Modeling large deformations of thin-walled SMA structures by shell finite elements

Porenta, Luka (author), Lavrenčič, Marko (author), Dujc, Jaka (author), Brojan, Miha (author), Tušek, Jaka (author), Brank, Boštjan (author)

Many shape memory alloy (SMA) applications, such as biomedical devices, electromechanical actuators, and elastocaloric cooling devices, are based on thin-walled flat or shell-like structures. An advanced design of such structures requires the development of an efficient and accurate numerical tool for simulations of very thin and curved SMA structures that may experience large deformations and even buckling upon thermo-mechanical loading. So far, finite element models for finite strain deformations of SMA structures have been based on 3D solid formulations, which are relatively inefficient for solving (thin) shell problems. In this paper, we present a finite element model for the analysis of shape memory alloy shells. Our model is based on a 7-parameter, large-rotation, one-director shell formulation, which takes into account a fully three-dimensional form of the constitutive equations for the isothermal transformations of isotropic superelasticity, as well as the shape-memory effect in a simplified way. In fact, we present three 4-node shell finite elements for SMAs. Two of them use the assumed natural strain concepts for the transverse shear strains, through-the-thickness normal strain, and membrane strains. The third element is a combination of the assumed natural strain and the enhanced assumed strain concepts, applied to satisfy the zero through-the-thickness-normal-stress condition for thin geometries to a high degree of accuracy. After a detailed description of the SMA finite element models for shells in the first part of the paper, numerical examples in the second part illustrate the approach. Compared to 3D solid SMA formulations, our results show excellent accuracy, even with a significantly reduced number of degrees of freedom, which consequently translates into a reduction in the computational time.

• Language: English
• Keywords: shape memory alloys, superelasticity, large strains, thin-walled structures, finite strains, seven-parameter shell model
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering; FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2021
• Number of pages: 29 str.
• Numbering: Vol. 101, art. 105897
• PID: 20.500.12556/RUL-127201
• UDC: 539.37
• ISSN on article: 1007-5704
• DOI: 10.1016/j.cnsns.2021.105897
• COBISS.SI-ID: 64322307
• Publication date in RUL: 24.05.2021

PORENTA, Luka, LAVRENČIČ, Marko, DUJC, Jaka, BROJAN, Miha, TUŠEK, Jaka and BRANK, Boštjan, 2021, Modeling large deformations of thin-walled SMA structures by shell finite elements. Communications in nonlinear science and numerical simulation [online]. 2021. Vol. 101, no. 105897. [Accessed 8 April 2025]. DOI 10.1016/j.cnsns.2021.105897. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=127201

Record is a part of a journal

• Title: Communications in nonlinear science and numerical simulation
• Shortened title: Commun. nonlinear. sci. numer. simulat.
• Publisher: Elsevier
• ISSN: 1007-5704
• COBISS.SI-ID: 1454101

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: zlitine z oblikovnim spominom, superelastičnost, velike specifične deformacije