City Research Online

Abstract

In this work, a mathematical formulation based on variational asymptotic method (VAM) has been proposed to determine the effect of damage on the auxetic properties of two-dimensional (2D) and three-dimensional (3D) re-entrant geometries. The influence of damage progression on the auxetic behavior was captured using a geometrically exact one-dimensional beam theory and an isotropic damage law, implemented in a nonlinear finite element framework. The effect of material degradation on the macroscale effective elastic properties such as the elastic modulus and Poisson’s ratio for the two-dimensional and three-dimensional re-entrant auxetic geometries was quantified. The mechanical behavior as predicted by the in-house Python-based implementation of the proposed VAM-based formulation is verified with the results from the commercial finite element solver Abaqus, wherein the user material subroutine was used to capture damage evolution. The numerical examples presented in this paper reveal that the macroscale auxetic behavior of the geometries was affected significantly by damage progression. The results of this research will provide insights into the design and analysis of auxetic materials for applications that warrant consideration of damage evolution.

Publication Type:	Article
Additional Information:	This is an open access article distributed under the terms of the Creative Commons CC-BY license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Publisher Keywords:	Auxetic materials, Damage evolution, Variational asymptotic method, Re-entrant geometry, Negative Poisson’s ratio
Subjects:	Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery
Departments:	School of Science & Technology School of Science & Technology > Engineering
SWORD Depositor:	Symplectic Administrator

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