The instability of plant ribbons in orthotropic materials induced by growth strain

Abstract

The aim of this paper is to investigate the influence of orthotropic material parameters on the buckling behavior of infinitely long ribbons induced by growth strain under natural boundary conditions, encompassing both linear buckling and post-buckling analyses. The ribbons were initially modeled as infinitely long elastic plates, and the boundary value problem related to their buckling behavior was formulated. This study adeptly employed the form functions of the ribbon during filamentary, saddle, and small amount torsion stages. We effectively decoupled these equations into ordinary differential equations through the method of separation of variables, subsequently solving them numerically using the BVP5C function in MATLAB to research the behavior of the ribbon across these buckling phases. The results show that the elastic modulus ratio, shear modulus ratio, and Poisson’s ratio in the elastic principal plane affect the ribbons behavior of filament buckling, saddle buckling, and small amount torsion stage to varying degrees, respectively, when the ribbon exhibits natural differential growth along the principal axis of the orthogonal material. The findings of this research are anticipated to yield novel insights into the understanding and regulation of the morphological evolution of soft materials derived from either natural or engineered composites.