A one-dimensional model for mechanical coupling metamaterials using couple stress theory

Abstract

A new model for a one-dimensional (1D) metamaterial model is formulated based on the couple stress theory. Different point groups of crystal will affect the mechanical couplings in the 1D metamaterial model. We find that when the material belongs to D2 point group, an unusual set of equations is decoupled from governing equations: axial force–torsion–warping (FTW) metamaterial model, which describes an unusual mechanical coupling that cannot occur in traditional materials. The deformation behaviors of the current model under a different axial force are analyzed by using the FTW metamaterial model. The numerical results show that the middle part of the current model has maximum torsional deformation when subjected to sine-type axial force. Since the end of the current model is fixed, the current model does not have compressional deformation globally. Moreover, when the current model is subjected to cosine-type axial force, the FTW coupling is successfully achieved. Then, we study a rod-like metamaterial model under an axial end force. The results show that the compressional deformation occurs at the free end, with a counterclockwise torsion. The current work provides guidance for the structural design and theoretical analysis of the rod-like metamaterial when using the couple stress theory.

Size and Temperature Effects on Band Gap Analysis of a Defective Phononic Crystal Beam

“…The size effect induces distinct mechanical properties in microstructures compared to macrostructures. Currently, many high-order theories are proposed to describe the size effect [35][36][37][38][39][40][41][42][43][44], such as the couple stress theory [45], strain gradient theory [46], non-local elasticity theory [47], surface elasticity theory [48], and reformulated strain gradient elasticity theory [49][50][51]. Utilizing the couple stress theory, Yang et al established the modified couple stress theory (MCST), which specifically accounts for the symmetric curvature tensor with one additional material parameter for isotropic material.…”

Study on the Equivalent Stiffness of a Local Resonance Metamaterial Concrete Unit Cell

“…Although these studies have calculated the bandgap values of the concrete cells of metamaterials under different parameter conditions and obtained the corresponding parameter laws, we cannot establish the specific correspondence between the bandgap frequency and the parameter values, and in actual engineering, when facing a project-specific frequency, we cannot directly determine the parameter conditions of the concrete cells of metamaterials, which creates a need to study the specific numerical relationships between equations. Gongye Zhang et al [31] proposed a new one-dimensional metamaterial model, where they studied a rod-like metamaterial model under an axial end force, with the results showing that compressional deformation occurred at the free end, with counterclockwise torsion. Youchuan Zhou et al [32] designed a novel three-dimensional mechanical metamaterial with lowfrequency bandgaps and a negative Poisson's ratio, and the bandgap characteristics of the proposed metamaterial were determined computationally, with the mechanism for bandgap occurrence characterized as the local resonance of ligaments and resonators.…”