on 08-Mar-2021 (Mon)

Apart from ANN constitutive models, there exist other strategies which smartly employ data directly into a numerical model. These so-called ’data-driven’ techniques aim to improve the efficiency and/or accuracy of numerical computational procedures. A well-written overview to data-driven mechanics is presented by Kirchdoerfer and Ortiz [46]. Herein, an alternative to traditional (empirical) material law modelling is introduced and pre- sented. Instead, experimental material data, constraints and conservation laws are directly used to find an equilibrium material response. This approach directly employs material test data and finds the material equilibrium based on an energy minimisation formulation. It is shown that the data-driven approach converges to the classical approach when the latter is based on a high- fidelity data-set. It is proven that currently unmodelled materials or materials with highly complex behaviour may be modelled directly by the presented method.

The training process of an ANN is based on a so-called ’labeled’ data set, which consists of input data of which the corresponding result (output) is known. It can be generated through experiments, numerical simulations or another means. A data set is fit for training when it has sufficient data points, covers a domain that matches the application of the ANN and consists of all relevant inputs on which the output depends. The training process is an optimisation problem that minimises the cost function within a given domain. Thus, the network’s optimisation parameters are adjusted by an optimisation algorithm. A popular method specifically suited for ANNs is the gradient-descent based backpropagation algorithm, which relies on the availability of an analytical derivative of the cost function with respect to each parameter to determine the optimal ’step’ direction. This approach is only reliable for convex cost functions however, whereas non-convex problems require a more costly and complex alternative such as a genetic algorithm.

In order to construct an accurate material model, the ANNs from literature are sometimes trained with an autoprogressive training algorithm. This type of training features an adaptive ANN architecture as there are currently no guidelines concerning the choice of hyperparameters (such as network dimensions).