Study of auxetic beams under bending: A finite element approach

Abstract

Materials with a negative Poisson’s ratio are termed as auxetic materials. A negative Poisson’s ratio implies a lateral strain in accordance to a longitudinal strain under application of load, that is, it expands laterally when under tensile load and contracts under compressive loading. The key feature that imparts the auxetic behavior to a structure is its geometry. This paper initially discusses about the single cell honeycomb and re-entrant configurations. Analytical formulations are used to calculate the Poisson’s ratio for various structures and numerical analysis is carried out using the ABAQUS software. Further, various beam configurations such as homogeneous, truss and auxetic re-entrant structures are investigated under four point bending to understand the scope of application of these structures and to observe their behavior when employed in a practically significant entity. The auxetic beam is found to have lowest level of stress in most of the regions. This paper also discusses the reasons why there is a need for a combined analysis of these auxetic structures using Experimental/Numerical and analytical methods.