NICE
h
: a higher-order explicit numerical scheme for integration of constitutive models in plasticity |
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Authors: | Miroslav Halilovi? Marko Vrh Boris ?tok |
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Affiliation: | 1. Laboratory for Numerical Modelling and Simulation, Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, Slovenia 2. Faculty of Mechanical Engineering, University of Ljubljana, A?ker?eva 6, 1000, Ljubljana, Slovenia
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Abstract: | The article introduces, as a result of further development of the first-order scheme NICE, a simple and efficient higher-order explicit numerical scheme for the integration of a system of ordinary differential equations which is constrained by an algebraic condition (DAE). The scheme is based on the truncated Taylor expansion of the constraint equation with order h of the scheme being determined by the highest exponent in the truncated Taylor series. The integration scheme thus conceived will be named NICE h , considering both principal premises of its construction. In conjunction with a direct solution technique used to solve the boundary value problem, the NICE h scheme is very convenient for integrating constitutive models in plasticity. The plasticity models are defined mostly by a system of algebraic and differential equations in which the yield criterion represents the constraint condition. To study the properties of the new integration scheme, which, like the forward-Euler scheme, is characterised by its implementation simplicity due to the explicitness of its formulations, a damage constitutive model (Gurson–Tvergaard–Needleman model) is considered. The general opinion that the implicit backward-Euler scheme is much more accurate than the thus-far known explicit schemes is challenged by the introduction of the NICE h scheme. The accuracy of the higher-order explicit scheme in the studied cases is significantly higher than the accuracy of the classical backward-Euler scheme, if we compare them under the condition of a similar CPU time consumption. |
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