Engineering Lattice Metamaterials – Simulation and Experimental Validation

Engineering Lattice Metamaterials – Simulation and Experimental Validation Assoc. Prof. Melanie Todt Institute of Lightweight Design and Structural Biomechanics www.tuwien.ac.at MEBioSys, Brno 2025 Motiviation – Lattice Metamaterials Slender lattices High strength to density ratio Allow for tailoring towards desired properties -Auxetic metamaterials -Bi-stable metameterials Huge potential for optimization 2 B. Hanks, et al, Additive Manufacturing, Vol. 35, 101301, 2020 V.V. Vasiliev, A.F. Razin, Compos. Struct., Vol. 76, 182–189, 2006 Modeling Concepts 3 Discrete Models Each lattice member resolved Detailed geometric model Load introduction? Computational demanding Local phenomena can be captured in detail Continuum Models Homogeneous solid Effective response Material Parameters? Computationally efficient Local phenomena not/partly captured M. Schasching, PhD Thesis, TU Wien 2023 Modeling Concepts 4 Combined Approaches – e.g. embedding approach M. Schwab, M. Todt, H.E. Pettermann, Journal of Composite Materials, Vol 52, https://doi.org/10.1177/0021998318755865 Overview Discrete Models Continuum Modeling Summary 5 Overview Discrete Models -Modeling -Examples Continuum Modeling Summary 6 Modeling 7 Beam Element Models Lattice members discretized with beam elements How to represent -material aggregation at nodes? -material nonlinearities? -boundary conditions / load introduction? -geometric imperfections? Computationally efficient Postprocessing Continuum Element Models Lattice members discretized using continuum elements Discretization is trade off between -required elements over the strut thickness. -computational resources. Computationally more demanding Example – Pre Stressed Lattices Fibers are pre-stressed to increase the buckling load of the lattice Aims: -Proof of concept -Investigate influence of pre-stress on buckling load Beam model of single cell, elastic material Comparison with experiments 8 A. Köllner, M. Todt, G. Ganzosch, C. Völlmecke, Thin-Walled Structures 145, 106396, https://doi.org/10.1016/j.tws.2019.106396 Example – Pre Stressed Lattices Pre-stress leads to an increase of the buckling load Good agreement with experiments Manufacturing of multi-cell arrangements? 9 Example – Superelastic Lattices 16 Stiff lattice Compliant lattice Loading scenario Simulation of cell structures Example – Superelastic Lattices ASM model overestimates the reaction forces for finite structures Applicability of ASM model? 17 Overview Discrete Models Continuum Modeling -Micropolar Continuum Model -Example Summary 18 Micropolar Continuum Model 19 Micropolar Theory Scenarios where criteria of separation of scales is not met Displacement and additional rotational DOFs Material constants e.g. by energy based homogenization [1,2] [1] Z.P. Bazant, Int. J. Solids Struct. 8 , 1972, 327–346, https://doi.org/10.1016/0020-7683(72)90093-5 [3] R.S. Kumar, D.L. McDowell, Int. J. Solids Struct. 41, 7399–7422, 2004, https://doi.org/10.1016/j.ijsolstr.2004.06.038 Micropolar Continuum Model 20 FEM Implementation Geometric nonlinear behavior – large rotations Stiffness matrix via finite differences of perturbed residuals [3] FEM implementation as 3D user element [3] S. Bauer et al., Comput. Methods Appl. Mech. Eng. 199, 2010, 2643–2654, https://doi.org/10.1016/j.cma.2010.05.002 Example – Lattice Beam Buckling 21 Example – Lattice Beam Buckling 22 Critical load slightly overestimated Unstable post-buckling response captured with MC model Example – Lattice Beam Buckling 23 Results for 2 different discretizations Good agreement for displacements and rotations Model still needs further improvement in terms of computational efficiency Overview Discrete Models Continuum Modeling Summary 24 Summary There exists no “one-fits-all” model Model has to be appropriate for the questions asked -It is has to be built correctly -It has to be able to capture the underlying physics Validation against experiments or more sophisticated models necessary -Experiments should be mappable to a model. -Effect of boundary conditions has to be addressed. Interpretation of results always under consideration of the modeling assumptions 25