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Numerical simulation of thermomechanical behaviours of shape memory alloys via a non‐linear mesh‐free Galerkin formulation
Author(s) -
Liew K. M.,
Ren J.,
Reddy J. N.
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1320
Subject(s) - shape memory alloy , constitutive equation , computer simulation , galerkin method , displacement (psychology) , transformation (genetics) , deformation (meteorology) , stress (linguistics) , computer science , finite element method , mathematics , structural engineering , materials science , engineering , simulation , composite material , psychology , biochemistry , chemistry , artificial intelligence , psychotherapist , gene , linguistics , philosophy
Abstract A new computational approach is developed based on the mesh‐free method for the numerical simulation of shape memory alloys. A thermomechanical constitutive model is used to describe the complex material response. The incremental displacement‐based mesh‐free formulation is constructed in a total Lagrangian description by employing the moving least square shape function and rate form of the shape memory alloy constitutive model in the variational equations. This mesh‐free formulation is not only applicable to large deformation problems, but also accounts for both stress and thermally induced phase transformation. Moreover, the newly developed mesh‐free codes can deal with complex loading paths and multiple temperature cycles in numerical simulation. The performance of the proposed mesh‐free scheme for the simulation of shape memory alloys is demonstrated in several numerical examples. Copyright © 2005 John Wiley & Sons, Ltd.