Abstract
This work investigates the capabilities of anisotropic theory-based, purely data-driven and hybrid approaches to model the homogenized constitutive behavior of cubic lattice metamaterials exhibiting large deformations and buckling phenomena. The effective material behavior is assumed as hyperelastic, anisotropic and finite deformations are considered. A highly flexible analytical approach proposed by Itskov (Int J Numer Methods Eng 50(8): 1777–1799, 2001) is taken into account, which ensures material objectivity and fulfillment of the material symmetry group conditions. Then, two non-intrusive data-driven approaches are proposed, which are built upon artificial neural networks and formulated such that they also fulfill the objectivity and material symmetry conditions. Finally, a hybrid approach combing the approach of Itskov (Int J Numer Methods Eng 50(8): 1777–1799, 2001) with artificial neural networks is formulated. Here, all four models are calibrated with simulation data of the homogenization of two cubic lattice metamaterials at finite deformations. The data-driven models are able to reproduce the calibration data very well and reproduce the manifestation of lattice instabilities. Furthermore, they achieve superior accuracy over the analytical model also in additional test scenarios. The introduced hyperelastic models are formulated as general as possible, such that they can not only be used for lattice structures, but for any anisotropic hyperelastic material. Further, access to the complete simulation data is provided through the public repository https://github.com/CPShub/sim-data.
Highlights
With recent progress in additive and advanced manufacturing methods, there has been increasing interest in the development of soft and flexible metamaterials [3,26], which can be subjected to large and tailorable, e.g., auxetic, elastic defor-To efficiently model the mechanical behavior of large scale structures that are constituted of soft metamaterials at a microscopic level, nonlinear multiscale simulation methods are required, for which the effective microstructural behavior must be homogenized, see, e.g., [15,30]
In the field of nonlinear elasticity, [25] shows how artificial neural networks (ANNs) can be used in order to calibrate hyperelastic laws, but the approach is limited to small deformations and does not offer strategies for specific material symmetries
The ansatz is demonstrated for Nickel with cubic material symmetry, where the ANNs are trained on the deformation gradient or specific invariants with structure tensors up to fourth-order for cubic behavior
Summary
With recent progress in additive and advanced manufacturing methods, there has been increasing interest in the development of soft and flexible metamaterials [3,26], which can be subjected to large and tailorable, e.g., auxetic, elastic defor-To efficiently model the mechanical behavior of large scale structures that are constituted of soft metamaterials at a microscopic level, nonlinear multiscale simulation methods are required, for which the effective microstructural behavior must be homogenized, see, e.g., [15,30]. In the field of nonlinear elasticity, [25] shows how ANNs can be used in order to calibrate hyperelastic laws, but the approach is limited to small deformations and does not offer strategies for specific material symmetries. The RNEXP approach of [14] offers a highly efficient method for hyperelastic materials, but it is formulated for small deformations and specific material symmetries can only be approximated through patterns in the provided calibration data. In [16] an interesting approach for the data-driven calibration of corrections of given hyperelastic models for finite strain is presented This approach shows very promising results due to its thermodynamical properties and its application in biomechanics, see [17], but is only demonstrated for isotropic material behavior. The work of [35] introduces efficient sampling strategies and ANN-based models for hyperelasticity at finite deformations for isotorpic material behavior
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