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The simulation of deep drawing processes and its quality is intrinsically dependent on the accuracy of the constitutive model in reproducing the mechanical behaviour of the sheet metal material. Today, the calibration of elastoplastic models – correspondent to the inverse identification of the material parameters – often uses full-field measurements, through Digital Image Correlation (DIC) techniques, to capture non-homogeneous strain fields and states, coupled with non-straightforward numerical inverse methodologies. In the last decade, new parameter identification methodologies, such as the Finite Element Model Updating (FEMU), the Constitutive Equation Gap (CEG) method, the Equilibrium Gap Method (EGM) and the Virtual Fields Method (VFM) have been developed and have proven to be effective for non-linear plasticity models. Nonetheless, the FEMU and the VFM have distinguished themselves from the others. More recently, supervised Machine Learning (ML) techniques have been also used as an inverse identification method. These artificial intelligence-based methods use large datasets of numerical tests to train an inverse model in which the input is the history of the strain field and loads during the test, and the output are directly the material parameters. The goal of this paper is to analyse, compare and discuss these inverse identification methods, with particular focus on the FEMU, VFM, and ML methodologies. A heterogeneous tensile-load test is considered to compare in detail the FEMU, VFM, and ML strategies.

Accurate numerical simulations require constitutive models capable of providing precise material data. Several calibration methodologies have been developed to improve the accuracy of constitutive models. Nevertheless, a model’s performance is always constrained by its mathematical formulation. Machine learning (ML) techniques, such as artificial neural networks (ANNs), have the potential to overcome these limitations. Nevertheless, the use of ML for material constitutive modelling is very recent and not fully explored. Difficulties related to data requirements and training are still open problems. This work explores and discusses the use of ML techniques regarding the accuracy of material constitutive models in metal plasticity, particularly contributing (i) a parameter identification inverse methodology, (ii) a constitutive model corrector, (iii) a data-driven constitutive model using empirical known concepts and (iv) a general implicit constitutive model using a data-driven learning approach. These approaches are discussed, and examples are given in the framework of non-linear elastoplasticity. To conveniently train these ML approaches, a large amount of data concerning material behaviour must be used. Therefore, non-homogeneous strain field and complex strain path tests measured with digital image correlation (DIC) techniques must be used for that purpose.

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Abstract. The training of an Artificial Neural Network (ANN) for implicit constitutive modelling mostly relies on labelled data pairs, however, some variables cannot be physically measured in real experiments. As such, the training should preferably be carried out indirectly, making use of experimentally measurable variables. The unconstrained training of an ANN’s parameters often leads to spurious responses that do not comply with the physics of the problem. Applying constraints during training ensures not only the physical meaning of the ANN predictions but also potentially increases the convergence to a global minimum, while improving the model’s performance. An ANN material model is trained using a novel indirect approach, where the local and global equilibrium conditions are ensured employing the Virtual Fields Method (VFM). An example of physical constraint is analyzed and applied during the training process.