TY  - JOUR
AB  - 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.
VL  - 33
IS  - 1
SN  - 0264-4401
DO  - 10.1108/EC-02-2015-0044
UR  - https://doi.org/10.1108/EC-02-2015-0044
AU  - May Stefan
AU  - Vignollet Julien
AU  - de Borst René
PY  - 2016
Y1  - 2016/01/01
TI  - A new arc-length control method based on the rates of the internal and the dissipated energy
T2  - Engineering Computations
PB  - Emerald Group Publishing Limited
SP  - 100
EP  - 115
Y2  - 2024/09/19
ER  -