In the present work, two machine learning based constitutive models for finite deformations are proposed. Using input convex neural networks, the models are hyperelastic, anisotropic and fulfill the polyconvexity condition, which implies ellipticity and thus ensures material stability. The first constitutive model is based on a set of polyconvex, anisotropic and objective invariants. The second approach is formulated in terms of the deformation gradient, its cofactor and determinant, uses group symmetrization to fulfill the material symmetry condition, and data augmentation to fulfill objectivity approximately. The extension of the dataset for the data augmentation approach is based on mechanical considerations and does not require additional experimental or simulation data. The models are calibrated with highly challenging simulation data of cubic lattice metamaterials, including finite deformations and lattice instabilities. A moderate amount of calibration data is used, based on deformations which are commonly applied in experimental investigations. While the invariant-based model shows drawbacks for several deformation modes, the model based on the deformation gradient alone is able to reproduce and predict the effective material behavior very well and exhibits excellent generalization capabilities. Thus, in particular the second model presents a highly flexible constitutive modeling approach, that leads to a mathematically well-posed problem.
翻译:在目前的工作中,提出了两个基于机械学习的固定变形构成模型。使用输入共振神经网络,这些模型具有超弹性、厌异性并满足多孔化条件,这意味着椭圆性,从而保证物质稳定性。第一个构成模型以一组具有高度挑战性的多孔、厌异和客观变异物为基础。第二种方法以变形梯度、其共构物和决定因素为基础,使用组对称来满足材料对称条件和数据扩增以大致达到客观性。数据扩增方法的数据集扩展基于机械考虑,不需要额外的实验或模拟数据。模型由一套具有高度挑战性的立方体元材料模拟数据校准,包括定型变形和不易变异性。使用适度的校准数据,以通常用于实验性调查的变形为根据。虽然基于变形的模型显示若干变形模型的反向,但基于模型扩展方法的扩展基于机械性考虑,不需要额外的实验性或模拟数据。这种模型的变形能力能够复制高的变形性,因此,一种极易的变形能力能够复制,一种非常灵活的变形,一种高的变形,一种特殊的变形,一种特殊的变形,一种特殊的变形能力可以复制。