Computational contact mechanics: geometry, detection and numerical techniques

Computational solid mechanics

Towards all geometrical developments

In his PhD thesis Vladislav Yastrebov provides a self-consistent manual on computational contact mechanics which includes an exhaustive presentation of classical numerical methods and some original developments: new geometrical projection techniques, an efficient contact detection algorithm for parallel computer architectures, an efficient method to treat contact between a rigid and a deformable solids and an algorithm to simulate wear. He also introduced a generalized tensor algebra, which aids all geometrical developments. 

The goal of his work is to derive a consistent framework for the treatment of three-dimensional bilateral frictional contact problems within the Finite Element Method using the Node-to-Segment discretization. Three main components of the computational contact have been considered: geometry, detection and resolution techniques. For the sake of completeness, the mechanical aspects of contact as well as numerous numerical algorithms and methods have been discussed.

Fig 1: "Up to now the scientific community cannot solve complex frictional contact problems in a reliable way, that is why the domain of computational contact mechanics is so inspiring and active. Here you can compare 4 results of different European research groups for a shallow ironing problem, all of them are different. The question on accuracy of all existing methods and convergence is still open."

Fig 2: "2D Finite Element Analysis of post-buckling folding of a thin walled cylinder: finite strain plasticity and self-contact"

''S-structures'', ZéBuLoN...

A new mathematical formalism called ''s-structures'' has been employed through the entire dissertation. It results in a comprehensive coordinate-free notations and provides an elegant apparatus, available for other mechanical and physical applications. Several original ideas and extensions of standard techniques have been proposed and implemented in the parallel finite element software ZeBuLoN (Zset); namely, a parallel detection algorithm, a contact element enrichment for simulation of complex geometries and wear, a new point projection technique and a robust parallel method for unilateral contact. Numerical case studies, presented in the dissertation, demonstrate the performance and robustness of the employed detection and resolution schemes.

Fig 3: "3D Finite Element Analysis of post-buckling folding of a thin walled cylinder: finite strain plasticity and self-contact"

Vladislav obtained a bachelor (2005) and master degree (2007) in Applied and Computational Mechanics at St Petersburg Polytechnic University in Russia. Next, he spent three years on his PhD thesis on Computational Contact Mechanics at MINES ParisTech and defended it in March 2011.

After his thesis, he worked as a postdoctoral researcher at Ecole Polytechnique Fédérale de Lausanne in Switzerland. He is back to MINES ParisTech - Centre of materials since April 2012 and actually working on a book on computational contact mechanics. You can get more information concerning his research by visiting his home web-page at

He started his PhD thesis because he aimed a scientific career and a PhD degree is a must. He is happy with the subject of his thesis, very deep and which requires some knowledge in many domains: differential geometry, non-convex analysis, a deep understanding of the finite element method, etc. So he could study many things and broaden his skills.

During his PhD thesis, at MINES ParisTech - Centre of materials he was with great people: Georges Cailletaud and Frédéric Feyel (ONERA), their careful and helpful supervision enabled him to do a very good job. The PhD thesis of Vladislav Yastrebov obtained CSMA (Computational Structural Mechanics Association) award and Prix Paul Caseau by French Academy of Technology and Electricité de France.

Click here for the electronic version of the PhD thesis of Vladislav Yastrebov.