Physics-infused deep neural network for solution of non-associative Drucker–Prager elastoplastic constitutive model

• Published in: Journal of the mechanics and physics of solids Vol. 185; p. 105570
• Main Authors: Roy, Arunabha M., Guha, Suman, Sundararaghavan, Veera, Arróyave, Raymundo
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.04.2024
• Subjects: Data-driven approach; Deep Learning; Drucker–Prager yield criterion; Non-associative flow rule; Physics-augmented multi-objective loss functional; Physics-infused neural networks; Drucker–Prager yield criterion; Physics-infused neural networks; Data-driven approach; Non-associative flow rule; Physics-augmented multi-objective loss functional; Deep Learning
• ISSN: 0022-5096
• DOI: 10.1016/j.jmps.2024.105570

In the present work, a physics-informed deep learning-based constitutive modeling approach has been introduced, for the first time, to solve non-associative Drucker–Prager elastoplastic solid governed by a linear isotropic hardening rule. A purely data-driven surrogate modeling approach for representing complex and highly non-linear elastoplastic constitutive response prevents accurate predictions due to the absence of prior physical information. To mitigate this, we design an efficient physics-constrained training approach leveraging prior physics-driven optimization procedures. It has been achieved by formulating a highly physics-augmented multi-objective loss function that includes elastoplastic constitutive relations, Drucker–Prager yield criterion, non-associative flow rule, Kuhn–Tucker consistency conditions, and various boundary conditions. Utilizing multiple densely connected independent feed-forward deep neural networks fed with high-fidelity numerical solutions in a data-driven loss function, the model obtains the accurate elastoplastic solution by minimizing the proposed loss function. The strength and robustness of the approach have been demonstrated by accurately solving the benchmark problem where a plastically deformed isotropic shallow stratum has been subjected to compressive pressure under plane strain Drucker–Prager yield condition. To optimize the performance and trainability of the model, extensive experiments on network architecture and various degrees of data-driven estimate shed light on significant improvement in terms of the accuracy of the elastoplastic solution, particularly, that exhibits sharp, or very localized features. Moreover, we propose a transfer learning-based PINNs modeling approach that elucidates the possibility of predicting solutions for different sets of applied stress and material parameters. Requiring significantly less training data, the framework can simultaneously enhance the accuracy of the solution and adaptability of training by demonstrating rapid convergence in critical loss components. The current study highlights a systematic development of a novel physics-informed deep learning approach which is quite generic in nature, yet robust and highly physics-augmented for transferability of known knowledge for vastly accelerated convergence with improved accuracy of predicting an accurate description of non-associative elastoplastic solution in the regime of continuum mechanics. [Display omitted] •A robust data-driven deep learning-based PINNs computational framework has been developed for solving Drucker–Prager elastoplastic solid.•A novel multi-objective loss functional is proposed, when minimized, results in accurate elastoplastic solution.•The strength of the approach have been demonstrated by solving benchmark problems.•Current study illustrates the applicability of using the transfer learning (TL)-based approach in reducing training time, simultaneously improving accuracy.•It combines the benefits of the available physical information with a data-driven construction of lightweight, yet accurate neural networks.