Comments to the paper ‘‘Differential and integrated form consistency　in 1-D phenomenological models for shape memory alloy constitutive　behavior” by V.R. Buravalla and A. Khandelwal [Int. J. Solids and Struct.44 (2007) 4369–4381]

摘要

In summary, for one-dimensional SMA modeling, an inconsistency was found by Buravalla and Khandelwal (2007) in the differential form of the original Brinson model of 1993. While we are grateful for their diligence, their paper also contained inconsistencies. Thus we use this opportunity to present complete and consistent derivations of both integrated and differential forms of the Brinson 1D SMA constitutive model in this response. We wish to stress that all previous and existing applications of the integrated form of the Brinson constitutive law have been and remain correct. For future work with one-dimensional modeling, the constitutive law in integrated form (optimally, the ollapsed form in Eq. (30)) or the differential form (Eq. (28) or (29)), can be invoked in conjunction with the appropriate transformation kinetics for evaluation of ns and nT. Robust kinetics, significantly improved from the original paper, are discussed in Bekker and Brinson (1998) and Gao et al. (2007).