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Short Course held at 3rd ECCOMAS MSF 2017, entitled "Current Research on Solids & Fluids : Computations, FE Code Coupling, Model Reduction, Probability… " has attracted over 40 participants. The lectures were given by Professors Adnan Ibrahimbegovic, Abdellatif Ouahsine and Florian de Vuyst from UTC France, along with Professor Hermann Matthies from TU Bruanschweig Germany and Professor Jose Luis Perez Aparicio from UP Valencia Spain.

The main objective of this course is to provide graduate students and researchers, with an extensive review of numerical models for computational solid and fluid mechanics, and pertinent modern developments in model reduction, probability aspects and uncertainty quantification. It presents the current state-of-the-art in finite element, finite volume and discrete element modeling of nonlinear problems in solid and fluid mechanics, and their coupling with thermal fields and interaction. It will illustrate the difficulties (and their solutions), which appear in a number of applications from mechanical, aerospace and civil engineering or material science. All the sources of nonlinear behavior are presented in a systematic manner, related to kinematics, equilibrium, constitutive equations, or boundary and coupling conditions. Special attention is paid to dealing with a class of problems with nonlinear constitutive behavior of materials, large deformations, and rotations in solid and fluid mechanics. In addition, a detailed presentation of modern probability aspects is given, which is of great interest for current research for quantifying the epistemic uncertainties pertinent to the material heterogeneities, and aleatoric uncertainties pertinent to evolution problems.
Our second objective is to provide the participants with a solid basis for using the FEM, FVM or particle based models and software in trying to achieve the optimal design, and/or to carry out a refined analysis of nonlinear behavior of structures or multibody systems in real-life simulations. The course finally provides a basis to account for any pertinent multi-physics and multi-scale effects, which are most likely to provide significant innovations and break-through in a number of industrial applications.