Semi-analytical Study of Large Bending Strains of the Inhomogeneous Bar

Abstract

This paper presents an analysis of the problem of pure bending of an inhomogeneous nonlinearly elastic bar with rectangular cross-section. The character of heterogeneity corresponds to the case of hard coating on the inner or outer bar surface. Two types of continuous heterogeneity, linear and exponential, as well as laminated bar, or case of piecewise constant values of material parameters are considered. The commonly used models of compressible nonlinearly elastic media are applied to describe the mechanical properties of bar’s material at large strains. The 2D problem is reduced to the boundary value problem for second order differential equations by means of a semi-inverse method. The nonlinear boundary value problems are solved using an automation package developed by the authors within the framework of the computer algebra system Maple. The influence of coating on the load diagram and the stability of the bent bar is evaluated.