Damage-Free Cyclic Loading of Rock Salt: Experiments and Constitutive Modeling
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Powder metallurgy hot isostatic pressing (PM-HIP) is an advanced manufacturing process that can efficiently produce near net shape parts with high material utilization and uniform microstructures. While the PM-HIP process is used frequently to produce small-scale components, its application to large-scale components is still limited due to inadequate understanding of its complex processes that cause unpredictable post-HIP shape distortions. A computational model can be a cost-effective alternative to exhaustive experimentation required to understand the PM-HIP process fully. Therefore, we present a comparison of plastic and visco-plastic models that are frequently used to model the PM-HIP process. We show that the predictions of powder densification behavior and shape distortions obtained from both the models are similar under most conditions and agree well with experimental observations.
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The evaluation of constitutive models, especially for high-risk and high-regret engineering applications, requires efficient and rigorous third-party calibration, validation and falsification. While there are numerous efforts to develop paradigms and standard procedures to validate models, difficulties may arise due to the sequential, manual, and often biased nature of the commonly adopted calibration and validation processes, thus slowing down data collections, hampering the progress towards discovering new physics, increasing expenses and possibly leading to misinterpretations of the credibility and application ranges of proposed models. This work attempts to introduce concepts from game theory and machine learning techniques to overcome many of these existing difficulties. Here, we introduce an automated meta-modeling game where two competing AI agents systematically generate experimental data to calibrate a given constitutive model and to explore its weakness such that the experiment design and model robustness can be improved through competitions. The two agents automatically search for the Nash equilibrium of the meta-modeling game in an adversarial reinforcement learning framework without human intervention. In particular, a protagonist agent seeks to find the more effective ways to generate data for model calibrations, while an adversary agent tries to find the most devastating test scenarios that expose the weaknesses of the constitutive model calibrated by the protagonist. By capturing all possible design options of the laboratory experiments into a single decision tree, we recast the design of experiments as a game of combinatorial moves that can be resolved through deep reinforcement learning by the two competing players. Our adversarial framework emulates idealized scientific collaborations and competitions among researchers to achieve a better understanding of the application range of the learned material laws and prevent misinterpretations caused by conventional AI-based third-party validation. Numerical examples are given to demonstrate the wide applicability of the proposed meta-modeling game with adversarial attacks on both human-crafted constitutive models and machine learning models.
This study presents an AI-based constitutive modelling framework wherein the prediction model directly learns from triaxial testing data by combining discrete element modelling (DEM) and deep learning. A constitutive learning strategy is proposed based on the generally accepted frame-indifference assumption in constructing material constitutive models. The low-dimensional principal stress-strain sequence pairs, measured from discrete element modelling of triaxial testing, are used to train recurrent neural networks, and then the predicted principal stress sequence is augmented to other high-dimensional or general stress tensor via coordinate transformation. Through detailed hyperparameter investigations, it is found that long short-term memory (LSTM) and gated recurrent unit (GRU) networks have similar prediction performance in constitutive modelling problems, and both satisfactorily predict the stress responses of granular materials subjected to a given unseen strain path. Furthermore, the unique merits and ongoing challenges of data-driven constitutive models for granular materials are discussed.
High temperature design requires accurate constitutive models to describe material inelastic deformation and failure behavior. Oftentimes, calibrating accurate models devolves into the problem of fitting the model parameters against experimental test data. Here, we present the pyopmat package, an open source framework for calibrating constitutive models against experiment data subjected to various loading conditions using machine learning techniques. The package calculates the exact gradient of the model response with respect to the parameters using a combination of automatic differentiation and the adjoint method. Given this exact gradient, we compare the performance of several gradient-based optimization techniques in fitting realistic constitutive models against data. Here, we demonstrate the efficiency and accuracy of our package through example problems using both synthetic data, generated using known parameter sets, under monotonic and cyclic loading conditions and also with an example applying the techniques developed here to actual high temperature creep-fatigue test data.