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:以数据驱动和深层次学习的方法证明,有可能取代复杂材料的古典构成模型。然而,有必要以递增配方来构建构成模型,从而形成由数据驱动的方法,即物理量,例如变形,与人工和非物理量相结合,例如变形和时间增量。神经网络和随之而来的构成模型取决于特定的增量配方,从而取决于特定的增量配方,无法及时确定当地的物质表现,并受到不甚一般化的概括化影响。在这里,我们提出了一个新的方法,首次将材料代表与增量配制脱钩。在基于热动力的人工神经网络(TANN)和内部变量理论的启发下,进化TANN(ETANN)的进化过程是连续的,因此与上述人工量无关。拟议方法的关键特征是,以普通差异方程式的形式识别内部变量的进化方程,而不是以递增的离散式速度形式呈现出。在这项工作中,我们将注意力集中在基于基于热量动力的神经网络网络网络网络网络化分析以及内部变异性应用中,我们从一系列的演算出了各种变数的内变数的内变数,而显示,从结构的变数的变数的变数的变数的变数和变数的变数的变数是可能的变数。我们从一个变数的变数的变数的变数,从一个变数的变数的变数的变数,从一个变数的变数的变数的变数的变数的变数,我们的变数,我们的变数的变数的变数的变数的变数的变数,从一个变数,从一个变数,从一个变数的变数的变数的变数的变数到整个的变数,从一个变数,从一个变数的变数到整个的变数的变数的变数的变数的变数,从一个变数的变数的变数的变数的变数的变数的变数到整个的变数的变数,从一个的变数的变数的变数的变数的变数的变数从一个变数的变数的变数的变数,从一个变数,从一个变数,从一个变数,从一个变数,从</s>