Data-Driven Constitutive Modeling for Solid Mechanics
Core Concepts
This review article presents a comprehensive taxonomy of data-driven techniques to discover, encode, surrogate, or emulate constitutive laws that describe the path-independent and path-dependent response of solids. It discusses the benefits and drawbacks of various interpretable and uninterpretable machine learning-based methods as well as model-free approaches.
Abstract
The review article provides an organized overview of data-driven techniques for constitutive modeling in solid mechanics. It distinguishes between machine learning-based and model-free methods, further categorizing them based on interpretability and the learning process/type of required data.
The key highlights include:
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Machine learning-based approaches are divided into interpretable and uninterpretable (black-box or grey-box) methods. Interpretable approaches aim to define an analytical expression for the constitutive law, while uninterpretable methods obtain constitutive laws where the relation between inputs and outputs cannot be physically explained.
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Model-free approaches directly inform the forward problem with a set of discrete material behavior observations, bypassing an explicit analytical link between inputs and outputs.
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The review discusses the importance of data sampling strategies, both one-shot and sequential/adaptive, for efficiently extracting relevant data to train the data-driven models.
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For path-independent constitutive laws, the review covers small-strain elasticity and finite-strain hyperelasticity, highlighting the use of machine learning techniques like neural networks, symbolic regression, and sparse regression.
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For path-dependent constitutive laws, the review examines plasticity, viscoelasticity, damage, fracture, fatigue, and multiphysics problems, discussing the challenges and opportunities in applying data-driven modeling.
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The article also touches upon aspects of verification, validation, and performance metrics for evaluating the data-driven constitutive models.
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A review on data-driven constitutive laws for solids
Stats
"Problems in solid mechanics are formulated in terms of three sets of equations: the first encodes basic conservation principles (e.g., balance of linear momentum) and governs the equilibrium of deformable bodies following the definition of a stress tensor; the second describes the kinematics of motion in terms of displacements, strains and strain rates."
"The development of full-field experimental methods such as digital image correlation (DIC), X-ray computed tomography and digital volume correlation (DVC) and advances in the related computational approaches have shifted the constitutive modeling paradigm from a limited- to a large-data regime."
Quotes
"Since the introduction of Young's modulus in the 19th century, engineers have predominantly defined constitutive laws using the so-called phenomenological approach, where experimental observations and physical requirements are distilled into a priori selected analytical ansatz relationships whose parameters are meant to be characteristic of the material."
"The great promise of fast and highly accurate predictions for mechanistic simulations as well as cost reduction in an industrial setting has led to numerous attempts to integrate a wide spectrum of these techniques in the simulation workflow and also to facilitate material innovation."
Deeper Inquiries
How can data-driven constitutive modeling approaches be extended to capture the evolution of internal state variables in path-dependent material behavior?
In path-dependent material behavior, the current state of a material point depends on its previous states, making it crucial to capture the evolution of internal state variables. Data-driven constitutive modeling approaches can be extended to incorporate this complexity by integrating historical data into the modeling process. Here are some key steps to achieve this:
Data Collection: Gather a comprehensive dataset that includes not only the current stress and strain states but also the historical evolution of these variables. This dataset should cover a wide range of loading conditions to capture the full behavior of the material.
Feature Engineering: Define relevant features that can represent the internal state variables of the material. These features could include the history of deformation, damage accumulation, or any other internal variables that influence the material response.
Model Selection: Choose a suitable machine learning model that can capture the temporal dependencies in the data. Recurrent Neural Networks (RNNs) or Long Short-Term Memory (LSTM) networks are effective for modeling sequential data and can be used to capture the evolution of internal state variables.
Training Process: Train the model on the dataset, ensuring that it learns the patterns and dependencies in the historical data to predict the material response accurately. Incorporate mechanisms for updating the internal state variables based on the previous states.
Validation and Testing: Validate the model's performance by testing it on unseen data and evaluating its ability to predict the material behavior under different loading conditions. Ensure that the model can generalize well beyond the training data.
Iterative Refinement: Continuously refine the model based on new data and insights gained from its predictions. This iterative process helps improve the model's accuracy and robustness in capturing the evolution of internal state variables.
By following these steps and leveraging advanced machine learning techniques, data-driven constitutive modeling approaches can effectively capture the evolution of internal state variables in path-dependent material behavior, enabling more accurate and reliable predictions of material responses over time.
How can the synergy between experimental mechanics and data-driven modeling be further strengthened to enable efficient material design and optimization?
The synergy between experimental mechanics and data-driven modeling plays a crucial role in advancing material design and optimization. Here are some strategies to further strengthen this synergy:
Integrated Experimental Design: Develop experimental setups that are specifically designed to generate data that can be used for training data-driven models. Ensure that the experiments cover a wide range of conditions to capture the full behavior of the material.
Data Preprocessing: Implement robust data preprocessing techniques to clean and prepare the experimental data for input into data-driven models. This step is essential for ensuring the quality and reliability of the training data.
Feature Selection: Collaborate with experimentalists to identify relevant features and parameters that can be extracted from experimental data and used as inputs for data-driven models. This collaboration helps in selecting the most informative features for accurate modeling.
Model Validation: Validate the data-driven models using experimental data to ensure that the predictions align with real-world observations. This iterative process of model validation and refinement enhances the reliability of the models for material design and optimization.
Feedback Loop: Establish a feedback loop between experimentalists and data scientists to continuously improve the models based on new experimental insights. This collaborative approach allows for the incorporation of domain knowledge into the data-driven models, leading to more accurate predictions.
Automation and Optimization: Implement automated workflows that streamline the process of data collection, model training, and optimization. By integrating experimental data with data-driven models in an automated fashion, the efficiency of material design and optimization processes can be significantly enhanced.
By strengthening the synergy between experimental mechanics and data-driven modeling through collaborative efforts, efficient material design and optimization can be achieved. This integrated approach leverages the strengths of both experimental data and machine learning techniques to drive innovation and advancements in material science.
