Anisotropic hyperelastic constitutive models for finite deformations combining material theory and data-driven approache
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ORIGINAL PAPER
Anisotropic hyperelastic constitutive models for finite deformations combining material theory and data-driven approaches with application to cubic lattice metamaterials Mauricio Fernández1
· Mostafa Jamshidian2 · Thomas Böhlke3 · Kristian Kersting4 · Oliver Weeger1
Received: 5 August 2020 / Accepted: 18 November 2020 © The Author(s) 2020
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 datadriven 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. Keywords Finite hyperelasticity · Anisotropy · Metamaterials · Data-driven modeling · Machine learning · Artificial neural networks
1 Introduction 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-
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Mauricio Fernández [email protected]
1
Cyber-Physical Simulation Group, Technical University of Darmstadt, Dolivostr. 15, 64293 Darmstadt, Germany
2
Digital Manufacturing and Design Centre, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore
3
Institute of Engineering Mechanics, Karlsruhe Institute of Technology (KIT), Kaiserstr. 10, 76131 Karlsruhe, Germany
4
Department of Computer Science, Technical University of Darmstadt, Hochschulstr. 10, 64289 Darmstadt, Germany
mations [2,4,12,23,34], harness mechanical instabilities and buckling [28], absorb energy or dissipate vibrations [5]. This functional behavior of soft me
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