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

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