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Main Title: A novel phase‐field approach to brittle damage mechanics of gradient metamaterials combining action formalism and history variable
Author(s): Abali, Bilen Emek
Klunker, Andre
Barchiesi, Emilio
Placidi, Luca
Type: Article
Abstract: Metamaterials response is generally modeled by generalized continuum based theories. Their inherent substructure leads to a necessity for higher‐order theories, and especially in damage mechanics, such a generalization is difficult to acquire. We exploit the action formalism in order to obtain the governing equations in generalized damage mechanics for metamaterials. Additionally, by using auxilliary variables, the variational formulation is endowed with the first rate of damage variable that is missing in standard approaches. The presented action formalism with auxilliary variables leads directly to the weak form. We implement a finite element method based approach by using open‐source computing platform called FEniCS and solve this weak in order to obtain the deformation and damage numerically. Metamaterials simulations are demonstrated for simple geometries in mixed mode (I and II) as well as in mode III.
Subject(s): damage mechanics
generalized mechanics
variational formalism
Issue Date: 5-Mar-2021
Date Available: 10-Sep-2021
Language Code: en
DDC Class: 530 Physik
Journal Title: ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Publisher: Wiley
Volume: 101
Issue: 9
Article Number: e202000289
Publisher DOI: 10.1002/zamm.202000289
EISSN: 1521-4001
ISSN: 0044-2267
TU Affiliation(s): Fak. 5 Verkehrs- und Maschinensysteme » Inst. Mechanik » FG Stabilität und Versagen funktionsoptimierter Strukturen
Appears in Collections:Technische Universität Berlin » Publications

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