Sequentially linear solution procedure for non-proportional loading

miscellaneous

English

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. General non-proportional loading (replaced here by sequence of loading vectors) 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. The present paper is a promotion of recent journal paper by the authors

Non-Proportional Loading, Sequentially Linear Solution, Brittlw Elements, Local Instabilities

ELIÁŠ, J.; VOŘECHOVSKÝ, M.; FRANTÍK, P.

14. 11. 2011

Luxor

279

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