Improved sequentially linear solution procedure

The article proposes an improvement over the widely used sequentially linear solution procedure often utilized for fracture simulations. In the classical secant version of this method, a partial solution of a step is scaled to reach a stress limit in exactly one element and the mechanical properties of the critical element are reduced. Non-proportional loading is generally unfeasible due to avalanches of ruptures caused by stress redistribution. Because only one loading vector can be scaled at a time, all others have to remain constant during the step. However, the constant load vectors do not allow proper determination of the critical element. A modified procedure based on redistribution of released stresses is developed here. It preserves the linearity of each step. After rupture of the critical element, a sequentially linear redistribution process of stress release takes place until a static equilibrium state is reached. During the redistribution, other elements may break.The proposed enhanced sequential procedure is also compared with another recently published “event-by-event” linear method for non-proportional loading. It is shown here, with the help of simple examples, that the proposed redistribution method yields correct results for non-proportional loading, unlike the other methods under comparison.