Measurement of length-scale and solution of cantilever beam in couple stress elasto-plasticity  

作　　者：Bin Ji Wanji Chen Jie Zhao 

机构地区：[1]State Key Laboratory for Structural Analysis of Industrial Equipment, Dalian University of Technology, 116023 Dalian, China [2]Department of Aeronautics and Space Navigation, Shenyang Institute of Aeronautical Engineering, Daoyi South Street 37, 110136 Shenyang, Liaoning, China

出　　处：《Acta Mechanica Sinica》2009年第3期381-387,共7页力学学报（英文版）

基　　金：the National Natural Science Foundation of China (50479058, 10672032)

摘　　要：Owing to the absence of proper analytical solution of cantilever beams for couple stress/strain gradient elasto-plastic theory, experimental studies of the cantilever beam in the micro-scale are not suitable for the determination of material length-scale. Based on the couple stress elasto-plasticity, an analytical solution of thin cantilever beams is firstly presented, and the solution can be regarded as an extension of the elastic and rigid-plastic solutions of pure bending beam. A comparison with numerical results shows that the current analytical solution is reliable for the case of σ0 〈〈 H 〈〈 E, where σ0 is the initial yield strength, H is the hardening modulus and E is the elastic modulus. Fortunately, the above mentioned condition can be satisfied for many metal materials, and thus the solution can be used to determine the material length-scale of micro-structures in conjunction with the experiment of cantilever beams in the micro-scale.Owing to the absence of proper analytical solution of cantilever beams for couple stress/strain gradient elasto-plastic theory, experimental studies of the cantilever beam in the micro-scale are not suitable for the determination of material length-scale. Based on the couple stress elasto-plasticity, an analytical solution of thin cantilever beams is firstly presented, and the solution can be regarded as an extension of the elastic and rigid-plastic solutions of pure bending beam. A comparison with numerical results shows that the current analytical solution is reliable for the case of σ0 〈〈 H 〈〈 E, where σ0 is the initial yield strength, H is the hardening modulus and E is the elastic modulus. Fortunately, the above mentioned condition can be satisfied for many metal materials, and thus the solution can be used to determine the material length-scale of micro-structures in conjunction with the experiment of cantilever beams in the micro-scale.

关 键 词：Material length-scale Couple stress elasto-plasticity Analytical solution Cantilever beam 

分 类 号：TU528.31[建筑科学—建筑技术科学] O344.3[理学—固体力学]