Mechanical Metamaterial Design Using Topology Optimization Method

This paper focused on the designs of chiral multi-material negative poisons ratio microstructure,two-scale later-wise graded lattice structure and three-dimensional microstructures.Firstly,we have presented a new bi-material microstructural design method for chiral auxetic metamaterials.We have designed the anisotropic,orthogonal anisotropic and isotropic bimaterial microstructures of chiral auxetic metamaterials based on the independent point-wise density interpolation(iPDI)method,bi-material model and the asymptotic homogenization method.The optimized results were validated through the finite element simulations;Some representative tension-twist coupling meta-structures were assembled by the optimized twodimensional isotropic chiral microstructure.Additionally,the effective mechanical of microstructures can also be affected by the macro-scale loads and boundary conditions of the macroscopic.Therefore,we designed layer-wise graded lattice two-scale lattice structure;Two new design constraints,namely the structural coverage constraint and the average porosity constraint,are introduced into the proposed optimization formulation to reduce the complexity of the constraints in the previous layer-wise graded design.Numerical examples show validity of the proposed method.It is also found that layer-wise graded lattice structures outperform those with uniform lattice microstructures in terms of structural stiffness.Finite element simulations of constructed models of the optimized designs suggest that graded lattice structures exhibit higher buckling resistance and ultimate load bearing capacity than singlescale solid material structures or uniform lattice structures under the same material usage.Subsequently,we have extended this method to the design of multi-layer two-scale lattice structure with the maximization of fundamental frequency,and extended the two-dimensional homogenization theory to the three-dimensional problems and designed the maximum volume modulus,shear modulus and negative Poisson's ratio microstructure.It is found that the microstructure of the maximum volume modulus is similar to the traditional tensile octahedral structure in the case of sparse mesh.Subsequent studies show that the octahedral lattice structure will become a bending-dominated octahedral closed cavity structure with the increase of the number of grids.For the microstructure with the maximum bulk modulus,the two orthogonal plates are formed with the mesh refining.Finally,we study the negative Poisson's ratio metamaterials,in the case of different volume fraction ratios,the appearance of chiral rotating hinge greatly improves the deformation capacity of the structure.