papers

2025

1. (In)efficacy of auxetic metamaterials for impact mitigation

   Til Gärtner, Richard Dekker, Dennis van Veen, Sanne J. van den Boom, and Lucas Amaral

   International Journal of Impact Engineering 206, Dec 2025, 105402

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   It has been demonstrated that auxetic materials, characterized by a negative Poisson’s ratio, offer enhanced resistance to indentation, shear forces, fracture toughness and the absorption of energy. As such, they are reported in literature to be promising options for impact mitigation in military and space contexts. Auxetic materials are rare in nature, and must therefore be designed and manufactured artificially in order to be applied. Densification of auxetic materials in order to absorb impact energy in a limited area has been the focus in the literature to date. However, this results in a concentration of the force paths, which is not desirable for impact mitigation. In this work, the effects of auxetic densification on the stress distribution over the backside of the auxetic material are addressed using both experimental and simulative trials. In this study, the distinction between auxetic and conventional honeycombs in force transmission characteristics is examined. This is achieved through an analysis of experimental data and the utilization of numerical techniques to enhance comprehension of the internal mechanisms of architected materials in response to impact.

   @article{gärtner25b,
     author = {Gärtner, Til and Dekker, Richard and {van Veen}, Dennis and {van den Boom}, Sanne J. and Amaral, Lucas},
     doi = {10.1016/j.ijimpeng.2025.105402},
     journal = {International Journal of Impact Engineering},
     eid = {105402},
     title = {(In)efficacy of auxetic metamaterials for impact mitigation},
     volume = {206},
     year = {2025},
     month = {12},
   }

2. Force transmission and dissipation in dynamic compression of architected metamaterials

   Til Gärtner, Sanne J. van den Boom, J. Weerheijm, and L. J. Sluys

   Materials Today Advances 28, Dec 2025, 100656

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   Materials engineered with an internal architecture in order to achieve unusual properties, so-called mechanical metamaterials, are a promising candidate in the ongoing quest for lightweight impact mitigation. During impact events, these materials are subject to high strain rates, and the forces occurring due to the deceleration of the impactor are transmitted in a non-uniform way. The prevailing research in the field of impact mitigation focuses largely on the global effects of architected materials, with less attention being paid to the internal mechanisms of these structured materials. While there have been recent studies on the distribution of forces throughout an impact event, less research is devoted to the transmission of forces and the distribution of energy dissipation. The objective of this study is to examine the transition from static deformation patterns to dynamic phenomena for different types and sizes of microstructure, and to understand both the force transmission through the patch and the energetic distributions in different strain rate regimes. To enable this investigation discretized—geometrically as well as materially—nonlinear Timoshenko-Ehrenfest beams are used in implicit and explicit finite element schemes. The transmitted force levels and energy dissipation are investigated for two auxetic architectures (one for each mechanism resulting in a negative Poisson’s ratio) and one non-auxetic architecture. The dynamic force levels transmitted to the back face exhibit an initial peak of a similar magnitude for all investigated strain rates and stabilize to the static stress plateau for each architecture. While the global amount of potential energy remains largely unchanged for all investigated rates, the amount of dissipation and kinetic energy demonstrates a non-linear increase from static deformation to slow and high rate deformation. The phenomena observed in different architectures are highlighted, and the differences are explained and related back to the configurations of the lattices. Notably, the prevalent notion in literature asserting the superiority of negative Poisson’s ratio materials for impact mitigation applications is not replicated in this study.

   @article{gärtner25c,
     author = {Gärtner, Til and {van den Boom}, Sanne J. and Weerheijm, J. and Sluys, L. J.},
     doi = {10.1016/j.mtadv.2025.100656},
     journal = {Materials Today Advances},
     eid = {100656},
     title = {Force transmission and dissipation in dynamic compression of architected metamaterials},
     volume = {28},
     year = {2025},
     month = {12},
   }

3. A strategy for scaling the hardening behavior in finite element modelling of geometrically exact beams

   Til Gärtner, Sanne J. van den Boom, J. Weerheijm, and L. J. Sluys

   Computational Mechanics 75(5), pp. 1471–1482, May 2025

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   A yield function in the stress resultant space of geometrically exact beams based on the elastoplastic cross-sectional warping problem has been proposed by Herrnböck et al. (Comput Mech, 67(3):723–742, 2021). This plasticity framework has been extended with a hardening tensor to model the kinematic hardening effects in Herrnböck et al. (Comput Mech, 71(1):1–24, 2022). While this framework provides scaling for the yield surface in ideal plasticity, scaling in hardening plasticity has not yet been explored. This paper focuses on the numeric modelling of hardening beams and beam assemblies at different geometric scales. Discretization effects from the introduction of plasticity into the geometrically exact beam model are demonstrated. Furthermore, the effects of scaling are explored, and a method to mitigate undesirable effects in order to achieve a size-agnostic formulation is proposed. Consistent geometric scaling is demonstrated for two alternative scaling approaches of the yield function.

