An analytic solution for bending under tension of a two-layer strip of strain hardening materials

Abstract

Abstract A semi-analytic solution for the process of plane strain bending under tension of a two-layer sheet of elastic-plastic, isotropic, incompressible, strain hardening material is provided. No restriction is imposed on the strain hardening law. A numerical technique is only necessary for solving transcendental equations and evaluating an ordinary integral to find the bending moment. The solution is constructed as a combination of three elementary analytic solutions. The general solution is simple but very cumbersome. In particular, the process usually consists of several stages. Several conditions control the range of validity of the solution in each stage. In order to find the correct solution, it is necessary to check all these conditions. However, for any given initial geometry of the sheet and any given constitutive equations it is straightforward to construct the solution.