A data‐driven framework for evolutionary problems in solid mechanics. Issue 3 (17th November 2022)

• Record Type: Journal Article
• Authors: Poelstra, Klaas; Bartel, Thorsten; Schweizer, Ben
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 103:Issue 3(2023)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-11-17
• Subjects: Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.202100538
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: Data‐driven schemes introduced a new perspective in elasticity: While certain physical principles are regarded as invariable, material models for the relation between strain and stress are replaced by data clouds of admissible pairs of these variables. A data‐driven approach is of particular interest for plasticity problems, since the material modeling is even more unclear in this field. Unfortunately, so far, data‐driven approaches to evolutionary problems are much less understood. We try to contribute in this area and propose an evolutionary data‐driven scheme. We present a first analysis of the scheme regarding existence and data convergence. Encouraging numerical tests are also included. Abstract : Data‐driven schemes introduced a new perspective in elasticity: While certain physical principles are regarded as invariable, material models for the relation between strain and stress are replaced by data clouds of admissible pairs of these variables. A data‐driven approach is of particular interest for plasticity problems, since the material modeling is even more unclear in this field. Unfortunately, so far, data‐driven approaches to evolutionary problems are much less understood. We try to contribute in this area and propose an evolutionary data‐driven scheme. We present a first analysis of the scheme regarding existence and data convergence. Encouraging numerical tests are also included.…