Size-dependent buckling instability and recovery of beam-like, architected microstructures

Abstract

Beam-like, architected microstructures (BAMs) can be used in various functional applications, such as micro-electro-mechanical systems (MEMS), energy harvesting, actuation, etc. Designing with high aspect ratios under large deformations, BAMs typically experience severe buckling instability. Therefore, it is of necessity to investigate the mechanical behaviors with respect to the geometric and material nonlinearities. This paper proposes a bilinear size-dependent model using the modified couple stress theory to full formulate the buckling response of the BAMs. Buckling-induced large deformation is studied using the geometric nonlinearity, and the recoverability is investigated based on the material nonlinearity. Experiments and numerical simulations are conducted to validate the theoretical results at the macroscale and microscale, respectively, and satisfactory agreements are obtained. Parametric studies are carried out to study the effects of the material length scale factor-to-thickness ratio χ=lt (i.e., geometric nonlinearity) and plastic factor η (i.e., material nonlinearity). χ and η are further discussed with respect to the effective bending stiffness B¯PAM and volume V¯PAM of the microstructures. The theoretical model presented in this study can be used to predict and tune the mechanical response of BAMs with different architected webbing patterns. Keywords: Beam-like, architected microstructures (BAMs), Modified couple stress theory, Size-dependent large deformation model, Buckling instability and recovery, Bilinear elastic stress-strain relations