Data-driven and deep learning approaches have demonstrated to have the potential of replacing classical constitutive models for complex materials, displaying path-dependency and possessing multiple inherent scales. 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 laws of thermodynamics are hardwired in the structure of the network and allow predictions which are always consistent, independently of the range of the training dataset.

Inspired by previous works, we propose a methodology that allows to identify, from data and first principles, admissible sets of internal variables from the microscopic fields in complex materials. 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 state-of-the-art 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.

数据驱动和深度学习方法已证明有可能取代复杂材料的经典本构模型，显示出路径依赖性并具有多个固有尺度。然而，构建具有增量公式的本构模型的必要性已经产生了数据驱动的方法，其中物理量（例如变形）与人工的非物理量（例如变形和时间的增量）混合。因此，神经网络和随之而来的本构模型依赖于特定的增量公式，无法及时识别局部材料表示，并且泛化能力差。

在此，我们提出了一种新方法，该方法首次允许将材料表示与增量公式分离。受基于热力学的人工神经网络 (TANN) 和内部变量理论的启发，演化 TANN ( e TANN) 是连续时间的，因此独立于上述人工量。所提出方法的主要特征是以常微分方程的形式识别内部变量的演化方程，而不是增量离散时间形式。

在这项工作中，我们将注意力集中在并列并展示固体力学的各种一般概念是如何在e TANN 中实现的。热力学定律在网络结构中是固定的，并且允许始终一致的预测，与训练数据集的范围无关。

受先前工作的启发，我们提出了一种方法，该方法允许从数据和第一原理中识别复杂材料微观场中可接受的内部变量集。通过涉及广泛的复杂材料行为的多个应用程序，从塑性到损坏和粘度（以及它们的组合），证明了所提出方法的能力和可扩展性。最后，我们证明了所提出的方法可以通过渐近均质化来加速最先进的多尺度分析。与详细的精细模拟相比，e TANN 提供了出色的结果，并且不仅可以描述平均宏观材料行为，还可以描述微观机械、复杂机制。