Solving strategies for data-driven one-dimensional elasticity exhibiting nonlinear strains
For computational mechanics researchers, this work offers an incremental improvement in solving data-driven elasticity problems with nonlinear strains, but the higher cost limits practical impact.
The authors extend a greedy optimization algorithm combined with ADM for data-driven elasticity, achieving better global optimality in nonlinear strain problems at higher computational cost. They reproduce cyclic testing of a nylon rope and show improved accuracy and robustness with unsymmetrical/noisy data.
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.