Estimating Deformation Behavior of Re-entrant Auxetic Structures by the Finite Element Method Based on Modified Couple Stress Theory


Pehlivanoglu Y., Al-Qahtani H., SUNAR M.

Arabian Journal for Science and Engineering, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Publication Date: 2025
  • Doi Number: 10.1007/s13369-025-10905-4
  • Journal Name: Arabian Journal for Science and Engineering
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Keywords: FE Model, Length Scale Parameter, Modified Couple Stress Theory, Re-entrant Auxetic Structures, Size Effects
  • Ankara Yıldırım Beyazıt University Affiliated: Yes

Abstract

In this study, the mechanical behavior of re-entrant auxetic structures is investigated. Unlike the prevailing literature, instead of analyzing the negativity of Poisson’s ratio resulting from re-entrant geometry, the study focuses on the mechanics of deformation by utilizing analytical, numerical, and experimental (test) methods. Tensile testing is applied to the specimens produced with additive manufacturing. The force–displacement curves of the tested specimens are derived for the loadings from two different directions. It is shown that not only the magnitudes of force and displacement differ, but also the type of deformation curve varies depending on the loading direction. Elastic moduli of the specimens derived from tests are compared with those obtained by the analytical model in the literature and the current finite element model, which is based on modified couple stress theory. Since the current model can capture the size effect occurring in small scales, the elastic modulus of the structures is further analyzed by simulating the small-scale effects. It is also shown that as the size effects become dominant, the elastic modulus significantly increases, which implies that standard analytical or numerical methods based on classical elasticity fail to estimate the increase in the elastic modulus of auxetic structures.