Towards virtual forming and design: data-driven material  modelling using Machine Learning techniques and physics based constraints
Creators: name: Lourenço, Rúben
Publisher: name: Zenodo
Year: 2024
Subjects: Recurrent Neural Networks
Virtual Fields Method
Indirect training
Data driven Constitutive Models
Elastoplasticity
Physics-based Constraints

description: Finite Element Analysis (FEA) revolutionized the engineering field virtu alizing the product design to reduce the development time and costs of physical prototypes. The growing importance of FEA also increased the need for accurate material models. Although widely available in commercial FEA simulation packages, constitutive models are not ready-made solutions and their quality depends on an accurate inverse parameter identification procedure. Classical methods for material characterization and parameter identification rely on simplified experiments unable to capture complex strain paths observed in sheet metal forming processes. As such, advanced models require numerous tests to build comprehensive experimental databases, making the process costly and time-consuming. The concept of Material Testing 2.0 (MT2.0) changed the paradigm for material characterization using full-field measurements to provide extensive material behaviour data over the entire test specimen. This concept unlocked the development of new heterogeneous tests that yield richer material behaviour data, reducing the number of tests needed for model calibration. Nevertheless, despite these advancements, phenomenological constitutive models are still limited by their explicit formulation that is naturally biased due to simplifying assumptions. Along with MT2.0, Artificial Neural Networks (ANNs) can potentially lead the next paradigm shift in the field of constitutive modelling. Besides the computational efficiency and the seamless integration with FEA solvers, a key advantage of ANNs is the ability to leverage the vast datasets from full-field measurements to capture the material behaviour purely from data, avoiding postulating an explicit formulation and the need for parameter identification. Nonetheless, common approaches rely on labelled datasets based on variables that are not available experimentally. Despite the advantages, ANNs are parameter-rich models, not easily interpretable, and can be hard to configure/train due the large number of hyperparameters. The predictive accuracy is highly dependent on the quantity and quality of the training data, which may be cost-prohibitive to acquire. ANNs also often struggle to provide physically consistent solutions, unless ad ditional physics-based knowledge is encoded, especially in low-data regimes. This thesis contributes to the field of material modelling through the pro posal of a disruptive methodology coupling Recurrent Neural Networks (RNNs) with the Virtual Fields Method (VFM) to implicitly capture the unified elastoplastic behaviour of metals. The developed method relies on experimentally measurable data only, effectively harnessing the information available from full-field measurements to indirectly train the RNNs. The approach is also computationally efficient, as it does not resort to FEA for further calculations. Physical-consistency is ensured with the prediction of the material tangent stiffness and additional physics-based penalty terms. New validation procedures employing external Key Performance Indicators (KPIs) and experiments based on heterogeneous mechanical tests are also proposed to better evaluate the model predictive accuracy beyond standard error metrics. The final results show stable training dynamics and good accuracy is achievevable, dependending on the number and nature of the virtual fields. The models show, in general, a response in good agreement with the reference registering low errors compared to the overall magnitude of the stresses. When evaluated on unseen data from different heterogeneous speciments, extrapolation capacity is retained and correct force reconstruction is achieved, indicating good physical agreement. The resulting impacts from this research are (i) increased computacional efficiency gained through the coupling data-driven modelling with the VFM, (ii) the data-centric capabilities of the ANNs not only allow for improved model accuracy, leading to reliable FEA simulations, but also (iii) unlock the full potential of the information-rich datasets from full-field measurements, thus (iv) reducing the number of experimental tests needed for material characterization and (v) bypassing the need for parameter identification, (vi) leading to improved development lead-time and cost reduction of the overall process.
description: This project has received funding from the Research Fund for Coal and Steel under grant agreement No 888153.