Abstract
This paper deals with some recent results obtained with a simplified second gradient model to simulate localized patterns. The simplification is based on the use of the gradient of the volume variation only. It is first shown that this model is very efficient since it is less time consuming than a classical one. Consequently, such a model can be useful for 3-D computations. Finally some results show once more that even for 3-D computations, enhanced models such as second gradient ones do not restore the mathematical well posedness of the initial boundary value problem.
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Acknowledgements
This paper is dedicated to the memory of Ioannis Vardoulakis. He suggested us some references during friendly discussions. He was the referee of the Ph. thesis of the first author. He supported by a very kind letter the scientific project, about second gradient dilation model allowing the third author to obtain a six months full time research position.
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Fernandes, R., Ducoin, B., Chambon, R. (2011). 2D and 3D Modelling of Geomaterials Using a Second Gradient Dilation Model. In: Bonelli, S., Dascalu, C., Nicot, F. (eds) Advances in Bifurcation and Degradation in Geomaterials. Springer Series in Geomechanics and Geoengineering. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1421-2_27
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DOI: https://doi.org/10.1007/978-94-007-1421-2_27
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