Collapse of periodic planar lattices under uniaxial compression, part II: Dynamic crushing based on finite element simulation

The collapse strength is analyzed for periodic planar lattices under uniaxial compression. In part I, the quasi-static strengths of the lattices are predicted by limit analysis [1]. In contrast to part I, the dynamic crushing is studied by finite element simulations in this part. Under different impact velocities, the deformation modes and the average stress of lattices with various relative densities are studied, whilst the emphasis is put on the inertia effect. It is found that the average stress increases with the impact velocity, the density of the base material and the relative density of the lattice. Therefore, the average dynamic stress can be expressed as the sum of the average static stress and the dynamic enhancement caused by the inertia effect. The average dynamic stress for membrane-dominated lattices is higher than that of bending-dominated lattices, but the difference in the dynamic enhancement is not as significant as that in the static collapse stress. According to the shock wave theory, the empirical formula of a hexagonal lattice under uniaxial compression is modified and generalized to all the interested lattices. The empirical formulas based on the shock wave theory agree well with the FE simulations, especially for the membrane-dominated lattice that has less transverse expansion.