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Explicit finite element implementation of an improved three dimensional constitutive model for shape memory alloys

Stebner, A. P. and Brinson, L. C. (2013) Explicit finite element implementation of an improved three dimensional constitutive model for shape memory alloys. Computer Methods in Applied Mechanics and Engineering, 257 . pp. 17-35. ISSN 0045-7825. doi:10.1016/j.cma.2012.12.021. https://resolver.caltech.edu/CaltechAUTHORS:20130614-145401440

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Abstract

This article documents a new implementation of a three dimensional constitutive model that describes evolution of elastic and transformation strains during thermo-mechanical shape memory alloy loading events assuming a symmetric, isotropic material response. In achieving this implementation, improvements were made to the original formulation of the constitutive model. These improvements allow for robust three-dimensional calculations over a greater range of thermo-mechanical loadings. Furthermore, a new explicit scheme for solving the model equations was derived. This scheme removed the need for user calibration of the numerical integration parameters and greatly reduced the sensitivity of this explicit finite element implementation of a rate independent model to mass scaling. Studies were performed that quantified both simulation times and convergence of the new scheme along with the original solution scheme of Panico and Brinson for single element and multi-element simulations. The effectiveness of the new scheme is apparent in 6 and 30 times reductions in computation expense for selected single and multi element simulations, respectively.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.cma.2012.12.021DOIUNSPECIFIED
http://www.sciencedirect.com/science/article/pii/S0045782513000042PublisherUNSPECIFIED
Additional Information:© 2013 Elsevier B.V. Received 19 September 2012. Received in revised form 20 November 2012. Accepted 27 December 2012. Available online 16 January 2013. A.S. acknowledges funding through fellowships from the Toshio Mura Endowment, Predictive Science and Engineering Design Cluster at Northwestern (PSED), Initiative for Sustainability and Energy at Northwestern (ISEN). A.S. and C.B. acknowledge the support of the Army Research Office, Grant # W911NF-12-1-0013/P00002. Catherine Tupper is thanked for creating the model of the beam with the hole as well as many fruitful discussions and testing development versions of the VUMAT. Pingping Zhu is thanked for continuing validation efforts for the VUMAT.
Funders:
Funding AgencyGrant Number
Toshio Mura Endowment fellowshipsUNSPECIFIED
Northwestern Predictive Science and Engineering Design Cluster (PSED)UNSPECIFIED
Northwestern Initiative for Sustainability and Energy (ISEN)UNSPECIFIED
Army Research Office (ARO)W911NF-12-1-0013/P00002
Subject Keywords:Shape memory alloy; Constitutive model; Numerical implementation; Phase transformation
DOI:10.1016/j.cma.2012.12.021
Record Number:CaltechAUTHORS:20130614-145401440
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130614-145401440
Official Citation:A.P. Stebner, L.C. Brinson, Explicit finite element implementation of an improved three dimensional constitutive model for shape memory alloys, Computer Methods in Applied Mechanics and Engineering, Volume 257, 15 April 2013, Pages 17-35, ISSN 0045-7825, 10.1016/j.cma.2012.12.021. (http://www.sciencedirect.com/science/article/pii/S0045782513000042)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38949
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:18 Jun 2013 15:46
Last Modified:09 Nov 2021 23:41

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