应变梯度形变理论的无网格数值方法研究  

Study on meshless method for strain gradient deformation theory

作　　者：李雷[1,2] 周毅英[1] 谢水生[2] 贺睿[1] 

机构地区：[1]河南理工大学材料科学与工程学院,焦作454000 [2]北京有色金属研究总院有色金属材料制备加工国家重点实验室,北京100088

出　　处：《塑性工程学报》2009年第4期152-156,共5页Journal of Plasticity Engineering

基　　金：河南省教育厅基金资助项目(2008A460009);河南理工大学博士基金;青年骨干教师基金资助项目(648524;649027)

摘　　要：金属材料的微塑性成形过程中,会体现出强烈的尺度效应,应变梯度形变理论能够预测材料尺度效应,但该理论的数值实施需要实现位移函数C1连续,这对传统有限元方法是巨大的挑战。新兴的无网格法能够实现位移函数的高阶导数连续,该文导出了应变梯度理论的无网格数值实施方法,采用发展的数值方法分析了超薄梁弯曲成形过程中的尺度效应,数值结果与理论解相吻合。Strong size effect will occur in the metal micro-forming process. Strain gradient deformation theory can predict such size effects. However, C^1 continuity is required for the displacement functions in the numerical implementation of this theory,which is a great challenge for the traditional finite element method. The rising numerical method, namely meshless method, can realize high order of derivatives to be continuous. The meshless implementation formulation of strain gradient deformation theory is developed. The size effects of the ultra-thin beam＇s bending are studied with the developed meshless method, and the numerical results agree well with the analytical solutions.

关 键 词：微成形 尺度效应 应变梯度 无网格方法 

分 类 号：TG115[金属学及工艺—物理冶金]