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 manufacturingtechniques, lattice materials with man-tailored mechanical properties are easily manufactured. Incombination with superelastic parent materials, such as NiTi alloys, lattice materials allow for largedeformation states without reaching the yield limit of the parent material. The reversibility of thedeformations due to the phase-transformation of the parent material is of interest in any applicationrelying on re-usability or where the initial state must be restored.An adequate prediction of the mechanical response of lattice materials requires models to properlycapture both the deformation mechanisms of the internal architecture and the material response ofthe parent material. The available material models often represent an idealized form of superelasticmaterial 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 whenbeam elements are used instead of continuum elements. For beam elements, uniaxial constitutivematerial 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 facilitatecorrect 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 piecewiselinear 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 elementsin ABAQUS. To study the capabilities of the beam-based models, a comparison is made for variouslattices using the hypoelastic models developed for beam elements and the standard superelasticmodel for continuum elements.The results show that the beam-based models in combination with the hypoelastic material modelsare suitable for describing the effective mechanical response of the additive manufactured latticematerials. The numerical efficiency allows for the employment of the developments in a wide varietyof applications, including large scale lattice materials.