Numerical and constitutive modeling of quasi-static and dynamic mechanical behavior in graded additively manufactured lattice structures

Metallic lattice structures based on triply periodic minimum surfaces (TPMS) have attracted extensive attention for their potential application in lightweight and energy absorption. The underlying phenomena, mechanisms and modelling under the crushing responses from quasi-static to shock conditions still remain to be revealed. This work systematically investigates the mechanical behaviour of graded additively Schoen-F-RD (FRD) lattice structures under various loading rates. Under dynamic compression, FRD lattices exhibit the ability to withstand larger densification strains at higher plateau strengths, thus, holding enhanced energy absorption capabilities. At medium strain rates, it is the rate-dependence of lattice base material dominates in the strength enhancement, while, at higher strain rates, the role of inertia effect becomes notable. Furthermore, an empirical formula is introduced to predict the shock stress responses. Finally, constitutive models with strain-rates are proposed for the uniform and graded lattices. These findings can provide excellent guidance on the design of energy-absorbing structures.