presentations

2025

1. Are Auxetics Better for Protection?

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

   poster presentation, 28th Engineering Mechanics Symposium, Hotel Papendal, Arnhem, 30. – 31. Oct 2025

   Poster Prize Poster

   The poster won the poster contest at the 28th Engineering Mechanics Symposium.

2. Numerical Investigation into Rate Effects in Architected Metamaterials under Extreme Loading Conditions

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

   oral presentation, 8th International Conference on Computational Modelling of Fracture and Failure of Materials and Structures, Universidade do Porto, 4. – 6. Jun 2025

   Abs Slides

   The introduction of advanced manufacturing technologies has made architected metamaterials widely available for use in a variety of applications. Of these applications, impact mitigation in sports, space, and military contexts is of particular interest. Herein, rapid loading regimes may lead to both material and geometric nonlinearities. While the behavior of architected materials in static conditions has been widely documented, the dynamic response remains largely unexplored. In the dynamic regime, investigations tend to focus on the global response of the structure for impact mitigation [1]. However, the meso-structure of the architected material has been shown to exert a significant influence on the overall response [2]. To ensure informed design decisions in impact mitigation, it is of paramount importance to consider the dynamic response of architected materials for protection purpose. Experiments are constrained to recording the global response. Computational tools, however, facilitate insight into the processes at meso-scale of architected materials. In particular, the collapse patterns of individual truss members and their effects on the surrounding material are of interest to assess load spreading and transmission characteristics. Numerical tools allow investigation of the local loading conditions of each member of the structure and the subsequent effects on the global protection efficacy of the structure. This research examines the influence of varying loading rates on architected materials of different geometries and meso-scale structure sizes, employing the use of structural finite elements. To this end, the algorithmic aspects are first presented, along with relevant numerical examples that demonstrate the capabilities of the model. Subsequently, the investigated architectures are described. A comparison of these structures in a static context is established, and the effects of different loading rates on the response as well as local and global collapse patterns are presented. The scaling of the internal structures and subsequent changes in collapse patterns are investigated, and the interplay between geometric structural scaling, loading rate, and plastic deformation is analyzed. [1] Bohara, R. P., Linforth, S., Nguyen, T., Ghazlan, A., & Ngo, T. (2023). Anti-blast and -impact performances of auxetic structures: A review of structures, materials, methods, and fabrications. Engineering Structures, 276, 115377. [2] Gärtner, T., van den Boom, S., Weerheijm, J., & Sluys, L. (2024). Geometric effects on impact mitigation in architected auxetic metamaterials. Mechanics of Materials, 191, 104952.

2024

1. Architectural Choices for Auxetic Metamaterials and their Effects on Impact Mitigation

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

   invited presentation, 27th Engineering Mechanics Symposium, Hotel Papendal, Arnhem, 22. – 23. Oct 2024

   Abs Slides

   Auxetic (negative Poisson’s ratio) materials are claimed to offer distinct advantages for the mitigation of high-velocity impacts in military or space applications, such as the impact of bullets and fragments on personal protective equipment or the mitigation of space debris threatening satellites at orbital velocities. These advantages include enhanced indentation resistance, shear resistance, fracture toughness, and energy absorption [1]. The existence of auxetic materials in nature is scarce, requiring the artificial design of such materials. The methodology for engineering materials with specific static properties is well-established for a range of lattice architectures. However, there has been limited investigation into the behavior of architected materials with different auxetic designs under finite deformations at high deformation rates, which are prevalent during impact events. A deeper understanding of the influence of architectural choices on structural transformations and their subsequent capabilities to mitigate impact events is essential for the development of lightweight protective structures. These transformations and their influence on the desired performance in impact mitigation remain a topic of ongoing research [2]. A particular challenge is posed by the accurate representation of high-speed, large deformation in heterogeneous materials, the accompanying material and geometric nonlinearities, as well as inertia effects in a computationally efficient manner. This study examines the changes in different lattice geometries resulting from large deformations at high strain rates, including the effects of material inelasticity and contact phenomena. The modeling of lattice structures using beam discretization in both static and dynamic conditions is discussed, as is the influence of the internal structure on the reaction to localized impact events. To ensure a fair comparison between the architectures, a range of base unit cells with comparable initial linear properties are designed and examined. The change in these properties under simple, static deformation is then demonstrated. Finally, the performance of the structures in localized impact scenarios is explored and related back to the change of properties in the unit cells. [1] Bohara, R. P., Linforth, S., Nguyen, T., Ghazlan, A., & Ngo, T. (2023). Anti-blast and - impact performances of auxetic structures: A review of structures, materials, methods, and fabrications. In Engineering Structures (Vol. 276, p. 115377). Elsevier BV. https://doi.org/10.1016/j.engstruct.2022.115377 [2] Gärtner, T., van den Boom, S. J., Weerheijm, J., & Sluys, L. J. (2024). Geometric effects on impact mitigation in architected auxetic metamaterials. In Mechanics of Materials (Vol. 191, p. 104952). Elsevier BV. https://doi.org/10.1016/j.mechmat.2024.104952

