Mechanical Properties Analysis And Optimization Of Several Lattice Metamaterials

Metamaterials have been extensively studied due to their excellent properties,which are caused by their internal structures rather than source materials.A broad range of applications has been achieved through special structural designs.The mechanical properties of several lattice metamaterials,related to damage and fracture,acoustics,energy absorption,are investigated.A SOS-based optimization algorithm is developed for efficient meterial design.This work includes the following parts:(1)The effect of prestress on the damage strengths of lattice metamaterials is investigated.We aim to adjust the loading bearing capability of lattices by periodically introducing prestress into particular lattice segments.Based on existing studies,we focus on the following two problems deserving further investigations.First,results have been provided based on a single cell with/without taking into account the interactions between each two of neighboring individual cells.Second,it is interesting to search for the optimal distribution of prestress in lattices subjected to a specific load.For the former,we propose a set of constraint equations for implementing periodic boundary conditions(PBC)on a periodic unit cell and confirm its correctness.We then use the proposed method to calculate the initial damage surface of four kinds of prestressed lattice unit cells under PBC.For the latter,we build a new optimization algorithm with the help of the so-called Symbiotic-Organisms-Search technique(SOS),to calculate the optimal prestress setting corresponding to the requested properties.The iterative results show that the optimal prestress setting can result in a significant improvement in the failure load of the structure in a specific direction.As an example,the optimal prestress setting is found to almost double the critical load to failure of the lattice in a special direction.(2)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.(3)We investigate the energy absorption and dissipation mechanisms of large deformable lattices made of source materials that can only bear small elastic deformations.Since conventional energy-absorbing structures often absorb energy through microstructure-level plastic deformations,irreversible damages remain after unloading.In contrast,the present lattice is based on corrugated beams,which allow the structure to undergo large elastic deformation.The mechanical properties of the structure can be programmed by adjusting geometric parameters.This lattice has a smoother force-displacement curve and more adjustable deformation patterns compared with other existing multi-stable structures.Numerical analyses show that adjusting loading speed and the curvature of the corrugated beam can program the smoothness of the force-displacement curve,the energy dissipation capacity of the structure and the sequence of snap-through in corrugated beams.