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. In addition, the models are calibrated with transversely isotropic data, generated with an analytical polyconvex potential. For this case, both models show excellent results, demonstrating the straightforward applicability of the polyconvex neural network constitutive models to other symmetry groups.
翻译:在目前的工作中,提出了两套基于机器学习的固定变形构成模型。使用输入的 convex 神经神经网络,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。第一个构成模型基于一套具有高度挑战性的多孔、厌异和客观的变异物。第二种方法以变形梯度、其共构和决定因素为基础,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形。在实验性调查中通常应用的变形数据的基础上,使用适度的校准数据。虽然基于变形的模型显示若干变形模型的变形模型,但基于极好的变异性模型的易变异性分析能力,仅以极易变形的变异性模型展示了这种变形性数据。