GALCIT Colloquium

Recent advances in highly deformable structures necessitate simulation tools that can capture nonlinear geometry and nonlinear material. We propose machine learning, neural networks (NN) in particular, to capture this nonlinearity and solve highly nonlinear inverse problems in structural mechanics. Two representative problems will be discussed in this talk.

In the first problem, we use NN to reduce the number of variables and speed up the simulation by orders of magnitude. As a test case, we explore the dynamical simulation of a slinky, a pre-compressed elastic helix that is widely used as a toy for children. However, most often the deformation of a slinky can be fully captured by the deformation of its helix axis. Instead of simulating the entire helical structure, the axis of the helix is a reduced-order representation of this system. We use NN to store the elastic forces of the slinky in its reduced-order representation, utilizing the concept of neural ordinary differential equations. The NN is trained using data from a fine-grained 3D rod simulation called the Discrete Elastic Rods (DER). Once the elastic forces in the reduced representation are stored in the NN, force balance equations can be solved in this representation for the dynamic simulation. This results in savings in computational time without much impact on its physical accuracy.

In the second problem, we explore shape morphing structures that spontaneously transition from planar to 3D shapes. This is a transformative technology with broad applications in soft robotics and deployable systems. However, realizing these morphing structures that can achieve certain target shapes is challenging and typically involves a painstaking process of trials and errors with complex local fabrication and actuation. We propose a rapid design approach for fully soft structures that can achieve targeted 3D shapes through a fabrication process that happens entirely on a 2D plane. By combining the strain mismatch between layers in a composite shell and locally relieving stress by creating kirigami cuts, we are able to create 3D free buckling shapes from planar fabrication. However, the large design space of the kirigami cuts and strain mismatch presents a challenging task of inverse form finding. We develop a symmetry-constrained active learning approach to learn how to explore the large design space strategically. Interestingly, we report that, given a target 3D shape, multiple design solutions exist and our physics-guided machine learning approach can find them in a few hundred iterations. Desktop-controlled experiments and finite element simulations are in good agreement in examples ranging from peanuts to flowers.