Data‐driven computing in dynamics

Abstract

SUMMARYWe formulate extensions to Data Driven Computing for both distance minimizing and entropy maximizing schemes to incorporate time integration. Previous works focused on formulating both types of solvers in the presence of static equilibrium constraints. Here formulations assign data points a variable relevance depending on distance to the solution and on maximum-entropy weighting, with distance minimizing schemes discussed as a special case. The resulting schemes consist of the minimization of a suitablydefined free energy over phase space subject to compatibility and a time-discretized momentum conservation constraint. We present selected numerical tests that establish the convergence properties of both types of Data Driven solvers and solutions.

Model-Free Data-Driven inelasticity

“…The convergence properties of the fixed-point solver (13) have been investigated in [1]. The Data-Driven paradigm has been extended to dynamics [3], finite kinematics [34] and objective functions other than phase-space distance can be found in [2]. The well-posedness of Data-Driven problems and properties of convergence with respect to the data set have been investigated in [4].…”

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

“…Under the framework of the third approach, Kirchdoerfer and Ortiz [41][42][43] have proposed a material model-free data-driven method, so called distance-minimizing data-driven computing (DMDD), for modeling elasticity problems. This method is motivated by the fact that there exist two very different types of knowledge in the context of computational mechanics that need to be integrated.…”

Model-free data-driven methods in mechanics: material data identification and solvers

“…The convergence properties of the fixed-point solver (13) have been investigated in [7]. The Data-Driven paradigm has been extended to dynamics [9], finite kinematics [13] and objective functions other than phase-space distance can be found in [8]. The well-posedness of Data-Driven problems and properties of convergence with respect to the data set have been investigated in [1].…”

“…Kirchdoerfer and Ortiz [7,8,9] have recently proposed a new class of problems in static and dynamic elasticity, referred to as Data-Driven problems, defined on the space of strain-stress field pairs, or phase space. The problems consist of minimizing the distance between a given material data set and the subspace of compatible strain fields and stress fields in equilibrium.…”