The elastic properties of materials derive from their electronic and atomic nature. However, simulating bulk materials fully at these scales is not feasible, so that typically homogenized continuum descriptions are used instead. A seamless and lossless transition of the constitutive description of the elastic response of materials between these two scales has been so far elusive. Here we show how this problem can be overcome by using Artificial Intelligence (AI). A Convolutional Neural Network (CNN) model is trained, by taking the structure image of a nanoporous material as input and the corresponding elasticity tensor, calculated from Molecular Statics (MS), as output. Trained with the atomistic data, the CNN model captures the size- and pore-dependency of the material's elastic properties which, on the physics side, can stem from surfaces and non-local effects. Such effects are often ignored in upscaling from atomistic to classical continuum theory. To demonstrate the accuracy and the efficiency of the trained CNN model, a Finite Element Method (FEM) based result of an elastically deformed nanoporous beam equipped with the CNN as constitutive law is compared with that by a full atomistic simulation. The good agreement between the atomistic simulations and the FEM-AI combination for a system with size and surface effects establishes a new lossless scale bridging approach to such problems. The trained CNN model deviates from the atomistic result by 9.6\% for porosity scenarios of up to 90\% but it is about 230 times faster than the MS calculation and does not require to change simulation methods between different scales. The efficiency of the CNN evaluation together with the preservation of important atomistic effects makes the trained model an effective atomistically-informed constitutive model for macroscopic simulations of nanoporous materials and solving of inverse problems.
A novel class of electro-magneto-elastic (EME) materials comprise electro-active and magneto-active particles in the polymer matrix that change their elastic behavior with an applied electromagnetic field. The material response for such a material class is usually formulated in terms of Lagrangian strain tensor along with Lagrangian electromagnetic field vectors as pushed forward to the current configuration. This letter article presents a novel formulation of an electro-magneto-elasticity in terms of an Eulerian strain tensor and Eulerian electromagnetic field vectors referring to the current…
Micromorphic theories became an established tool to model size effects in materials like dispersion, localization phenomena or (apparently) size dependent properties. However, the formulation of adequate constitutive relations with its large number of constitutive relations and respective parameters hinders the usage of the full micromorphic theory, which has 18 constitutive parameters already in the isotropic linear elastic case. Although it is clear that these parameters are related to predicted size effects, the individual meaning of single parameters has been rather unclear. The present wo…
The transformation method is a powerful tool for providing the constitutive parameters of the transformed material in the new coordinates. In transformation elasticity, a general curvilinear change of coordinates transforms conventional Hooke's law into a different constitutive law in which the transformed material is not only anisotropic but also polar and chiral and no known elastic solid satisfies. However, this state-of-the-art description provides no insight as to what the underlying microstructure of this transformed material could be, the design of which is a major challenge in this fie…
Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models
Computational Mechanics in Medicine, Applied Medical Engineering, RWTH Aachen University（医学计算力学与应用医学工程，亚琛工业大学）；Institute for Continuum and Material Mechanics, Hamburg University of Technology（连续力学与材料力学研究所，汉堡工业大学）；Institute of Applied Mechanics, University of Erlangen-Nuremberg（应用力学研究所，埃尔朗根-纽伦堡大学）；Institute of Material Systems Modeling, Helmholtz-Zentrum Hereon（材料系统建模研究所，海德堡中心）
A generalized dual potential for inelastic Constitutive Artificial Neural Networks: A JAX implementation at finite strains
Institute of Applied Mechanics, RWTH Aachen University, Germany（应用力学研究所，亚琛工业大学，德国）；Institute for Continuum and Material Mechanics, Hamburg University of Technology, Germany（连续介质与材料力学研究所，汉堡技术大学，德国）；Department of Mechanical Engineering, Stanford University, United States（机械工程系，斯坦福大学，美国）
Concurrent enforcement of polyconvexity and true-stress-true-strain monotonicity in incompressible isotropic hyperelasticity: application to neural network constitutive models
Graz University of Technology（格拉茨工业大学）；TU Darmstadt（达姆施塔特工业大学）；University of Applied Sciences Bingen（宾根应用科学大学）；Norwegian University of Science and Technology（挪威科技大学）；University of Duisburg-Essen（杜伊斯堡-埃森大学）
