Improved sequentially linear solution procedure

✍ Scribed by Jan Eliáš; Petr Frantík; Miroslav Vořechovský

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 936 KB
• Volume: 77
• Category: Article
• ISSN: 0013-7944
• DOI: 10.1016/j.engfracmech.2010.05.018

✦ Synopsis

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.