ANN material modeling for SMA fibers enhanced with a physical constraint and its application to FE computations

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Abstract So-called shape memory alloys (SMAs) show intriguing multi-physical and history-dependent behavior. This includes most prominently the recovery of their initial shape after inelastic deformation, if the temperature is increased afterwards. This is known as the shape memory effect. The precise and reliable description of this and other SMA phenomena is crucial for industrial applications. Therefore, in addition to the wide range of analytical material models for SMA, we want to apply the material modeling strategy with artificial neural networks (ANN) to SMAs. We define an ANN material model in order to represent the SMA behavior with a feedforward ANN. Therefore, the correct setup of input and output vectors for rate-independent material behavior is investigated. The training is done based on synthetic data. The resulting SMA ANN material model is able to represent the SMA strain–stress behavior generally, for arbitrary strain and temperature fields. The resulting one-dimensional ANN material model is used within finite element computations. This increases the accuracy requirements due to the need for a material tangent. Therefore, we improve the performance of the ANN material model in terms of numerical stability by enforcing a material tangent related constraint during the ANN training process. In order to evaluate the performance of ANN material models during training reliably for these accuracy requirements, in depth studies on different target variables during the training process are done.

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