Material modeling for parametric, anisotropic finite strain hyperelasticity based on machine learning with application in optimization of metamaterials

International Journal for Numerical Methods in Engineering, vol. 123, pp. 577–609

Abstract

Abstract Mechanical metamaterials such as open‐ and closed‐cell lattice structures, foams, composites, and so forth can often be parametrized in terms of their microstructural properties, for example, relative densities, aspect ratios, material, shape, or topological parameters. To model the effective constitutive behavior and facilitate efficient multiscale simulation, design, and optimization of such parametric metamaterials in the finite deformation regime, a machine learning‐based constitutive model is presented in this work. The approach is demonstrated in application to elastic beam lattices with cubic anisotropy, which exhibit highly nonlinear effective behaviors due to microstructural instabilities and topology variations. Based on microstructure simulations, the relevant material and topology parameters of selected cubic lattice cells are determined and training data with homogenized stress‐deformation responses is generated for varying parameters. Then, a parametric, hyperelastic, anisotropic constitutive model is formulated as an artificial neural network, extending a recent work of the author extending a recent work of the author, Comput Mech., 2021;67(2):653‐677. The machine learning model is calibrated with the simulation data of the parametric unit cell. The authors offer public access to the simulation data through the GitHub repository https://github.com/CPShub/sim‐data . For the calibration of the model, a dedicated sample weighting strategy is developed to equally consider compliant and stiff cells and deformation scenarios in the objective function. It is demonstrated that this machine learning model is able to represent and predict the effective constitutive behavior of parametric lattices well across several orders of magnitude. Furthermore, the usability of the approach is showcased by two examples for material and topology optimization of the parametric lattice cell.

Authors 3

1. Mauricio Fernández corresponding Aachen Multiscale and Data-Driven Material Modeling

   Access · Technische Universität Darmstadt

   Affiliation as printed

   Cyber‐Physical Simulation Technical University of Darmstadt Darmstadt Germany

   Multiscale and Data‐Driven Material Modeling ACCESS e.V. Aachen Germany

   Cyber-Physical Simulation, Technical University of Darmstadt, Darmstadt, Germany

   Multiscale and Data-Driven Material Modeling, ACCESS e.V., Aachen, Germany

2. Felix Fritzen

   University of Stuttgart

   Affiliation as printed

   Data Analytics in Engineering University of Stuttgart Stuttgart Germany

   Data Analytics in Engineering, University of Stuttgart, Stuttgart, Germany

3. Oliver Weeger

   Technische Universität Darmstadt

   Affiliation as printed

   Cyber‐Physical Simulation Technical University of Darmstadt Darmstadt Germany

   Cyber-Physical Simulation, Technical University of Darmstadt, Darmstadt, Germany