Additive manufacturing has enabled the fabrication of lightweight materials with
intricate cellular architectures. These materials are interesting due to their
properties which can be optimized upon the choice of the parent material and the
topology of the architecture, making them appropriate for a wide range of
applications including lightweight aerospace structures, energy absorption,
thermal management, metamaterials, and bioscaffolds. In this paper we
present the simplest initial computational framework for the analysis, design,
and topology optimization of low-mass metallic systems with architected
cellular microstructures. A very efficient elastic-plastic homogenization of a
repetitive Representative Volume Element (RVE) of the microlattice is proposed.
Each member of the cellular microstructure undergoing large elastic-plastic
deformations is modeled using only one nonlinear three-dimensional (3D) beam
element with 6 degrees of freedom (DOF) at each of the 2 nodes of the
beam. The nonlinear coupling of axial, torsional, and bidirectional-bending
deformations is considered for each 3D spatial beam element. The plastic hinge
method, with arbitrary locations of the hinges along the beam, is utilized
to study the effect of plasticity. We derive an explicit expression for the
tangent stiffness matrix of each member of the cellular microstructure using a
mixed variational principle in the updated Lagrangian corotational reference
frame. To solve the incremental tangent stiffness equations, a newly proposed
Newton homotopy method is employed. In contrast to the Newton’s method
and the Newton–Raphson iteration method, which require the inversion of
the Jacobian matrix, our homotopy methods avoid inverting it. We have
developed a code called CELLS/LIDS (CELLular Structures/Large Inelastic
DeformationS), which provides the capabilities to study the variation of
the mechanical properties of the low-mass metallic cellular structures by
changing their topology. Thus, due to the efficiency of this method we can
employ it for topology optimization design and for impact/energy absorption
analyses.
Keywords
architected cellular microstructures, large deformations,
plastic hinge approach, nonlinear coupling of
axial-torsional-bidirectional bending deformations, mixed
variational principle, homotopy methods
Center for Advanced Research in the
Engineering Sciences, Institute for Materials, Manufacturing,
and Sustainment
Texas Tech University
Lubbock, TX
United States
Center for Advanced Research in the
Engineering Sciences, Institute for Materials, Manufacturing,
and Sustainment
Texas Tech University
Lubbock, TX
United States
Center for Advanced Research in the
Engineering Sciences, Institute for Materials, Manufacturing,
and Sustainment
Texas Tech University
Lubbock, TX
United States