Data-driven and deep learning approaches have demonstrated to have the potential of replacing classical constitutive models for complex materials. Yet, the necessity of structuring constitutive models with an incremental formulation has given rise to data-driven approaches where physical quantities, e.g. deformation, blend with artificial, non-physical ones, such as the increments in deformation and time. Neural networks and the consequent constitutive models depend, thus, on the particular incremental formulation, fail in identifying material representations locally in time, and suffer from poor generalization. Herein, we propose a new approach which allows, for the first time, to decouple the material representation from the incremental formulation. Inspired by the Thermodynamics-based Artificial Neural Networks (TANN) and the theory of the internal variables, the evolution TANN (eTANN) are continuous-time and, therefore, independent of the aforementioned artificial quantities. Key feature of the proposed approach is the identification of the evolution equations of the internal variables in the form of ordinary differential equations, rather than in an incremental discrete-time form. In this work, we focus attention to juxtapose and show how the various general notions of solid mechanics are implemented in eTANN. The capabilities as well as the scalability of the proposed approach are demonstrated through several applications involving a broad spectrum of complex material behaviors, from plasticity to damage and viscosity (and combination of them). Finally, we show that the proposed approach can be used to speed-up multiscale analyses, by virtue of asymptotic homogenization. eTANN provide excellent results compared to detailed fine-scale simulations and offer the possibility not only to describe the average macroscopic material behavior, but also micromechanical, complex mechanisms.

翻译：数据驱动和深度学习方法已展现出替代复杂材料经典本构模型的潜力。然而，构建增量形式本构模型的必要性催生了数据驱动方法，其中物理量（如变形）与人工非物理量（如变形和时间增量）混杂在一起。神经网络及其产生的本构模型因此依赖于特定的增量公式，无法在时间上局部识别材料表征，且泛化能力较差。本文首次提出一种新方法，使得材料表征与增量公式解耦成为可能。受基于热力学的人工神经网络（TANN）及内变量理论启发，演化TANN（eTANN）采用连续时间形式，因此独立于上述人工量。该方法的关键特征在于将内变量的演化方程识别为常微分方程形式，而非增量离散时间形式。本文着重对比并展示固体力学中各种通用概念如何在eTANN中实现。通过涵盖从塑性、损伤到粘性（及其组合）的广泛复杂材料行为的多个应用案例，论证了所提方法的能力及可扩展性。最后，我们表明借助渐近均匀化理论，该方法可用于加速多尺度分析。与精细尺度仿真相比，eTANN不仅提供了优异的结果，还具备描述宏观平均材料行为及微观力学复杂机制的能力。