Further Insights by Theoretical Investigations of the Multiscale Arlequin Method

On the use of XFEM within the Arlequin framework for the simulation of crack propagation

“…A Lagrangian Arlequin formulation of our problem, using an energy scalar product as coupling operator, reads as following: (see e.g. [10,11,16])…”

“…The internal energy weight parameter functions (α i ), i = 0, 1, are defined in th whole domain Ω 0 and satisfy: ( [12,16])…”

“…• Stability: the mixed Arlequin problem, defined by (19)-(28), has been analyzed mathematically and proved to be well-posed in [16] and previously in [9], but under more stringent conditions on the α i (not allowing for regular α i ).…”

“…Our ultimate goal being the simulation of physically-based damage, localisations and crack propagation, we propose a novel and alternative approach, experienced in this paper on basic tests. The approach is based on the multimodel and multiscale Arlequin framework [8,10,33,11,12,16]. The method essentially consists in superimposing a fine scale model (in a patch) to a large scale model combined together using a partition of energy.…”

Electro-mechanical analysis of composite and sandwich multilayered structures by shell elements with node-dependent kinematics

“…This method was recently adopted by Carrera et al [32] to couple beam elements of different orders and, thus, to develop variable kinematic beam theories. Ben Dhia et al [33][34][35] proposed the Arlequin method to couple different numerical models by means of a minimization procedure. This method was adopted by Hu et al [36,37] for the linear and non-linear analysis of sandwich beams modelled via one-dimensional and twodimensional finite elements, and by Biscani et al [38] for the mechanical analysis of beams, by Biscani et al [39] for the mechanical analysis of plates, and by Biscani et al [40] for the electro-mechanical analysis of plates.…”