Three dimensional large deformation analysis of phase transformation in shape memory alloys

• Published in: Applied mathematics and mechanics Vol. 31; no. 10; pp. 1261 - 1272
• Main Author: 夏开明 潘同燕 刘山洪
• Format: Journal Article
• Language: English
• Published: Heidelberg Shanghai University Press 01.10.2010; Division of Engineering, Colorado School of Mines, Golden 80401, USA%Department of Civil and Environmental Engineering, Virginia Tech,Blackburg, VA 24061, USA%Department of Bridge Engineering, Chongqing Jiaotong University,Chongqing 400074, P. R. China
• Subjects: Applications of Mathematics; Classical Mechanics; Deformation; Fluid- and Aerodynamics; Hysteresis loops; Martensite; Martensitic transformations; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Partial Differential Equations; Shape memory alloys; Stresses; Superelasticity; 偏应力张量; 大变形分析; 奥氏体相变; 形状记忆合金; 智能传感器; 智能材料; 有限元程序; shape memory alloys; finite element; phase transformation; TG113.26; superelasticity; large deformation; 74B20; O343.5
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-010-1359-7

Shape memory alloys（SMAs）have been explored as smart materials and used as dampers,actuator elements,and smart sensors.An important character of SMAs is its ability to recover all of its large deformations in mechanical loading-unloading cycles without showing permanent deformation.This paper presents a stress-induced phenomenological constitutive equation for SMAs,which can be used to describe the superelastic hysteresis loops and phase transformation between Martensite and Austenite.The Martensite fraction of SMAs is assumed to be dependent on deviatoric stress tensor.Therefore,phase transformation of SMAs is volume preserving during the phase transformation.The model is implemented in large deformation finite element code and cast in the updated Lagrangian scheme.In order to use the Cauchy stress and the linear strain in constitutive laws,a frame indifferent stress objective rate has to be used.In this paper,the Jaumann stress rate is used.Results of the numerical experiments conducted in this study show that the superelastic hysteresis loops arising with the phase transformation can be effectively captured.