Simulations of superelastic lattice materials manufactured by additive manufacturing using a hypoelastic material model

Presentation given at GAMM2024 held in Magdeburg

Lattice materials offer great potentials in engineering applications as their internal architecture sig-
nificantly influences their effective mechanical response. With progressing additive manufacturing
techniques, lattice materials with man-tailored mechanical properties are easily manufactured. In
combination with superelastic parent materials, such as NiTi alloys, lattice materials allow for large
deformation states without reaching the yield limit of the parent material. The reversibility of the
deformations due to the phase-transformation of the parent material is of interest in any application
relying on re-usability or where the initial state must be restored.
An adequate prediction of the mechanical response of lattice materials requires models to properly
capture both the deformation mechanisms of the internal architecture and the material response of
the parent material. The available material models often represent an idealized form of superelastic
material behavior, from which the experimentally measured response of real materials often deviate.
The modeling of lattice materials by means of the Finite Element Method is often more efficient when
beam elements are used instead of continuum elements. For beam elements, uniaxial constitutive
material models are sufficient.
To give adequate predictions using beam-based models, a user defined material model is imple-
mented to account for the superelastic constitutive behavior of an additive manufactured material.
The uniaxial material model is based on a hypoelastic constitutive law using the UHYPEL user sub-
routine of ABAQUS 2023/Standard (Dassault Systèmes Simulia Corp., Providence, RI, USA). To facilitate
correct predictions of unloading/reloading loops at intermediate (transformation) strains, case dis-
tinction is utilized. A least squares fit is used to obtain a smooth function for representing the me-
chanical response of the parent material obtained by experimental tests. Additionally, a piecewise
linear function is fitted by hand. The intersection points of the piecewise linear functions are fur-
ther used as input for the standard superelastic model readily available only for continuum elements
in ABAQUS. To study the capabilities of the beam-based models, a comparison is made for various
lattices using the hypoelastic models developed for beam elements and the standard superelastic
model for continuum elements.
The results show that the beam-based models in combination with the hypoelastic material models
are suitable for describing the effective mechanical response of the additive manufactured lattice
materials. The numerical efficiency allows for the employment of the developments in a wide variety
of applications, including large scale lattice materials.