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Anisotropic hyperelastic constitutive models for finite deformations combining material theory and data-driven approaches with application to cubic lattice metamaterials

Fernández, Mauricio ; Jamshidian, Mostafa ; Böhlke, Thomas ; Kersting, Kristian ; Weeger, Oliver (2021):
Anisotropic hyperelastic constitutive models for finite deformations combining material theory and data-driven approaches with application to cubic lattice metamaterials. (Publisher's Version)
In: Computational Mechanics, 67, pp. 653-677. Springer, ISSN 0178-7675, e-ISSN 1432-0924,
DOI: 10.26083/tuprints-00019872,
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Item Type: Article
Origin: Secondary publication service
Status: Publisher's Version
Title: Anisotropic hyperelastic constitutive models for finite deformations combining material theory and data-driven approaches with application to cubic lattice metamaterials
Language: English
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.

Journal or Publication Title: Computational Mechanics
Journal volume: 67
Publisher: Springer
Classification DDC: 000 Allgemeines, Informatik, Informationswissenschaft > 004 Informatik
500 Naturwissenschaften und Mathematik > 530 Physik
600 Technik, Medizin, angewandte Wissenschaften > 600 Technik
600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften
Divisions: 16 Department of Mechanical Engineering > Cyber-Physical Simulation (CPS)
Date Deposited: 15 Dec 2021 10:37
Last Modified: 15 Dec 2021 10:37
DOI: 10.26083/tuprints-00019872
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-198728
Additional Information:

Finite hyperelasticity, Anisotropy, Metamaterials, Data-driven modeling, Machine learning, Artificial neural networks

Further, access to the complete simulation data is provided through the public repository https://github.com/CPShub/sim-data.

URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/19872
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