号：O345[理学—固体力学]