Constitutive Modeling of Lightweight Metamaterials Derived from Triply Periodic Minimal Surface Lattices for 3D Printing

Abstract

Due to the advancements in additive manufacturing and increased applications of additive manufactured structures, it is essential to fully understand both the elastic and plastic behavior of cellular materials, which include the mathematically-driven sheet/shell lattices based on triply periodic minimal surface (TPMS) that have received significant attention recently. The compressive elastic and plastic behaviors have been well established for many TPMS latticed structures, but not under multiaxial loading. Furthermore, TPMS lattices are computationally expensive to model explicitly (i.e. micromechanical) when used in latticing various structures for enhanced multi-functionality. In this study, the TPMS lattice structure is viewed as a novel material class at the macroscopic scale, and a complete framework is presented to develop a macroscopic constitutive model of these lattice structures. As a demonstration, a full constitutive model is developed to model the behavior of IWP sheet-based TPMS lattice with a 28% relative density, which incorporates macroscopic plasticity and damage models. This model is available as a UMAT and has been verified and validated numerically with the micromechanics model that consists of a one unit cell representative volume element of IWP sheet-based TPMS lattice with a 28% relative density, in various loading cases. In addition, the continuum model is validated with a cantilever beam problem made of the same lattice where a perfect match is seen between the two responses. This drastically reduces the computational cost of explicitly modeling these structures by hundreds and thousands of times, specially on a large scale, while accurately predicting their behavior under multiaxial and complex loading cases.

Date of Award	7 May 2024
Original language	American English
Supervisor	Rashid Abu Al Rub (Supervisor)