🤖 AI Summary
This work proposes a data-driven computational framework for geometrically exact beams that overcomes the limitations of traditional structural analysis, which relies on predefined constitutive models and often discards valuable experimental information, thereby failing to accurately capture the true nonlinear mechanical response. The proposed approach integrates greedy optimization with the alternating direction method (ADM), employs a director-based kinematic description, and introduces a finite element–assisted data initialization strategy alongside a thermodynamically consistent penalty formulation to weakly enforce physical admissibility. Numerical results demonstrate that the method yields discrete stress–strain fields satisfying thermomechanical consistency and achieves solutions significantly closer to the global optimum than standard ADM, markedly enhancing both predictive accuracy and data utilization in modeling nonlinear beam behavior.
📝 Abstract
In the last decade, data-driven computational mechanics (DDCM) has emerged as a novel paradigm in computational mechanics, enabling the direct use of constitutive data - such as stress-strain pairs obtained from experiments, without relying on ad-hoc material models and thereby avoiding information loss. In this work, we extend our data-driven solving strategy GO-ADM, which combines a greedy optimization algorithm with the alternating direction method (ADM), to the structural analysis of geometrically exact beams formulated using director-based kinematics. We discuss a data initialization strategy for nonlinear systems based on a conventional finite element analysis of the same structure using a prescribed constitutive model. The resulting discrete stress and strain fields, possibly obtained under multiple loading scenarios, may also be employed as artificial datasets for the subsequent data-driven computations. Furthermore, we investigate the thermomechanical consistency of both the dataset and the discrete solution, and propose a weak enforcement of this consistency in the latter via a penalty approach. Numerical examples involving single- and multi-member structures demonstrate that the proposed penalty term leads to thermomechanically consistent discrete stress and strain fields. Moreover, for the studied examples, the solving strategy GO-ADM yields a generally improved approximation of the globally optimal solution compared to the standard ADM-based direct solver.