基于有理插值方法模拟SMAs循环加载下的变形行为  

Deformation Behavior Modeling of SMAs Under Cyclic Loading Based on Rational Interpolation

作　　者：王晓明 肖衡 WANG Xiaoming;XIAO Heng(Institute of Applied Mechanics,Ningbo Polytechnic,Ningbo,Zhejiang 315000,P.R.China;School of Mechanics and Construction Engineering,Jinan University,Guangzhou 510632,P.R.China)

机构地区：[1]宁波职业技术学院应用力学研究所,浙江宁波315000 [2]暨南大学力学和建筑工程学院,广州510632

出　　处：《应用数学和力学》2023年第6期694-707,共14页Applied Mathematics and Mechanics

基　　金：浙江省教育厅科研项目(Y202147389,FG2022042);国家自然科学基金项目(1217020816)。

摘　　要：提出了一个有限弹塑性模型,用来模拟形状记忆合金(shape memory alloys,SMAs)在循环荷载下的变形行为.首先,通过分析上下屈服阶段形函数的特点,利用有理插值方法给出循环荷载下的应力-应变形函数显式表达,可以精确匹配任意形状的实验数据;其次,基于对数客观率,构建了有限弹塑性J2流模型,耦合了屈服中心的移动和屈服面的增大;再次,从单轴情况出发,推导得到了单个循环下的三个硬化函数显式表达,再引入局部因子和多轴扩展不变量,构造了光滑统一且多轴有效的硬化函数;最后,将模型得到的结果与经典实验结果比较,证明了新方法的有效性.该文创新点如下:第一,通过改进传统的背应力演化方程,使得新模型产生强烈的Bauschinger效应,从而使新方法具备模拟SMAs特殊变形行为的能力;第二,新的光滑统一硬化函数在单个循环下会自动退化,得到精确符合实验数据的结果;第三,利用本构方程推导得到有效塑性功演化规律,而有理插值得到的形函数中包含依赖有效塑性功的参数,给出这些参数方程以后使得模型具备了预测变形的能力.A finite elastoplasticity model was proposed to simulate deformation behaviors of SMAs under cyclic loading.First,the explicit formulations of shape functions were given with the rational interpolation method to exactly match any given experimental data.Second,a finite elastoplasticity J2 flow model based on the logarith⁃mic objective rate was built to couple the moving of the yielding center and the expanding of the yielding sur⁃face.Third,3 explicit hardening functions under the single loading cycle were deduced in the uniaxial case,to construct the smooth,unified and multiaxial hardening function through introduction of the local factor and the multiaxial extended invariant.Finally,the model results were compared with the classical test data to prove the effectiveness of the new model.The research results show that,the new model can produce intense Bausch⁃inger effects and simulate the complex deformation of SMAs through improvement of the evolution equation of the back stress.The new smooth unified hardening function can automatically degenerate under the single load⁃ing cycle to give results exactly matching the test data.The effective plastic work evolution law deduced with the constitutional equation,and the parameter equations dependent on the effective plastic work contained in the shape functions through rational interpolation,enable the proposed model to predict deformations well.

关 键 词：J2流模型 形状记忆合金 对数客观率 屈服 硬化函数 形函数 

分 类 号：O343[理学—固体力学] O345[理学—力学]