Internet presentation of the ABAQUS-Implementation of the Müller-Achenbach-Seelecke model for shape memory alloys Dr.-Ing. Frank Richter and Dr.-Ing. Oliver Kastner Department of Materials Science, Institute for Materials, Faculty of Mechanical Engineering, Ruhr-University Bochum, D-44780 Bochum, Germany The work presented on this website is funded by DFG, grant number KA 2304/2-1. Background of the model: The Müller-Achenbach-Seelecke model ('MAS model') is a physical model for the interpretation of the thermomechanical behaviour of shape memory alloys. The physical reasoning of the model is presented here. This model was programmed as a FORTRAN code. The site features an interactive presentation where the behavior of a SMA wire under thermomechanical loading can be simulated. However, this implementation is limited to the modeling of a wire and does not incorporate thermal conduction and inner temperature gradients. The most extensive experience with the MAS model was gathered by the group headed by Prof. Stefan Seelecke, Associate Professor at North Carolina State University. Aim of the project: The current project aims at implementing the MAS model in the Finite-element-program ABAQUS. The abovementioned limitations can be overcome by incorporating this FORTRAN-program into the UMAT-interface (User material) of a Finite-Element-program like ABAQUS. This approach offers significant improvements when compared to the FORTRAN-program: · The geometry is arbitrary. · The discretization (number of nodes and elements) is arbitrary; enhancing the spatial resolution. · Full thermomechanical coupling is possible (not available for beam elements however). · Thermal conduction and temperature gradients can be resolved. · Heat exchange with the ambiance and with neighboring elements is included. Verification: The ABAQUS implementation was doublechecked against · data presented in publications directed by Prof. Seelecke · results from ideal elastic-plastic constitutive behavior; approximating the stress-strain curve for a single crystal SMA during loading with the one of an ideal elastic-plastic material. Selected results:
Click for animation	Spatial distribution of the martensite M+ phase in a cantilever under vertical loading. The straight cantilever is clamped at x=0 in the pseudoplastic state and bent by an external force acting in the y-direction at x = 0.1 m for one second and subsequently unloaded. During unloading the phase fractions remain unaltered. Plotted is the spatial distribution of the M+ phase content on and parallel to the beam axis as a function of spatial coordinates at the instant of maximum bending. The spatial resolution through the beam thickness is provided by colored section points equidistant through the thickness. The black dots on the base plane show the beam curvature. Original beam dimensions: Length = 0.1 m, thickness = 0.01 m. Reference: Fig. 3.49 in the PhD thesis Q. Li, "Modeling and Finite Element Analysis of Smart Materials", Ph.D. Thesis, North Carolina State University, USA, 2006.
Click for animation	Colored contour plot: beam bending in the +y-direction at x=l of a pseudoplastic beam initially in the martensitic state with 50% M+ and 50% M-. The contour plot shows the M+ fraction plotted on the undeformed configuration (only 30% of the beam from the clamped end are depicted). The area where the fraction deviates from 50% defines the transformation zone. Depicted is the result for the instant when the load equals 1.825 times the yield load as detected for the geometrically linear case. The black solid line indicates the analytical solution for the plastic deformation boundary obtained for an ideally elastic-plastic material. Reference: H. Parisch, Large displacement of shells including material nonlinearities, Comput. Meth. Appl. Mech. Eng., 27(2), 1981, p 183-214.
	Simulated stress/strain curve of a pseudoelastic, tetragonal polycrystalline SMA wire under uniaxial straining. Black dots: FEM based simulation, squares: reference solution (digitized data). Reference: Fig. 4.11 in the PhD thesis: O. Heintze, "A computationally efficient free energy model for shape memory alloys - experiments and theory", Ph.D. Thesis, North Carolina State University, USA, 2004

Publications:

1) F. Richter: "Finite-element-simulations of polycrystalline shape memory alloys", presentation at: ‘Smart Structures and Materials & Nondestructive Evaluation and Health Monitoring 2008', March 09-13, 2008, San Diego, USA

Copyright 2008 Society of Photo-Optical Instrumentation Engineers. This paper was published in ‘Modeling, Signal Processing, and Control for Smart Structures 2008’, edited by Douglas K. Lindner, Proc. of SPIE Vol. 6926, 69260V, (2008) and is made available as an electronic reprint with permission of SPIE. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.

2) F. Richter, O. Kastner: "Implementation of the Müller - Achenbach - Seelecke model for shape memory alloys in ABAQUS", submitted to: Journal of Materials Engineering and Performance, special issue on 'The International Conference on Shape Memory and Superelastic Technologies (SMST)', September 21-25, 2008, Stresa, Italy

Literature list to the MAS model

Last modified 15/01/2009