Spatio-Temporal stress modeling using an updated lagrangian framework for predictive 3D morphing of kirigami-inspired structures

Abstract

Accurate prediction of large-strain mechanics in thin-film actuators is crucial for designing shape-morphing electronics such as foldable, rollable, and stretchable display modules. We present a finite element framework based on the updated Lagrangian formulation, which evaluates stress and strain on the deformed configuration at each simulation step. By continuously remapping experimentally measured, temperature-dependent material properties, such as elastic modulus, Poisson’s ratio, and density, and accommodating evolving boundary conditions from kirigami cuts, the model captures the spatio-temporal evolution of stress anreveals how interactions between neighboring, stress-inducing, localized actuating regions influence the global three-dimensional shape transformation. Simulations reproduce key phenomena, including synclastic and anticlastic curvatures, asymmetric twisting from pre-strain misalignments, and stress coupling in double- and multi-hinge configurations, with strong agreement to experiments. Time-resolved stress distributions and intermediate shape configurations offer valuable insight into the mechanisms underlying complex deformation behaviors. Because the formulation is agnostic to the specific actuation stimulus, it can be readily extended to multi-stimulus morphing systems. Overall, the framework provides a general predictive tool that links actuator layout and spatio-temporal redistribution of material parameters to the resulting 3D morphology, thus enabling virtual prototyping of adaptive display structures and other morphable thin-film devices.