Data-driven design of well-behaved nonlinear structures: a case study on the von Mises truss

Well-behaved nonlinear structures, which exploit elastic instabilities for functionality, have garnered increasing interest for rapid shape shifting and energy dissipation applications. One of the current bottlenecks during design is the large computational cost associated with nonlinear solvers when targeting a specific function through inverse design. Advances in machine learning (ML) tools have enabled a more efficient inverse design process. However, generating sufficient data efficiently to train the ML models still remains a challenge. This paper presents a novel computational toolbox that automates the generation of nonlinear finite element models, submission of analyses, monitoring of ongoing analyses, termination of analyses upon meeting specified criteria, and post-processing of results. With this computational toolbox, we develop three types of ML models: two forward models that classify and characterise nonlinear equilibrium paths based on the structure’s properties (material and geometry), and one backward model for predicting the structure’s properties from key features of the nonlinear equilibrium path. We evaluate various ML algorithms for each model type, provide recommendations, and explore algorithmic modifications to enhance prediction accuracy. To illustrate the effectiveness of the proposed tools, we present two case studies where the von Mises truss plays a key role: a) a recoverable energy dissipating mechanical metamaterial and (b) a vibro-impact capsule robot. Our findings highlight the potential of data-driven approaches to efficiently enable the design of high-performance nonlinear structures that harness instabilities for targeted functionalities.