## Mathematical modelling of pseudoelastic SMA material

### Wiesław Grzesikiewicz , Andrzej Wakulicz , Artur Zbiciak

#### Abstract

The paper presents a procedure for the formulation of constitutive equations for rate-independent pseudoelastic SMA material models. The procedure applies a rheological scheme representing mechanical properties of the material. An additive decomposition of strains into two parts is proposed. The first part describes strains of a perfectly elastic body while the second part may be represented by a combination of a rigid perfectly elastic body and a rigid perfectly plastic body. It is demonstrated that the key problem of formulation of constitutive relationships is to derive the 1st order differential equation with respect to the tensor describing the second part of the strain field. This equation may be obtained in explicit form starting from the variational inequalities defining non-elastic parts of rheological model. The uniqueness of the obtained differential equation has been proved. A numerical implementation of the constitutive relationships of SMA material was done through the user subroutine module VUMAT within the FE commercial code ABAQUS/Explicit. As an example we analyzed the problem of vibration of a simple 3D structure made of SMA.
 Author Wiesław Grzesikiewicz (FACME / IAE) Wiesław Grzesikiewicz,, - Institute of Automotive Engineering , Andrzej Wakulicz - [Institute of Mathematics (IM PAN) [Polish Academy of Sciences (PAN)]] Andrzej Wakulicz,, - - Instytut Matematyczny Polskiej Akademii Nauk , Artur Zbiciak (FCE / IRB) Artur Zbiciak,, - The Institute of Roads and Bridges Journal series International Journal of Non-Linear Mechanics, ISSN 0020-7462, (A 35 pkt) Issue year 2011 Vol 46 No 6 Pages 870-876 Publication size in sheets 0.5 Keywords in Polish FEM, SMA Keywords in English FEM, Pseudoelasticity, SMA ASJC Classification 2604 Applied Mathematics; 2210 Mechanical Engineering; 2211 Mechanics of Materials DOI DOI:10.1016/j.ijnonlinmec.2011.03.013 URL http://www.sciencedirect.com/science/article/pii/S0020746211000370 Language en angielski Score (nominal) 35 Score source journalList Publication indicators Scopus Citations = 6; WoS Citations = 3; Scopus SNIP (Source Normalised Impact per Paper): 2011 = 1.602; WoS Impact Factor: 2011 = 1.209 (2) - 2011=1.543 (5) Citation count*
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