Constitutive Artificial Neural Networks (CANNs)
Numerous advances in experimental mechanics, imaging technology, and process data acquisition have led to the fact that today we have data available in a size and quantity that would have been considered unthinkable just a few decades ago. To which extent this data can be used to model the mechanical behavior of materials is one of the central questions we deal with within our research group.
As part of our research, we have therefore developed constitutive artificial neural networks (CANNs), a new type of machine learning architecture for the data-driven modeling of the mechanical behavior of materials (see Figure 1). CANNs combine the theoretical foundations of classical materials theory with machine learning algorithms, in particular artificial neural networks. The combination of these two modeling approaches has several advantages. While in the past a lot of effort has been made to functionally describe the experimentally determined stress-strain relationship, CANNs now take on this tedious task. Furthermore, in addition to this stress-strain data, any other relevant information can be used. Parameters of the manufacturing process, e.g. temperature or pressure, or microstructural descriptors of composite materials, e.g. inclusion size or volume fraction, can represent such relevant information. Since there are in principle no restrictions for these descriptors, they can also extend over several length scales, so that CANNs also cover classic multi-scale modeling. Besides, CANNs can be implemented in standard simulation software, e.g. finite element simulations, with little effort. Due to the theoretical foundation of CANNS, the amount of training data required for complex and anisotropic materials is lower compared to purely data-driven modeling approaches (see Figure 2). Another feature of CANNs is their ability to extrapolate the material behavior beyond the training data into parameter spaces for which no data is available.
A detailed description of the CANNs can be found in the journal article [1]. The associated source code for the CANN architecture and the data sets used in [1] are freely accessible on github.com/ConstitutiveANN/CANN.
Figure 2: With just a few data points, 15 per loading protocol (uniaxial tension, equi-biaxial tension, pure shear), the relative error in the strain energy (left) and nominal stress (right) is everywhere in the single-digit percentage range, mostly even below 1%. The error plots make it clear that CANNs not only show good generalizability but can also extrapolate well beyond the training data (Figures adopted from Figure 3c and 3d, Linka et. al. (2021) [1]).
Literature:
[1] Linka K, Hillgärtner M, Abdolazizi KP, Aydin RC, Itskov M, Cyron CJ (2021) Constitutive artificial neural networks: a fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics, Volume 437. (DOI= 10.1016/j.jcp.2020.110010)