Inelastic strain estimation based on line search and direct secant methods

Abstract

Approximate inelastic strain estimation is of great use in several types of applications. Besides classical nonlinear FEA, robust techniques such as Neuber's rule, EGLOSS, etc., are available for this purpose. These robust techniques are applicable for small loads just above the initial yield. These methods find secant modulus based on unbalanced local element energy. They do not account for change in the yield boundary while computing secant modulus. Several traditional secant techniques were developed to update the secant stiffness directly in FEA based on nonlinear schemes. The present study explores simple and systematic methods for determining inelastic effects based on line search and direct secant modulus. The main concept of these methods is the minimization of the total residual energy after first linear FEA. A line search with the displacements due to the unbalanced forces spreads the yield zone considerably closer to the actual state. -- The present study summarizes important categories of available techniques based on the Newton-Raphson and secant schemes (traditional as well as robust). Seven different possible alternatives for robust estimation of inelastic strain based on line search are examined. Two schemes based on Neuber's rule are examined. These are compared with full nonlinear analysis and EGLOSS, etc. The schemes are applied to study the problems of simply supported beam, propped cantilever, fixed beam (all with UDL), bending of rectangular plate with irregular boundary, simple truss, stretching of a plate with a hole, thick cylinder with internal pressure, thick cylinder with a circumferential notch, and torisherical shell. The problems were studied for load ranging from just above initial yield to nearly limit loads. The studies indicate that the line search techniques significantly improve the predictions as compared to those made by existing robust techniques. Recommendations based on these results have been made. Two alternatives have been found to be good for general bending and stretching type problems. Another alternative has been found to be good for strain concentration problems.