Robin Bouclier

Analysis of an Averaging Operator for Atomic-to-Continuum Coupling Methods by the Arlequin Approach

A new coupling term for blending particle and continuum models with the Arlequin framework is investigated in this work. The coupling term is based on an integral operator defined on the overlap region that matches the continuum and particle solutions in an average sense. The present exposition is essentially the continuation of a previous work (Bauman et al., On the application of the Arlequin method to the coupling of particle and continuum models, Computational Mechanics, 42, 511–530, 2008) in which coupling was performed in terms of an H 1-type norm. In that case, it was shown that the solution of the coupled problem was mesh-dependent or, said in another way, that the solution of the continuous coupled problem was not the intended solution. This new formulation is now consistent with the problem of interest and is virtually mesh-independent when considering a particle model consisting of a distribution of heterogeneous bonds. The mathematical properties of the formulation are studied for a one-dimensional model of harmonic springs, with varying stiffness parameters, coupled with a linear elastic bar, whose modulus is determined by classical homogenization. Numerical examples are presented for one-dimensional and two-dimensional model problems that illustrate the approximation properties of the new coupling term and the effect of mesh size.

Multiscale analysis of complex aeronautical structures using robust non-intrusive coupling

The multiscale analysis of large composite aeronautical structures involves the development of robust coupling strategies. Among the latter, non-intrusive coupling is attractive, since it is able to consistently connect a global simplified linear model to a local detailed one, using features available in commercial software. Up to now, such coupling methods were still limited to academic situations where global and local meshes are geometrically and/or topologically conforming and of low geometric complexity. To meet the goal of merging a complex non-planar global shell to a local detailed 3D model, an extension of these techniques is proposed to handle meshes of complex shapes that are not only non-matching but also geometrically and topologically non-conforming. The implemented strategy is original and robust: the innovative nature of the approach is to expand the initial local solid model by generating transitional shell meshing. The generated model incorporates two distinct coupling interfaces: (i) non-intrusive global–local coupling and (ii) shell–solid coupling. The multiscale strategy was successfully validated through different numerical experiments using standard Input/Output of a commercial finite element software. In particular, a representative use-case involving a realistic fuselage section of an aircraft was computed.

DD-DIC: A Parallel Finite Element Based Digital Image Correlation Solver

The computational burden associated to finite element based digital image correlation methods (FE-DIC) is mostly due to the inversion of global FE systems and to global image interpolations. On the contrary, subset based approaches require only subimages, and allow solving small independent systems in parallel. A variable separation technique was recently proposed that alleviate mesh constraints in FE-DIC. However, in digital volume correlation, the question of the interpolation of the images becomes a real issue. For that reason, a non-overlapping dual domain decomposition method is proposed to rationalize the computational cost of high resolution FE-DIC measurements when dealing with large datasets. It consists in splitting the global mesh into submeshes and the images into subimages. The displacement continuity at the interfaces between subdomains is obtained iteratively by using a preconditioned conjugate gradient. It will be shown that the method combines the metrological performances of finite element based DIC and the parallelization ability of subset based DIC methods.