Publication detail

Improved sequentially linear solution procedure

ELIÁŠ, J. FRANTÍK, P. VOŘECHOVSKÝ, M.

Original Title

Improved sequentially linear solution procedure

Type

journal article in Web of Science

Language

English

Original Abstract

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.

Keywords

Sequentially linear procedure, Elasto-brittle elements, Non-proportional load-path, Stress redistribution

Authors

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

RIV year

2010

Released

16. 5. 2010

Location

EU

ISBN

0013-7944

Periodical

Engineering Fracture Mechanics

Year of study

77

Number

12

State

United Kingdom of Great Britain and Northern Ireland

Pages from

2263

Pages to

2276

Pages count

14

URL

https://www.sciencedirect.com/science/article/pii/S0013794410002614

BibTex

@article{BUT50255,
  author="Jan {Eliáš} and Petr {Frantík} and Miroslav {Vořechovský}",
  title="Improved sequentially linear solution procedure",
  journal="Engineering Fracture Mechanics",
  year="2010",
  volume="77",
  number="12",
  pages="2263--2276",
  doi="10.1016/j.engfracmech.2010.05.018",
  issn="0013-7944",
  url="https://www.sciencedirect.com/science/article/pii/S0013794410002614"
}