Solution strategies and softening materials

Abstract The paper describes the application of a range of solution procedures to simple tie-bar models involving softening ‘stress-strain’ relationships. It illustrates the difficulties that can be encountered as a result of the associated localizations, ‘bifurcations’, and alternative equilibrium states. As a result of this study, a new solution procedure is tentatively proposed which requires the computer program to distinguish between ‘limit points’ and ‘bifurcations’. Once the latter has been detected, the solution is steered towards the ‘stable’ equilibrium path by adding to the current displacements a component of the eigenmode associated with the lowest eigenvector.

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