ABSTRACT

One possible realization for the new computing paradigm called Data-Driven Computational Mechanics (DDCM) relies on the formulation of a topological optimization problem that seeks to optimally assign experimental constitutive data to subdomains of the physical body under consideration, also to be determined as a part of the problem’s solution, while satisfying, in a weak sense, equilibrium, compatibility and boundary conditions. This topological optimization problem is, in general, very difficult to analyse, due to the functional/topological aspects involved, and extremely expensive to solve, due to its NP-hardness. Therefore, as a first step, we are going to set the focus on a collection of optimization problems that arise when the active data set and its corresponding active domain partition are fixed and given in advance. These nonlinear optimization problems can be formulated either on a single domain combined with a data extension by simple functions or on a smooth domain partition with simple data assignment over each subdomain. Moreover, by adopting two/three primal fields and one/two dual fields, we identify four main formulations for the realization of DDCM. Upon linearization, it can be shown that all optimization problems are well posed, and after further analysis, all of them turn out to be equivalent. To show the potential of the formulations proposed and their numerical treatment by means of the finite element method, we investigate two concrete examples, i.e., the fluid flow in a porous media and the linear elasticity problem, but this time in their data-driven form.

SPEAKER CV

Dr. Cristian Guillermo Gebhardt is a Full Professor at the Geophysical Institute, Universitetet i Bergen, Norway, specializing in offshore wind energy. With dual Argentine and German nationalities, he has a robust academic background, including a habilitation in Statics and Dynamics and a Doctorate in Engineering Science. His research interests lie in data-driven structural analysis, computational mechanics, and wind energy. Dr. Gebhardt has received numerous awards, including the Consolidator Grant from the European Research Council. He has a significant teaching and research career, with various publications and contributions to the field of wind energy and computational mechanics.