arXiv subjects

Serge Dumont

Publications and source records attributed to Serge Dumont.

3 recordsLinked to original sources

arXiv2024

Mixed Finite Element Method for Multi-layer Elastic Contact Systems

With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent saddle point problems with interlayer Tresca friction conditions and the mixed finite element method are proposed and analyzed. Then, the convergence of the numerical solution of the mixed finite element method is theoretically proven, and the corresponding algebraic dual algorithm is given. Finally, through numerical experiments, the mixed finite element method is not only compared with the layer decomposition method, but also its convergence relationship with respect to the spatial discretization parameter $H$ is verified.

math.NA↗

arXiv2013

An asymptotic approach to the adhesion of thin stiff films

In this paper, the asymptotic first order analysis, both mathematical and numerical, of two structures bonded together is presented. Two cases are considered, the gluing of an elastic structure with a rigid body and the gluing of two elastic structures. The glue is supposed to be elastic and to have its stiffness of the same order than those of the elastic structures. An original numerical method is developed to solve the mechanical problem of stiff interface at order 1, based on the Nitsche's method. Several numerical examples are provided to show the efficiency of both the analytical approximation and the numerical method.

physics.class-ph↗

arXiv2012

On enhanced descend algorithms for solving frictional multi-contact problems : applications to the Discrete Element Method

In this article, we present various numerical methods to solve multi-contact problems within the Non-Smooth Discrete Element Method. The techniques considered to solve the frictional unilateral conditions are based both on the bi-potential theory and the Augmented Lagrangian theory. A new Newton method is developed to improve the classical algorithms.

math.NA↗