In this work we present a hybrid physics-based and data-driven learning approach to construct surrogate models for concurrent multiscale simulations of complex material behavior. We start from robust but inflexible physics-based constitutive models and increase their expressivity by allowing a subset of their material parameters to change in time according to an evolution operator learned from data. This leads to a flexible hybrid model combining a data-driven encoder and a physics-based decoder. Apart from introducing physics-motivated bias to the resulting surrogate, the internal variables of the decoder act as a memory mechanism that allows path dependency to arise naturally. We demonstrate the capabilities of the approach by combining an FNN encoder with several plasticity decoders and training the model to reproduce the macroscopic behavior of fiber-reinforced composites. The hybrid models are able to provide reasonable predictions of unloading/reloading behavior while being trained exclusively on monotonic data. Furthermore, in contrast to traditional surrogates mapping strains to stresses, the specific architecture of the hybrid model allows for lossless dimensionality reduction and straightforward enforcement of frame invariance by using strain invariants as the feature space of the encoder.

翻译：本文提出了一种混合物理驱动与数据驱动的学习方法，用于构建复杂材料行为并发多尺度模拟的替代模型。我们从稳健但缺乏灵活性的物理本构模型出发，通过允许其部分材料参数根据从数据中学习的演化算子随时间变化，增强模型的表达能力。由此形成一种结合数据驱动编码器和物理驱动解码器的灵活混合模型。该模型不仅为替代模型引入物理机理导向的偏差，还通过解码器内部变量作为记忆机制，使路径依赖性自然产生。我们结合FNN编码器与多种塑性解码器，训练模型以复现纤维增强复合材料的宏观行为，展示了该方法的能力。混合模型仅在单调加载数据上进行训练，却能对卸载/再加载行为提供合理预测。此外，与传统将应变映射为应力的替代模型不同，混合模型的特定架构通过使用应变不变量作为编码器的特征空间，实现了无损降维和框架不变性的直接约束。