2019/03/31 by Laurent Stainier, Adrien Leygue, Michael Ortiz +1 · 117 citations
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Applied mathematics #Computational Science and Engineering #Computational mechanics #Computational science #Computer science #Drilling and Well Engineering #Engineering #Finite element method #Identification (biology) #Mathematics #Mineral Processing and Grinding #Structural engineering #cs.CE
paper · pdf · doi:10.1007/s00466-019-01731-1
published in Computational Mechanics 64(2), 381-393 (Springer Science+Business Media) · Revised version
crossref issued 2019/06/04 · crossref published 2019/06/04 · crossref published-online 2019/06/04 · openalex publication_date 2019/06/04 · crossref created 2019/06/04 · arxiv created 2019/06/18 · arxiv updated 2019/06/20 · crossref deposited 2019/07/03 · crossref published-print 2019/08/01 · openalex created_date 2025/10/10 · crossref indexed 2026/08/05 · openalex updated_date 2026/08/06
This paper presents an integrated model-free data-driven approach to solid mechanics, allowing to perform numerical simulations on structures on the basis of measures of displacement fields on representative samples, without postulating a specific constitutive model. A material data identification procedure, allowing to infer strain-stress pairs from displacement fields and boundary conditions, is used to build a material database from a set of mutiaxial tests on a non-conventional sample. This database is in turn used by a data-driven solver, based on an algorithm minimizing the distance between manifolds of compatible and balanced mechanical states and the given database, to predict the response of structures of the same material, with arbitrary geometry and boundary conditions. Examples illustrate this modelling cycle and demonstrate how the data-driven identification method allows importance sampling of the material state space, yielding faster convergence of simulation results with increasing database size, when compared to synthetic material databases with regular sampling patterns.