
Continuum Thermomechanics of Shape Memory Alloy Phase Transformation for Bodies Undergoing Thermally Induced Large Deformations
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The present paper adresses the consistent continuum mechanical modeling of thermally induced phase transformation in shape memory alloys [Lagoudas 2007]. Starting in within the two-way shape memory process in the detwinned martensite phase, storing the initially introduced deformation, the heating of the material is activating the transformation of the shape memory alloy into the austenitic phase. Since the phase transformation is activated by the certain austenitic start temperature and latent heat of the phase transformation is huge in comparison with the specific heat of the material, the temperature field and, consequently, also the phase transformation field is pronouncedly inhomogeneous across the test specimen. As a consequence of this, the large transformation strains are also inhomogeneously distributed over the material sample. Beside the large deformation of the test specimen this causes also considerable internal stresses. For this reason, the authors assume that the temperature-strain-stress curves measured on test specimens represent the homogenization of these complex thermomechanical interactions in the body and not the processes on the material point. To further investigate this issue scientifically, a consistent continuum thermomechanical model with large deformations, extending the models by [Maugin 2003, Eringen & Maugin 1990], is presented, which is able to describe the shape memory phase transformation at the material point. In perspective, this model will be used in the context of the finite element method and time integration of the two-way effect. Consequently, a realistic simulation of the shape memory processes at material point and component levels can be expected.