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Planar lattice metamaterials, such as periodic beam networks, are often considered as the micropolar continuum, where each material point has two translational degrees of freedom and one rotational degree of freedom. The joints through which bars are linked to one another are generally approximated as rigid. This study focuses on lattices with complex-structured deformable joints. The deformation field in each joint is obtained by conducting structural analyses. Once the "stiffness matrix" of the joint-centered unit cell is obtained by the finite element method, it can be used as the input for the standard procedure of calculating micropolar elastic moduli that are based on the equivalence of strain energy. As a result, effective moduli can be expressed in a semi-analytical form, meaning that only the cell structural stiffness is given numerically. The present model is validated by comparison to the FEM simulations. Particularly, the auxetic and anisotropic properties are discussed for various lattice metamaterials with deformable joints. We then take the obtained effective moduli as inputs to the in-house micropolar FEM code and obtain results agreeing well with the FEM structural simulations. [ABSTRACT FROM AUTHOR]

Based on the symbiotic organisms search (SOS) optimization algorithm, a robust strain gradient (SG) continuum model has been proposed to accurately capture the broadband dispersion relations of one-dimensional acoustic metamaterials. Under the continuous assumption, an unavoidable key step is the Taylor expansion of displacements, which directly influences the accuracy of the corresponding continuum theory. When the wavelength becomes comparable to the periodic characteristic size, the coefficients of Taylor expansions need necessary adjustments due to the discreteness of the microstructure. Thus, the continuum theories still face critical challenges in predicting the broadband dispersion feature. This remains widely open so far. In this study, we attempt to adopt the SOS optimization to determine the optimal Taylor expansion coefficients to guarantee the dispersion diagrams causing the minimal error throughout the first Brillouin zone. The robustness of the SOS-based SG continuum model is demonstrated with three benchmark examples, i.e., the monoatomic, diatomic, and mass-in-mass lattices. Such an attempt of constructing continuum models with the help of optimization tools may shed some new light on continuum mechanics of structure media. [ABSTRACT FROM AUTHOR]