Thermodynamics-based Artificial Neural Networks for constitutive modeling
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Abstract
Machine Learning methods and, in particular, Artificial Neural Networks\n(ANNs) have demonstrated promising capabilities in material constitutive\nmodeling. One of the main drawbacks of such approaches is the lack of a\nrigorous frame based on the laws of physics. This may render physically\ninconsistent the predictions of a trained network, which can be even dangerous\nfor real applications.\n Here we propose a new class of data-driven, physics-based, neural networks\nfor constitutive modeling of strain rate independent processes at the material\npoint level, which we define as Thermodynamics-based Artificial Neural Networks\n(TANNs). The two basic principles of thermodynamics are encoded in the\nnetwork's architecture by taking advantage of automatic differentiation to\ncompute the numerical derivatives of a network with respect to its inputs. In\nthis way, derivatives of the free-energy, the dissipation rate and their\nrelation with the stress and internal state variables are hardwired in the\nnetwork. Consequently, our network does not have to identify the underlying\npattern of thermodynamic laws during training, reducing the need of large\ndata-sets. Moreover the training is more efficient and robust, and the\npredictions more accurate. Finally and more important, the predictions remain\nthermodynamically consistent, even for unseen data. Based on these features,\nTANNs are a starting point for data-driven, physics-based constitutive modeling\nwith neural networks.\n We demonstrate the wide applicability of TANNs for modeling elasto-plastic\nmaterials, with strain hardening and strain softening. Detailed comparisons\nshow that the predictions of TANNs outperform those of standard ANNs. TANNs '\narchitecture is general, enabling applications to materials with different or\nmore complex behavior, without any modification.\n