2. (In)Efficacy of Auxetic Metamaterials for Impact Mitigation: Investigations of Energy Absorption and Force Distribution

   Til Gärtner*, Lucas Amaral, Richard Dekker, André M. Diederen, Alexander Niessen, Dennis van Veen, and Sanne J. van den Boom

   poster presentation, 27th Engineering Mechanics Symposium, Hotel Papendal, Arnhem, 22. – 23. Oct 2024

   Poster
3. (In)Efficacy of Auxetic Metamaterials for Impact Mitigation: Investigations of Energy Absorption and Force Distribution

   Til Gärtner*, Lucas Amaral, Richard Dekker, André M. Diederen, Alexander Niessen, Dennis van Veen, and Sanne J. van den Boom

   poster presentation, 14th International Conference on the Mechanical and Physical Behaviour of Materials under Dynamic Loading, ETH Zürich, 8. – 13. Sep 2024

   Abs Poster

   Auxetic (negative Poisson’s ratio) materials have been shown to provide improved indentation resistance, shear resistance, fracture toughness, and energy absorption [1]. As such, they are promising options for impact mitigation in military or space contexts. Auxetic materials are rare in nature, and must therefore be designed and manufactured artificially in order to be used practically. This design process is well understood in the linear and static regime, but little attention has been paid to the local behavior of such architected materials undergoing finite deformation at high rates and the subsequent effects of design choices for impact mitigation in practical protection scenarios. Global 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 [2]. The effects of auxetic densification on the stress distribution over the backside of the auxetic material have not been extensively discussed, but are of paramount importance to the efficacy of architected material as a protective layer. This research examines the behavior of different architected auxetic steel specimens in physical tests at high strain rates using high-speed cameras to characterize the deformation patterns throughout the structure, as can be seen in Figure 1. Different numerical and analytical modeling strategies are examined and used to scrutinize the impact protection of auxetic structures. Fully resolved and meshed simulations provide a detailed understanding of the physical processes in an impact. Beam-based simulations allow a fast but accurate study of different design choices and their effects during impact [3]. Finally, a simple analytical model allows the immediate, rough assessment of singular designs. Thus, this study presents a complete investigation of auxetic lattices for impact protection with experimental campaigns, numerical and analytical models. Furthermore, the evaluation of the consequences of using auxetic lattices to the protected structure is critically analyzed. [1] Bohara, R. P., Linforth, S., Nguyen, T., Ghazlan, A., & Ngo, T. (2023). Anti-blast and -impact performances of auxetic structures: A review of structures, materials, methods, and fabrications. In Engineering Structures (Vol. 276, p. 115377). Elsevier BV. https://doi.org/10.1016/j.engstruct.2022.115377 [2] Gupta, Y. M., & Ding, J. L. (2002). Impact load spreading in layered materials and structures: concept and quantitative measure. In International Journal of Impact Engineering (Vol. 27, Issue 3, pp. 277– 291). Elsevier BV. https://doi.org/10.1016/s0734-743x(01)00051-3 [3] Gärtner, T., van den Boom, S. J., Weerheijm, J., & Sluys, L. J. (2024). Geometric effects on impact mitigation in architected auxetic metamaterials. In Mechanics of Materials (Vol. 191, p. 104952). Elsevier BV. https://doi.org/10.1016/j.mechmat.2024.104952

