An incremental approach for springback analysis of elasto-plastic beam undergoing contact driven large deflection

Abstract

In this article the solution methodology for a beam on a vee-die undergoing large elasto-plastic deflection along with nonlinear contact development with the die is discussed. A bi-linear stress strain material model is converted into an incremental moment- curvature based constitutive law to ease formulation. The one dimensional governing equation obtained, is highly nonlinear owing to material and geometry and involve boundary condition change. The entire problem is solved in three steps: solving an end loaded cantilever under non-conservative force, followed by choosing the solutions which satisfy the configurational constraint and finally reanalyzing the contact data for springback analysis. The end loaded cantilever problem is solved by an incremental procedure coupled with Runge–Kutta fourth-order explicit initial value solver. Suitable normalization of the pertinent variables of the governing equation paved the way to identify dependence of the responses on a unique non-dimensional parameter. The presented methodology doesn't involve large matrix inversion and so is computationally economic. It may be used in sheet metal manufacturing control facilities to predict springback and reduce the expensive experimental iterations.