Solving strategies for data-driven one-dimensional elasticity exhibiting nonlinear strains

TL;DR

This paper introduces an enhanced data-driven solving strategy for nonlinear one-dimensional elasticity problems, combining greedy optimization, ADM, and Newton-Raphson methods to improve solution accuracy at increased computational cost.

Contribution

It extends previous methods by integrating greedy optimization with ADM and Newton-Raphson, improving solution accuracy for nonlinear elasticity problems with complex data.

Findings

Achieves better approximation of globally optimal solutions.

Reproduces cyclic testing results for nylon ropes.

Improves accuracy and robustness with noisy and unsymmetrical data.

Abstract

In this work, we extend and generalize our solving strategy, first introduced in [1], based on a greedy optimization algorithm and the alternating direction method (ADM) for nonlinear systems computed with multiple load steps. In particular, we combine the greedy optimization algorithm with the direct data-driven solver based on ADM which is firstly introduced in [2] and combined with the Newton-Raphson method for nonlinear elasticity in [3]. We numerically illustrate via one- and two-dimensional bar and truss structures exhibiting nonlinear strain measures and different constitutive datasets that our solving strategy generally achieves a better approximation of the globally optimal solution. This, however, comes at the expense of higher computational cost which is scaled by the number of "greedy" searches. Using this solving strategy, we reproduce the first cycle of the cyclic testing for a nylon rope that was performed at industrial testing facilities for mooring lines manufacturers. We also numerically illustrate for a truss structure that our solving strategy generally improves the accuracy and robustness in cases of an unsymmetrical data distribution and noisy data.