Polarization-dependent boundary modes in nonlinear mechanical metamaterials

•An analytical framework for soft modes of rotation-cross vector metamaterial chains is proposed.•An anomalous nonlinear phenomenon is found: the polarization index of all nodes are equal.•Through adjusting the polarization index, the morphology of the vector boundary mode can be tuned.•Existence conditions of static-topological-soliton vector boundary modes are clarified.•Different collision responses of boundary modes are revealed for even- and odd-nodes chains. The boundary modes of highly distorted mechanical metamaterials exhibit obvious nonlinear effects. However the characteristics of vector boundary modes (boundary modes with two coupled components—translation and rotation) of nonlinear mechanical metamaterials have not been revealed, which severely limits their applications in vector deformation controls of robots and intelligent structures. In this work, by building the continuous and discrete models of nonlinear mechanical metamaterials with vector couplings, an analytical framework for soft modes of rotation-cross vector metamaterial chains is proposed. An anomalous nonlinear phenomenon is found, namely, the polarization indices (the ratio of displacement to the increment of rotation angle) of all nodes are equal, which is further verified by the experiment. Specially, the results show that the morphology of the vector boundary mode can be tuned through adjusting the polarization index. Based on this, existence conditions of static-topological-soliton boundary modes under couplings of translation and rotation are revealed explicitly, and the results further show that the vector boundary modes based on static-topological-solitons are robust and immune to structural imperfections, which is crucial to achieve precise vector deformation controls. These novel rules and phenomena presented in this work can provide new ideas and important bases for vector deformation controls of nonlinear mechanical metamaterials and their applications in lightweight robots and intelligent structures. [Display omitted]