4. Effects of different architectural choices for auxetic metamaterials on impact mitigation

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

   oral presentation, 16th World Congress on Computational Mechanics, Vancouver Convention Centre, 21. – 26. Jul 2024

   Abs Slides

   For the mitigation of high-velocity impacts in military or space context, such as bullet and fragment impacts on personal protective equipment or space debris endangering satellites at orbital velocities, auxetic (negative Poisson’s ratio) materials are claimed to offer distinct advantages. These materials provide enhanced indentation resistance, shear resistance, fracture toughness, and energy adsorption [1]. Auxetic materials are rare in nature and must be artificially designed. The process of designing materials with desired static properties is well understood in the linear regime. However, there has been little attention given to the behavior of architected materials under finite deformations at high deformation rates, which are expected during impact events. The resulting microstructural changes and how they affect the desired properties are not yet well understood.A design and optimization process of these metamaterials, informed by their behavior in high-velocity impact, is necessary to enable the development of lightweight protective structures. Computational tools are needed to help engineers design these structures with the challenges of high-velocity impact scenarios in mind and to ensure a fast and reliable design process. For these tools a solid understanding of the material behavior under large deformations and high rates, including the highly dynamic and nonlinear effects in the heterogenous metamaterials, is crucial. A solid numerical representation of lattice structures is essential in achieving this understanding.This research examines the effects of changes to the geometry due to large deformations at high strain rates in architected auxetic lattice materials. It presents the modelling of these lattice structures as an assembly of nonlinear beams in both static and dynamic conditions. We discuss the changes in the internal structure of different architectures and the subsequent response to localized high velocity impacts. To ensure a fair comparison, we first design various auxetic architectures with the same initial linear properties. We then illustrate the differences in the evolution of these properties under simple deformation modes and relate them to the observed variations in the impact mitigation performance of the studied architectures. We also illustrate the geometrical features of these architectures and their influence on the response. Finally, we demonstrate the performance of the nonlinear computational model through relevant numerical examples. [1] Bohara, R. P., Linforth, S., Nguyen, T., Ghazlan, A., & Ngo, T. (2023). Anti-blast and -impact performances of auxetic structures: A review of structures, materials, methods, and fabrications. Engineering Structures, 276. doi:10.1016/j.engstruct.2022.115377

5. Kinematic Hardening and Size Effects in Elastoplastic Nonlinear Timoshenko Beams

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

   oral presentation, 94th Annual Meeting of the International Association of Applied Mathematics and Mechanics, Otto-von-Guericke-Universität Magdeburg, 18. – 22. Mar 2024

   Abs Slides

   Architected materials, like lattice structures composed of beams, have attracted increasing interest due to their unique properties. For instance, auxetic materials, which exhibit a negative Poisson’s ratio, offer potential advantages for impact protection, including increased indentation resistance, fracture toughness, and energy adsorption. These properties appear promising in the search for lighter materials for impact protection. In literature, numerous architectures have been proposed to achieve auxetic properties, however with limited insight into nonlinear effects. Efficient numerical models are required to capture geometric and material nonlinearities and to explore the behavior of different architectures. Nonlinear Timoshenko beams can be used to model lattice materials. These beams commonly account only for linear material behavior. Recently Herrnböck et al. [1,2] have developed a framework to determine the yield surface and hardening tensor in the full sixdimensional cross-sectional force and moment space. This extension to include plasticity in the modelling of beams allows the efficient simulation of elastoplastic lattice structures under large deformation in impact scenarios. In their framework, they describe the scaling of the yield surface in relation to the macroscopic geometric size and the scaling of the hardening tensor in relation to the microscopic hardening properties. For the study of different lattice architectures under finite deformation, the scaling of the hardening tensor with respect to the macroscopic geometric size is of further interest and has not been discussed so far. The objective of this research is to examine macroscopic geometrical scaling effects of the hardening tensor in the full six-dimensional cross-sectional force and moment space. A numerical framework is established for conducting elastic analysis of single non-linear Timoshenko beams and multi-beam structures. The framework is then extended to include the yield surface of Herrnböck et al. [1] for ideal plasticity. Careful consideration is given to meshing of the beams and to load-stepping in relation to the explicit return mapping scheme. Kinematic hardening, as described by Herrnböck et al. [2], is subsequently added to the analyses. The effects of geometric scale on the hardening tensor are explained and a method to adapt the hardening tensor in order to account for scale effects is presented. The investigations are conducted on both single cantilever beams and lattice architectures for auxetic metamaterials. [1] Herrnböck et al., Comput Mech. 67 (2021), pp. 723–742. [2] Herrnböck et al., Comput Mech. 71 (2022), pp. 1–24.

