Wavelength-dependent strain gradient modeling of two-dimensional lattice metamaterials

A robust generalized continuum model called the wavelength-dependent strain gradient continuum model (WDSGM) has been proposed to predict dispersion properties of two-dimensional (2D) periodic lattice metamaterials. The key idea lies in replacing the classical Taylor expansion of displacement fields with a wavelength-dependent one, naturally leading to new equations of motion and therefore a significantly improved capability of predicting dispersion characteristics. For different 2D lattices, dispersion results derived from the proposed WDSGM are verified by comparing with those obtained from the discrete model and the existing strain gradient continuum model (SGM) in the irreducible Brillouin zone. Based on the proposed model, the effects of SG orders have been investigated. Results suggest that considering the wavelength-dependent Taylor expansion and increasing the SG order are beneficial to improving the predictive performance of continuum models. The proposed model is free of any instability issue which is challenging for many existing SG methods. Under given parameters, the proposed WDSGM with eighth-order truncation is enough to predict the dispersion relation of three lattices, i.e., the square, triangular and hexagonal lattices throughout the irreducible Brillouin zone.