   @article{gärtner25a,
     author = {Gärtner, Til and {van den Boom}, Sanne J. and Weerheijm, J. and Sluys, L. J.},
     doi = {10.1007/s00466-024-02572-3},
     journal = {Computational Mechanics},
     pages = {1471--1482},
     title = {{A} strategy for scaling the hardening behavior in finite element modelling of geometrically exact beams},
     volume = {75},
     number = {5},
     year = {2025},
     month = {5},
   }

2024

1. Geometric effects on impact mitigation in architected auxetic metamaterials

   Til Gärtner, Sanne J. van den Boom, J. Weerheijm, and L. J. Sluys

   Mechanics of Materials 191, Apr 2024, 104952

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   Lightweight materials used for impact mitigation must be able to resist impact and absorb the maximum amount of energy from the impactor. Auxetic materials have the potential to achieve high resistance by drawing material into the impact zone and providing higher indentation and shear resistance. However, these materials must be artificially designed, and the large deformation dynamic effects of the created structures must be taken into consideration when deciding on a protection concept. Despite their promise, little attention has been given to understanding the working mechanisms of high-rate and finite deformation effects of architected auxetic lattice structures. This study compares the static and dynamic elastic properties of different auxetic structures with a honeycomb structure, a typical non-auxetic lattice, at equivalent mass and stiffness levels. In this study, we limit the investigation to elastic material behavior and do not consider contact between the beams of the lattices. It is demonstrated that the equivalent static and dynamic properties of individual lattices at an undeformed state are insufficient to explain the variations observed in impact situations. In particular, the initial Poisson’s ratio does not determine the ability of a structure to resist impact. To gain a thorough comprehension of the overall behavior of these structures during localized, high rate compression, the evolution of the elastic tangent properties under compression and shear deformation was monitored, leading to a more profound understanding. Observations made in one configuration of stiffness and mass are replicated and analyzed in related configurations.

   @article{gärtner24,
     author = {Gärtner, Til and {van den Boom}, Sanne J. and Weerheijm, J. and Sluys, L. J.},
     doi = {10.1016/j.mechmat.2024.104952},
     journal = {Mechanics of Materials},
     eid = {104952},
     title = {Geometric effects on impact mitigation in architected auxetic metamaterials},
     volume = {191},
     year = {2024},
     month = {4},
   }

2021

1. Nonlinear multiscale simulation of elastic beam lattices with anisotropic homogenized constitutive models based on artificial neural networks

   Til Gärtner, Mauricio Fernández, and Oliver Weeger

   Computational Mechanics 68(5), pp. 1111–1130, Nov 2021

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   A sequential nonlinear multiscale method for the simulation of elastic metamaterials subject to large deformations and instabilities is proposed. For the finite strain homogenization of cubic beam lattice unit cells, a stochastic perturbation approach is applied to induce buckling. Then, three variants of anisotropic effective constitutive models built upon artificial neural networks are trained on the homogenization data and investigated: one is hyperelastic and fulfills the material symmetry conditions by construction, while the other two are hyperelastic and elastic, respectively, and approximate the material symmetry through data augmentation based on strain energy densities and stresses. Finally, macroscopic nonlinear finite element simulations are conducted and compared to fully resolved simulations of a lattice structure. The good agreement between both approaches in tension and compression scenarios shows that the sequential multiscale approach based on anisotropic constitutive models can accurately reproduce the highly nonlinear behavior of buckling-driven 3D metamaterials at lesser computational effort.

   @article{gärtner21,
     author = {Gärtner, Til and Fernández, Mauricio and Weeger, Oliver},
     doi = {10.1007/s00466-021-02061-x},
     journal = {Computational Mechanics},
     pages = {1111--1130},
     title = {Nonlinear multiscale simulation of elastic beam lattices with anisotropic homogenized constitutive models based on artificial neural networks},
     volume = {68},
     number = {5},
     year = {2021},
     month = {11},
   }