2023

1. Effects of Material Architecture in Elastic Impact Mitigation

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

   poster presentation, 2nd International Conference on Computational Modeling of Complex Materials Across the Scales, Technische Universiteit Eindhoven, 10. – 13. Oct 2023

   Abs Poster

   Negative Poisson’s ratio or auxetic materials have the potential to offer benefits for impact protection such as higher indentation resistance, fracture toughness and energy adsorption. In the quest for lighter materials providing impact protection these properties seem promising. Literature describes a wide range of possible architectures to achieve auxetic properties. However, the understanding of the influence of architectural choices at large deformations, such as configuration changes and stresses on mechanical performance, is still limited. Inertia-effects due to high strain rates pose an additional challenge in impact scenarios for the prediction of the protection performance in different material architectures. In a first step this research investigates the effects of different architectural choices in high strain rate scenarios with large deformations. In order to do so, the materials are numerically modeled as a lattice structure of geometrically exact (Simo-Reissner) beams. The effective properties of different configurations and their performance in impact scenarios are evaluated through numerical experiments. Finally, the relations between the effective properties and the performance in impact mitigation are shown.

2. Effects of Material Architecture in Elastic Impact Mitigation

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

   poster presentation, 26th Engineering Mechanics Symposium, Hotel Papendal, Arnhem, 30. – 31. Oct 2023

   Poster
3. Architectural Choices for Auxetic Metamaterials and their Effects on Impact Mitigation

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

   oral presentation, 17th U. S. National Congress on Computational Mechanics, Albuquerque Convention Center, 23. – 27. Jul 2023

   Abs Slides

   Materials with a Negative Poisson’s Ratio (NPR), also called auxetic materials, are sought after for impact mitigation, especially in high velocity impacts. High velocity impacts occur in military or space applications, such as bullet and fragment impact on personal protective equipment or micro-meteorites and space debris endangering satellites at orbital velocities. Here, auxetics have the potential to offer benefits as higher indentation resistance, shear resistance, fracture toughness and energy adsorption [1]. However, auxetics are hardly found in nature and need to be architected artificially. Whilst this approach of designing materials to closely resemble the desired auxetic properties is well understood in the static and linear regime, so far litle atention has been dedicated to the auxetic properties under finite deformations at high deformation rates. The subsequent changes in the architecture of the microstructure and therefore also the persistence of the aforementioned beneficial properties are not yet well understood. For the development of lightweight protective structures, the guided design and optimization of these meta-materials based on their behavior in high velocity impacts is of paramount importance. In order to do so, it is necessary to develop proper computational tools, that allow fast and reliable numerical representation of the dynamic effects at large deformations on the mesoscale. These computational tools, providing the understanding of dynamic nonlinear effects, enable engineers to address challenges in impact mitigation quickly and reliably. In this research the effects of large deformations at high strain rates in anisotropic auxetic lattice materials are studied. The assembly of different auxetic lattice architectures using geometrically nonlinear beams in a static as well as a dynamic framework will be discussed. It will be shown how changes in the internal architecture even within an elastic framework show significant differences in the response to localized, high velocity impact. In a first step, a selected set of auxetic micro-architectures is tuned to exhibit comparable linear properties. Next, the effects of geometric nonlinearity at high strain rates on the macroscopic properties of the lattices are investigated using static and dynamic analyses and differences in the responses will be shown. These differences will be explained on the basis of geometrical features of the underlying architectures. Numerical examples will be presented to demonstrate the performance of the nonlinear computational model for auxetic lattice structures. [1] Kolken, H.M.A. and Zadpoor, A.A., Auxetic mechanical metamaterials. RSC Advances, 2017. 7(9): p. 5111-5129.

