Direct integration method for hyperplastic models

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4. Direct integration method for hyperplastic models

Hyperplasticity offers a reliable framework to construct thermodynamically consistent constitutive models. It starts by the specification of a free energy potential and a dissipation function (that is enriched by kinematic constrains), followed by a degenerate Legendre transformation to reach the regular elements of the traditional elastoplasticity, e.g. yield function. The latter step is mainly conducted for implementation purposes to follow the traditional elastoplasticity approach of integration. This transformation is a quite straightforward step for simple dissipation functions. For a more sophisticated choice, conducting the transformation might be hindered by mathematical complexities. This difficulty appears to limit the application of the hyperplasticity framework. However, the degenerate Legendre transformation is not a necessary step to capture the material behaviour since the free energy and dissipation functions already contain all necessary information of the model. In this paper, an implicit integration scheme to capture the elastoplastic response of the material directly from free energy and dissipation functions, is introduced. The scheme does not depend on the establishment of expressions for the yield and plastic potential surfaces. The method is successfully applied to a couple of sand models based on the Matsuoka-Nakai failure criterion with different kinematic constraints.

10th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE2023)

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