Sub-stepping procedures in constitutive modeling for low-cycle fatigue applications

Kristine Cochran, University of Illinois

The high load levels and relatively low number of cycles that can lead to fatigue failure in certain structural components, such as the space shuttle main engines, cause complex issues in numerical modeling. The constitutive models used in low-cycle fatigue analyses require high levels of numerical accuracy and efficiency to avoid error accumulation and excessive computation over the simulation of hundreds of cycles. At the time-continuum level, the material models of interest are posed as a system of differential equations and an algebraic consistency equation. Solving these equations in a finite element program requires time discretization of the material model at the Gauss point level and formation of the algorithmically consistent tangent. However, most first and second order accurate discretization schemes do not provide sufficient accuracy at reasonable step sizes and the influence of the algebraic equation causes higher order solutions to quickly become cumbersome. Sub-stepping schemes can improve accuracy by dividing the time step into several smaller steps, but at the cost of increased computation and possible reduction of the global convergence rate if the tangent is not consistent with the sub-stepping algorithm. In this poster the accuracy vs. efficiency tradeoff for two different sub-stepping procedures is examined at both the Gauss point and global solution level.

Abstract Author(s): Kristine B. Cochran, Keith D. Hjelmstad and Robert H. Dodds