Computational modelling of soft lattice metamaterials: micromechanical and multiscale procedures

Abstract: Metamaterials are composite materials properly designed to obtain desired optimized mechanical properties that conventional materials cannot exhibit. These have found various and wide applications in many engineering fields, ranging from the most traditional to modern and challenging areas. More recently, a growing interest in the designing and application of metamaterials made of soft lattices has emerged [1]. Lattice structures are cellular materials composed of truss- or beam-like microstructures able to dissipate large amounts of energy, based on the nonlinear constitutive behavior and/or nonlinear geometry of the UC at the microscale and the arrangement of these at the macroscale. These can achieve large elastic deformations, show mechanical instabilities and buckling, absorb energy and mitigate vibrations, exhibit auxetic behaviour, have shape-memory and shape-morphing properties. Thus, the mechanical modelling of soft lattice structures requires the inclusion of large displacements and finite strains [1].
This study presents the micromechanical modelling of soft beam-lattice structures focusing on pre- and post-buckling behaviour. A UC composed of the assemblage of 3D shear-deformable beam elements, including both nonlinear geometry and constitutive effects, is analyzed. Large displacements are included in the beam formulation relying on the corotational approach [2]. First, the linear buckling modes of the UC are evaluated and subsequently used to define its initial imperfect configuration by a randomly combination of the mode shapes. Nonlinear buckling analyses are, then, performed to investigate the effect of the assigned initial imperfection, as well as that of the UC size.
The numerical results are compared with those experimentally obtained for a specimen composed of 2 ×2 ×2 body-centered cubic unit cells 3D printed, obtaining a very satisfactory match. A computational multiscale procedure is, then, formulated. A fictitious 3D continuum model is adopted at the macroscale, where the constitutive relationship is considered as unknown. To derive the constitutive response at each macroscopic point a downscaling is performed, and the response of a UC linked to it, and properly selected to describe in detail all the geometric and mechanical properties of the UC components, is evaluated. To put into communications the macroscopic and microscopic scales homogenization techniques are resorted to.

References
[1] Jamshidian, M., Boddeti, N., Rosen, D.W., Weeger, O., (2020). Multiscale modelling of soft lattice metamaterials: Micromechanical nonlinear buckling analysis, experimental verification, and macroscale constitutive behaviour. International Journal of Mechanical Sciences, 188:105956.
[2] Di Re, P., Addessi, D., (2018). A mixed 3D corotational beam with cross-section warping for the analysis of damaging structures under large displacements. Meccanica, 53(6):1313-1332.

Le mardi 17 septembre 2024 à 15h00 / Amphithéâtre François Canac, LMA

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