Time integration of a model for martensite detwinning and reorientation under nonproportional loading using Lagrange multipliers

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:49

Article

Zaki, Wael

关键词: Shape memory alloys;    Nonproportional loading;    Constrained optimization;    Lagrange multipliers;    Martensite reorientation;   

DOI  :  10.1016/j.ijsolstr.2012.05.038

来源: Elsevier

【 摘 要 】

The paper presents a consistent integration scheme for a model of shape memory alloys that takes into account the processes of detwinning and reorientation of martensite. Lagrange multipliers are used to account for the saturation condition on the martensitic phase, which expresses the requirement on the inelastic deformation of martensite not to exceed a material-specific value. A detailed procedure for implicit time integration of the constitutive equations is given, including a comprehensive derivation of a closed-form expression for the consistent tangent moduli. The equations are implemented into a commercial finite element software, which is used to simulate the response of martensitic SMA structures to complex loading. The results are shown to agree with experimental data taken from the literature. (C) 2012 Elsevier Ltd. All rights reserved.

【 授权许可】

Free