On the modeling of large ratcheting strains with large time increments

Journal article, 2007

Purpose - This paper aims to speed up finite element analyses of structures with a highly nonlinear material response subjected to many loading cycles. Design/methodology/approach - An approach where large time increments are taken in an adaptive fashion is presented. The size of the large time increments typically spans several loading cycles and is based on Taylor series expansions of the response combined with error control. Findings - The suggested adaptive algorithm is simple compared with some well-known alternatives in the literature. It also has the inherent convergence property that it reduces to the classical time incrementation in the case where the estimated error is too large. Research limitations/implications - The algorithm is suitable for (restricted to) a special class of problems where the material response versus a representative time sequence are smooth curves. The simplicity of the method results in a robust algorithm. Originality/value - Similar algorithms have been presented earlier in the literature but the present work introduces some enhancements, e.g. accounting for general internal variables also in the error estimate. In addition, the present work considers a more complex constitutive model compared with earlier work within the research field.