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.
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.
The method requires only two parameters and can automatically trace equilibrium paths which display multiple snap-through and/or snap-back phenomena.
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.
The authors would like to express their gratitude towards Erik Jan Lingen at the Dynaflow Research Group for his support regarding the numerical toolkit jem/jive.
May, S., Vignollet, J. and de Borst, R. (2016), "A new arc-length control method based on the rates of the internal and the dissipated energy", Engineering Computations, Vol. 33 No. 1, pp. 100-115. https://doi.org/10.1108/EC-02-2015-0044Download as .RIS
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