Numerical investigation of the asymmetric inhomogeneous deformation in a nonreciprocal gel under cylindrical indentation

Abstract

Mechanical nonreciprocity is outside the scope of conventional symmetry in mechanical and physical systems, enabling a range of engineering applications such as asymmetric transmission, energy conversion, impact protection, and biological manipulation in unprecedented ways. This study numerically investigates the asymmetric inhomogeneous deformation of a nonreciprocal gel under cylindrical indentation. A nonreciprocal gel exhibits significant mechanical nonreciprocity owing to the buckling of the nanosheets embedded within the hydrogel matrix and is distinguished by three key characteristics: anisotropy, tension-compression asymmetry (TCA), and nonlinearity. To study the effects of these three factors systematically and quantitatively, finite element analysis of the cylindrical indentation is conducted using non-TCA (nTCA), TCA, and TCA-nonlinear (TCAn) models. The results reveal that the nTCA model shows almost no asymmetric deformation, whereas the TCA and TCAn models exhibit significant asymmetric deformation and show good quantitative agreement with the experimental results. The interaction between the TCA factor and the interfacial slip between the cylinder and the gel is essential for asymmetric inhomogeneous deformation. The frictionless condition is also validated in comparison with the previously reported experimental data. The slight difference in results between the TCA and TCAn models is attributed to strain relaxation in the unbuckled direction due to interfacial slip.