A new arc-length control method based on the rates of the internal and the dissipated energy. Issue 1 (7th March 2016)

• Record Type: Journal Article
• Authors: May, Stefan; Vignollet, Julien; de Borst, René
• Is Part Of: Engineering computations. Volume 33:Issue 1(2016)
• Page Start: 100
• Page End: 115
• Publication Date: 2016-03-07
• Subjects: Arc-length control -- Dissipation -- Internal energy -- Path-following technique; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-02-2015-0044
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : Purpose: – The purpose of this paper is to introduce a new arc-length control method for physically non-linear problems based on the rates of the internal and the dissipated energy. Design/methodology/approach: – In this paper, the authors derive from the second law of thermodynamics the arc-length method based on the rate of the dissipated energy and from the time derivative of the energy density the arc-length method based on the rate of the internal energy. Findings: – The method requires only two parameters and can automatically trace equilibrium paths which display multiple snap-through and/or snap-back phenomena. Originality/value: – A fully energy-based control procedure is developed, which facilitates switching between dissipative and non-dissipative arc-length control equations in a natural way. The method is applied to a plate with an eccentric hole using the phase field model for brittle fracture and to a perforated beam using interface elements with decohesion.