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.

中文翻译：

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用于求解非关联 Drucker-Prager 弹塑性本构模型的物理注入深度神经网络

在目前的工作中，首次引入了一种基于物理知识的深度学习本构建模方法，来解决由线性各向同性硬化规则控制的非关联德鲁克-普拉格弹塑性固体。由于缺乏先验物理信息，用于表示复杂且高度非线性弹塑性本构响应的纯粹数据驱动的替代建模方法无法进行准确的预测。为了缓解这一问题，我们利用先前的物理驱动优化程序设计了一种有效的物理约束训练方法。它是通过制定高度物理增强的多目标损失函数来实现的，其中包括弹塑性本构关系、德鲁克-普拉格屈服准则、非关联流动规则、库恩-塔克一致性条件和各种边界条件。利用多个密集连接的独立前馈深度神经网络，在数据驱动的损失函数中提供高保真数值解，该模型通过最小化所提出的损失函数来获得准确的弹塑性解。通过准确解决基准问题，证明了该方法的强度和鲁棒性，其中塑性变形的各向同性浅层在平面应变 Drucker-Prager 屈服条件下受到压缩压力。为了优化模型的性能和可训练性，对网络架构和不同程度的数据驱动估计进行的广泛实验揭示了弹塑性解决方案准确性的显着改进，特别是表现出尖锐或非常局部化特征的弹塑性解决方案。此外，我们提出了一种基于迁移学习的 PINN 建模方法，阐明了预测不同组应用应力和材料参数的解决方案的可能性。该框架需要显着减少的训练数据，可以通过展示关键损失分量的快速收敛来同时提高解决方案的准确性和训练的适应性。当前的研究强调了一种新颖的基于物理的深度学习方法的系统开发，该方法本质上非常通用，但具有鲁棒性和高度物理增强性，可用于已知知识的可转移性，从而大大加速收敛，并提高预测非非非复杂性的准确描述的准确性。连续介质力学体系中的关联弹塑性解。