Deep learning of buckling instability in geometrically symmetry-breaking kirigami

Abstract

Kirigami, subjected to escalating strain, frequently exhibits pronounced instability, coupled with remarkable flexibility and extraordinary extensibility. This behavior holds significant relevance for domains associated with malleable and reconfigurable surfaces, including stretchable electronics and modifiable functional devices. Nonetheless, conventional design methodologies, anchored in geometric symmetry and governed by minimum energy principles, tend to manifest buckling instabilities restricted to symmetric and anti-symmetric modes. To scrutinize the mechanisms of buckling behavior that disrupt geometric symmetry and comprehend the influence of geometry on programmability during reconfiguration, we propose an innovative strategy for kirigami’s design. This strategy capitalizes on advanced deep learning methodologies, employing convolutional neural networks (CNNs) for categorizing buckling modes and recurrent neural networks (RNNs) for prognosticating constitutive relationships. Our approach furnishes a programmable design solution adept at identifying optimal kirigami patterns, characterized by their superior tensile strength and distinct buckling conformations, thereby fulfilling a diverse array of functional necessities. Our results illustrate that the proposed method displays a high level of precision in distinguishing between buckling modes of geometric symmetry and patterns that deviate from such symmetry. The buckling mode space has been extended and rediscovered, allowing unique modes to have the potential to be adopted into functional devices. Additionally, it demonstrates minimal losses in predicting constitutive relationships. Intriguingly, we discovered that tensile responses are geometry-centric and adjustable. Buckling modes showcase a dependency on geometry, with certain geometric parameters either significantly augmenting the sensitivity of buckling modalities or causing the buckling instability modes to become apathetic and unresponsive. Guided by the principle of target-led pattern parameter design, we proffer prospective tactics for the design of kirigami capable of delivering the desired mechanical performance. Moreover, we explore the feasibility of employing alternative biological materials in these designs.