Design Principle in Localized Density Coefficient of 3D-Printing Foamlike Mechanical Metamaterials Toward a High-Compression Strain Energy

Due to the urgent requirements of high energy absorption and compression resistance in their potential and practical applications, 3D-printing mechanical metamaterials have attracted great passions and interests. However, there are few studies on the 3D models to hinder the analytical design and optimization of mechanical metamaterials from practice. This study reports on a 3D strain-energy model to explore the design principle in localized density coefficient and achieve a high-compression energy absorption. Initially, two 3D strain-energy models are formulated for the foamlike spatial mechanical metamaterials, based on the plate theory and principle of energy for unit, respectively. A constitutive equation between strain-energy density and localized density coefficient is developed to characterize the strain energy–displacement and deformation behaviors. Then, nonuniform foamlike spatial metamaterials are conducted to investigate the coupling principles in geometric parameters (pore morphology, porosity, pore position) and their programming deformation modes. A series of analytical simulations are carried out to present the mechanical behaviors of foamlike spatial mechanical metamaterials, and the simulation results are compared with the experimental measurements, where a good agreement is achieved. Finally, this study aims at the 3D strain-energy model to achieve a programmable deformation mode and largely extend the practical applications of foamlike spatial mechanical metamaterials.