Data-driven non-linear elasticity: constitutive manifold construction and problem discretization

Abstract

International audienceThe use of constitutive equations calibrated from data has been implemented into standard numerical solvers for successfully addressing a variety problems encountered in simulation-based engineering sciences (SBES). However, the complexity remains constantly increasing due to the need of increasingly detailed models as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. Standard simulation in computational mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy...), whereas the second one consists of models that scientists have extracted from collected, either natural or synthetic, data. Data-driven (or data-intensive) simulation consists of directly linking experimental data to computers in order to perform numerical simulations. These simulations will employ laws, universally recognized as epistemic, while minimizing the need of explicit, often phenomenological, models. The main drawback of such an approach is the large amount of required data, some of them inaccessible from the nowadays testing facilities. Such difficulty can be circumvented in many cases, and in any case alleviated, by considering complex tests, collecting as many data as possible and then using a data-driven inverse approach in order to generate the whole constitutive manifold from few complex experimental tests, as discussed in the present work

A physics-constrained data-driven approach based on locally convex reconstruction for noisy database

“…The data-driven solution could be strongly influenced by the outliers locating near to the physical manifold but do not conform to the hidden material data pattern (or the latent statistical model) of . Without the knowledge of the underlying data manifold, it requires a large amount of data to achieve sufficiently accurate predictions which is costly [20,31].…”

“…Nevertheless, pure data-driven methodology in the area of simulation-based engineering sciences (SBES) [30] is ineffective since in many physical systems well-accepted physical laws exist while useful data in SBES are very expensive to acquire [20,31]. Thus, it is imperative to develop data-driven simulation approaches that can leverage the physical principles with limited data for highly complex systems.…”

An augmented reality platform for interactive aerodynamic design and analysis

“…Our approach to the problem is data‐driven . This means that we employ manifold learning techniques over a data base of previously computed CFD results.…”

Simple heuristic for data-driven computational elasticity with material data involving noise and outliers: a local robust regression approach

“…The method proposed in [18] has recently been extended to static problems with geometrical nonlinearity [26], three-dimensional continua [8], and dynamic problems [20]. Independently, another data-driven approach that makes use of the manifold learning for estimating the material law has been developed [16,17].…”