论文标题
进化坦和识别内部变量和固体力学中的演化方程
Evolution TANN and the identification of internal variables and evolution equations in solid mechanics
论文作者
论文摘要
数据驱动和深度学习方法已证明具有代替复杂材料的经典本构模型的潜力。然而，以增量配方构建本构模型的必要性导致了数据驱动的方法，例如物理量，例如变形，与人工，非物理的变形，例如变形和时间的增量。神经网络和随之而来的本构模型依赖于特定的增量公式，无法在及时识别本地材料表示，并且概括不良。本文中，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相解配。受热力学的人工神经网络（TANN）和内部变量理论的启发，Evolution Tann（Etann）是连续的，因此与上述人工数量无关。所提出的方法的关键特征是以普通微分方程的形式识别内部变量的进化方程，而不是以增量离散时间形式。在这项工作中，我们将注意力集中在并置，并展示如何在Etann中实现各种固体力学的一般概念。通过几种应用涉及各种复杂的材料行为，从可塑性到损伤和粘度（以及它们的组合），可以证明所提出方法的功能以及所提出方法的可伸缩性。最后，我们表明，由于渐近均匀化，建议的方法可用于加速多尺度分析。与详细的细尺度模拟相比，Etann提供了出色的结果，并提供了不仅可以描述平均宏观材料行为的可能性，还提供了微力机械的复杂机制。
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.
