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Computational Mechanics

Prof. Carlo Callari
University of Molise, Italy


Prof. Günther Meschke
Structural Mechanics


In the period 2012-2013, a mobility project VIGONI 2012 financed by the German DAAD and by the Italian AIT gave me the opportunity to cooperate with the research team of Prof. Meschke, at the Institute for Structural Mechanics. Throughout this period, the project partners visited each other's institutions several times. Besides Günther Meschke, the doctoral student Abdullah Alsahly was principally involved in the research at RUB. Furthermore, also other graduate students of RUB participated to several discussions on the project topics (e.g. M.M. Zhou, V.E. Gall, D. Leonhart, H.G. Bui, J. Ninic, J.J. Timothy).

The VIGONI project was focused on the "Advanced computational modelling of shear failure in tunnelling", which is of major scientific interest for the research performed at the RUB Structural Mechanics Institute as well as for the Collaborative Research Center SFB 837 “Interaction Modelling in Mechanized Tunneling”. The experience of cooperation was extremely positive from both the professional and the personal perspective. The promising first results of this research received a very positive feedback at a prominent conference, the 11th World Congress on Computational Mechanics (WCCM 2014), Barcelona (A. Alsahly, C. Callari, G. Meschke 2014).

Hence, at the end of 2014, my nomination for a VIP Grant by Prof. Meschke was aimed to extend such a fruitful cooperation, with my commitment in providing high standards of supervision and mentoring of Abdullah Alsahly, as well as of other eventually involved doctoral students.

Research goals and activities

The project activities are focused on the development of a new 3D strategy for discontinuity tracking in the framework of finite element analysis of shear failure zones in soils and rocks with embedded strong discontinuities. The goal is to enable a high resolution of computational simulations of shear failure zones in soft soils. Such localized failure zones may lead to the sudden appearance of sinkholes, landslides or tunnel collapse, in particular in the presence of groundwater. It should be emphasized, that this joint research has a particular significance for the Ruhr-Area, as sinkholes (“Tagbrüche”) often occur in this region.

As a matter of fact, the tracking of displacement discontinuities is known to play a crucial role in a successful numerical analysis of localization zones such as shear failure bands. Available algorithms are typically based on the so-called “propagation” strategies and have proven to be effective for discontinuity tracking in 2D problems. In these algorithms, the discontinuity is progressively activated at the local level by means of element-wise segments, preserving its continuity across the common boundaries of traced finite elements. However, the extension of these algorithms to 3D problems is often difficult , motivating approaches based on the level set method or strategies involving the solution of a global elliptic problem.

In the present project, we are developing an alternative advantageous novel strategy for global tracking of the discontinuity surface. It is based on exploiting information obtained from the so-called "incompatible modes" employed in a special finite element technology denoted as Assumed Enhanced Strain formulations (AES-FEM). The enhanced-strain methods are able to capture localized shear deformations definitely better than standard finite elements (see the figure above).

This result can be explained as a consequence of the improved performance in bending. We observed that the approximation of the strain jumps delimiting the shear band is connected with a deformation field characterized by opposite bending curvatures across these two discontinuities. Thus we have formulated and verified a new scalar function of the enhanced modes to locate the surface of the potential shear failure zone.

Among the advantages of the strategy developed in this project, we remark its global character, which allows for the evaluation of discontinuity surfaces that are continuous by construction through the elements, with a negligible computational cost. However, still a number of problems observed in selected applications have to be solved. These problems will be tackled within the upcoming visits of Prof. Callari at RUB.


Alsahly, C. Callari and G. Meschke, A discontinuity tracking algorithm based on assumed enhanced modes, 11th World Congress on Computational Mechanics (WCCM XI), 5th European Conference on Computational Mechanics (ECCM V), 6th European Conference on Computational Fluid Dynamics (ECFD VI) , July 20-25, 2014, Barcelona, Spain

Alsahly, C. Callari and G. Meschke, A new approach for the shear localization analysis of strong discontinuous fields based on incompatible modes in frictional materials, EUROMECH Colloquium 572, February 22-24, 2016, Innsbruck, Austria.


Carlo Callari, DiBT, University of Molise, Campobasso, Italy - Günther Meschke, Ruhr-University at Bochum, Institute for Structural Mechanics, Universitätsstraße 150, 44801 Bochum, Abdullah Alsahly, Ruhr-University at Bochum, Institute for Structural Mechanics, Universitätsstraße 150, IC / 6 / 173, 44801 Bochum,