关于两种二阶应变梯度理论  

A STUDY ON THE TWO SECOND-ORDER STRAIN GRADIENT THEORIES

作　　者：赵杰[1] 陈万吉[1,2] 冀宾[1] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,大连116024 [2]沈阳航空工业学院飞行器结构分析研究所,沈阳130115

出　　处：《力学学报》2010年第1期138-145,共8页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金资助项目(10672032)~~

摘　　要：对常见的两种应变梯度理论进行了深入的理论分析,比较了它们在公式推导、能量表达、物理解释和应用领域方面的差异.选择钢筋拉拔弹性阶段和超薄悬臂梁受压弯曲两个典型的算例,采用可以通过C^(0-1)分片检验的18自由度应变梯度平面三角形单元和轴对称三角形单元,通过数值计算比较了两种理论在描述细观力学性能方面的差异.There are various strain gradient theories derived from phenomenal theory and nonlocal continuum mechanics.Meanwhile,there are two popular second-order strain gradient theories in which strain gradient term was introduced into the constitutive law with positive and negative signs respectively.In this paper,these two theories are discussed in the aspect of formula derivation,energy expression,and application fields.By using the 18-DOF triangle strain gradient plan element（RCT9＋RT9） and axisymmetric element（BCIZ＋ART9） which can pass C0-1 patch test,the elastic pull-out processes of the reinforced concrete bond specimen and the deformation of a cantilever beam are simulated to compare the limitation of the two theories in the analysis of microstructures.

关 键 词：应变梯度理论 材料长度参数 有限元 C1弱连续 C0-1分片检验 

分 类 号：O343.7[理学—固体力学]