2022

1. Comparison of the Nonlinear Elastic Behavior of Auxetic Lattice Architectures

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

   poster presentation, 25th Engineering Mechanics Symposium, Hotel Papendal, Arnhem, 25. – 26. Oct 2022

   Poster
2. Modelling Impact Behavior of Auxetic Meta-Materials using Geometrically Nonlinear Lattices

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

   oral presentation, 9th GACM Colloquium on Computational Mechanics, Universität Duisburg-Essen, 21. – 23. Sep 2022

   Abs Slides

   High velocity impacts often occur in military or space context such as bullet and fragment impact on personal protective equipment or satellites in orbit being endangered by micro-meteorites or space debris. In the quest for better mitigation of such impact events Negative Poisson’s Ratio (NPR) materials, also called auxetic materials, offer beneficial properties, such as higher indentation resistance, shear resistance, fracture toughness and energy adsorption [1]. Auxetic materials are hardly found in nature, but they can be constructed artificially, e.g. by careful design of lattice structures. This approach of designing materials is well understood in the static and linear regime and a myriad of different types of materials have been investigated. However, the understanding of the corresponding properties in the dynamic regime is still not complete and the topic of ongoing research. In this research the computational modelling of meta-materials in the dynamic regime is studied. The development of proper computational modelling techniques will allow the guided design and optimization of such meta-materials by means of understanding the effects at play as well as determining feasibility ranges. These computational techniques aim not only at a proper representation of the mesoscopic materials, but are directed towards the development of homogenized macroscopic models, that will help engineers to address design challenges quickly and reliably. However, in a first step a reliable numerical representation of the lattice structure of the metamaterials needs to be derived. The assembly of two- and three-dimensional auxetic lattices using geometrically nonlinear beams as well as the extension to a dynamical framework will be discussed. In the context of this numerical framework different architectures and their resulting properties for impact mitigation will be compared. First, the effect of nonlinearity on the macroscopic properties of the lattices is investigated using static analyses. Then the dynamic effects prevalent in aforementioned impact events are shown and compared for different lattice architectures, and their effects on the performance of materials in impact mitigation are discussed. For two-dimensional auxetics a comparison with experimental results is shown. Differences in auxetic architectures between two-dimensional and three-dimensional lattices as well as the resulting effects on the applicability for impact mitigation will be sketched together with different methods to create a three-dimensional structure from existing two-dimensional structures. Numerical examples will be presented to demonstrate the performance of the nonlinear computational model for the auxetic lattice structures. [1] Kolken, H.M.A. and Zadpoor, A.A., Auxetic mechanical metamaterials. RSC Advances, 2017. 7(9): p. 5111-5129.

3. Computational Modeling of Metamaterials for Impact Protection

   Sanne J. van den Boom*, Dennis van Veen, André M. Diederen, Jaap Weerheijm, and Til Gärtner

   3rd World Conference on Advanced Materials for Defense, Hotel de Guimarães, 6. – 8. Jul 2022

2021

1. Computational Modeling of Metamaterials for Impact Protection

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

   poster presentation, 24th Engineering Mechanics Symposium, Hotel Papendal, Arnhem, 26. Oct 2021

   Poster
2. Nonlinear multiscale simulation of elastic beam-lattices with anisotropic constitutive models based on artificial neural networks

   Til Gärtner, Mauricio Fernández, and Oliver Weeger*

   6th ECCOMAS Young Investigators Conference, Universitat Politècnica de València, 7. – 9. Jul 2021