Influence of nonlinear spatial distribution of stress and strain on solving problems of solid mechanics  

作　　者：Chunyu ZHANG Biao WANG 

机构地区：[1]Sino-French institute of nuclear engineering and technology,Sun Yat-Sen University Zhuhai,Guangzhou 519082,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2022年第9期1355-1366,共12页应用数学和力学（英文版）

基　　金：supported by the Original Exploration Project of Natural Science Foundation of China(No.12150001);the National Key Research and Development Program of China(No.2018YFB1900400);the National Natural Science Foundation of China(No.11832019);the Nuclear Power Technology Innovation Center of Science Technology and Industry for National Defense of China(No.HDLCXZX-2021-HD-035)。

摘　　要：The stress and the strain should be defined as statistical variables averaged over the representative volume elements for any real continuum system.It is shown that their nonlinear spatial distributions undermine the classical framework of solid mechanics and may cause non-ignorable errors to the solutions.With considering the high-order gradients of the stress and the strain,a two-step solution scheme is proposed to compensate for the influence.Through a revisit to three simple but typical problems,i.e.,the hole size-dependence of the fracture strength of perforated plates,the indentation depth-dependence of the measured elastic modulus by micro-indentation tests,and the tensile necking of metallic materials as well as hyperelastic materials,the effect of the nonlinear spatial distribution of stress and strain on solving these problems is illustrated.The observed size effect and the instability of deformation can be quantitatively explained if the effect is properly considered by the proposed method.

关 键 词：nonlinear spatial distribution homogenization error high-order gradient size effect 

分 类 号：O302[理学—力学] O343.1O343.4