Speaker
Description
Data-driven mechanics, introduced by Kirchdoerfer and Ortiz [1], replaces traditional material models with datasets of discrete stress-strain pairs. The solution to boundary value problems is obtained by minimizing a distance between these pairs, denoted material states, and pairs of stress and strain, which fulfill equilibrium and kinematic compatibility and are termed mechanical states.
While the original framework was introduced for elasticity, an extension to encompass inelastic material behavior is a crucial yet challenging step. In our extension [2,3], we address this challenge by introducing a history surrogate, which stores essential information about stress-strain paths of an associated material. At the end of each time step, a propagator updates this history surrogate. For truss structures, intuitive choices for the history surrogate are feasible and accurate results can be obtained, as shown in [3]. However, in higher dimensions, a manual construction of this quantity becomes impractical. To overcome this, we employ a neural network as the propagator, which autonomously handles the task of defining and updating the history surrogate based solely on discrete stress and strain data. We thereby eliminate the need for explicit update rules or user intervention and obtain a scalable framework for addressing higher-dimensional problems.
We apply this framework to truss structures with a path-dependent material response and compare results for an intuitive and neural network propagator. Furthermore, we extend the discussion to two-dimensional problems, examine the challenges associated with this higher-dimensional setting and offer insights into potential strategies for overcoming related issues. We demonstrate the scalability and flexibility of the enhancement by presenting results for two-dimensional boundary value problems.
[1] T. Kirchdoerfer, M. Ortiz, Data-driven computational mechanics, Comput. Methods Appl. Mech. Engrg. 304 (2016) 81-101
[2] T. Bartel, M. Harnisch, B. Schweizer, A. Menzel, A data-driven approach for plasticity using history surrogates: Theory and application in the context of truss structures, Comput. Methods Appl. Mech. Engrg. 414 (2023), 116-138
[3] K. Poelstra, T. Bartel, B. Schweizer, A data-driven framework for evolutionary problems in solid mechanics, J. Appl. Math. Mech (3) (2022), e202100538
