Abstract

Elastica theory studies large deformation of slender beams and rods. The elliptic integral solution (EIS) is an accurate and efficient theoretical solution to elastica problem. However, the sign of elliptic integral (SEI) will change with the sign of curvature along an elastica, and also depends on parameters of the coordinate origin, such as elliptical modular angle and curvature. Due to the uncertainty of SEIs, it is quite difficult to obtain an EIS with a uniform final expression. In this study, the sign of elliptic integral (SEI) will be discussed in detail, by classifying the elastica problems into two loading cases: force dominant case (FDC) and bending moment dominant case (MDC). A complete set of EISs and the general solving procedure of EISs, which are applicable to various planar elastica without axial deformation, are presented. The accuracy of current elastica analysis is confirmed by corresponding FE simulations. Employing this EIS method, some metamaterials under large deformation are analyzed efficiently. It is found that the predictions of the equivalent modulus, stress-strain relations, and deformation profiles are both accurate.