# Enhanced energy absorption in 3D printed copper micro-honeycombs

Kuan Ding, Manish Jain, Szilvia Kalácska, Amit Sharma, Wabe W Koelmans, Patrik Schürch, Gerhard Dehm, Johann Michler, Rajaprakash Ramachandramoorthy

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## To cite this version:

Kuan Ding, Manish Jain, Szilvia Kalácska, Amit Sharma, Wabe W Koelmans, et al., Enhanced energy absorption in 3D printed copper micro-honeycombs. Materials & Design, 2025, 260, pp.115090. 10.1016/j.matdes.2025.115090. emse-05392887

HAL Id: emse-05392887

https://hal-emse.ccsd.cnrs.fr/emse-05392887v1

Submitted on 2 Dec 2025

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# Enhanced energy absorption in 3D printed copper micro-honeycombs

Kuan Ding<sup>a, ID</sup>, Manish Jain<sup>b,c, ID</sup>, Szilvia Kalácska<sup>b,d ID</sup>, Amit Sharma<sup>b</sup>, Wabe W. Koelmans<sup>e ID</sup>,
Patrik Schürch<sup>e</sup>, Gerhard Dehm<sup>a ID</sup>, Johann Michler<sup>b</sup>, Rajaprakash Ramachandramoorthy<sup>a,b,*, ID</sup>

## ARTICLE INFO

### Keywords:

Additive micromanufacturing

Micro-honeycomb

In situ micromechanical testing

High strain rate

Grain refinement

Energy absorption

## ABSTRACT

A honeycomb architecture exhibits a high strength-to-weight ratio and excellent energy absorption properties. At the microscale, these architectures have great potential for packaging and protection applications. However, fabrication and testing of micro-honeycomb architectures remain challenging, particularly under extreme loading conditions. Here, we report the fabrication of microscale copper honeycomb architectures using an additive manufacturing technique – localized electrodeposition in liquid. The printed micro-honeycombs were mechanically tested under both quasi-static and high strain rate conditions using a piezo-based *in situ* setup inside an SEM. The honeycombs exhibit excellent energy absorption properties under both quasi-static and high strain rate conditions, with the specific energy absorption increasing by 65 % as the strain rate rises from 0.001 s⁻¹ to 110 s⁻¹. The copper honeycombs possess an ultrafine-grained microstructure that undergoes grain refinement during both quasi-static and high strain rate testing. Our work demonstrates the feasibility and potential of employing micro-honeycomb architectures as impact protection architectures for sensitive micro/nano-electromechanical systems and microelectronics operating in extreme environments.

## 1. Introduction

The honeycomb architecture, inspired by the bee's honeycomb, consists of a cellular network with a periodic topology [1]. Owing to their high strength-to-weight ratio, honeycomb architectures have been widely used in high-performance lightweight applications such as automotive, aerospace, and sporting equipment (e.g., skis) [2,3]. Due to their high energy absorption capacity under external loading, metallic honeycomb architectures are used as low-density cores in sandwich panels subjected to impact, crash, and blast loading [4,5]. Beyond large-scale applications, these advantageous properties render miniaturized honeycomb architectures – if successfully fabricated – promising candidates for lightweight packaging and impact protection of microelectronics and micro/nano-electromechanical systems (MEMS/NEMS) subjected to extreme loading conditions, impacts, and penetrations.

Traditional MEMS packaging can be broadly classified into three categories: ceramic cavity packaging, plastic mold packaging, and wafer-level packaging [6]. Among these categories, wafer-level

packaging offers advantages in terms of space-saving and cost-effectiveness. However, such packaging remains relatively bulky and lacks site-specific protection for MEMS devices. Even with conventional bulky and heavy packaging, the movable and sensitive features of a MEMS are still susceptible to damage under impact or vibrational loading [7].

The direct writing of miniaturized architectures – such as microscale metallic honeycombs – could provide site-specific protection to the most sensitive parts of MEMS devices. These micro-architectures can serve as strong yet lightweight protective layers, enhancing the mechanical resilience of a MEMS device. 3D printing has emerged as a versatile technique for manufacturing honeycomb architectures [8], offering high design flexibility. However, to integrate honeycomb architectures in MEMS or microelectronic systems, the fabrication resolution must reach the sub-micrometer scale. Conventional powder-based or energy-deposition-based 3D printing techniques cannot achieve such precision. Two-photon lithography (TPL) offers direct printing of arbitrary complex 3D architectures with sub-micrometer resolution, but its

<footnote><sup>a</sup> Max Planck Institute for Sustainable Materials, Max-Planck-Straße 1, 40237 Düsseldorf, Germany</footnote>

<footnote><sup>b</sup> Empa – Swiss Federal Laboratories for Materials Science and Technology, Laboratory for Mechanics of Materials and Nanostructures, Feuerwerkerstrasse 39, 3602</footnote>

<footnote>Thun, Switzerland</footnote>

<footnote><sup>c</sup> Department of Materials and Metallurgical Engineering, New Mexico Institute of Mining and Technology, 87801 NM, USA</footnote>

<footnote><sup>d</sup> Mines Saint-Étienne, Univ Lyon, CNRS, UMR 5307 LGF, Centre SMS, 158 cours Fauriel, Saint-Étienne, 42023, France</footnote>

<footnote><sup>e</sup> Exaddon AG, Sägereistrasse 25, Glattbrugg 8152, Switzerland</footnote>

<footnote>* Corresponding author at: Max Planck Institute for Sustainable Materials, Max-Planck-Straße 1, 40237 Düsseldorf, Germany.
E-mail address: r.ram@mpi-susmat.de (R. Ramachandramoorthy).</footnote>
applicability is largely limited to polymer materials [9]. Although positive polymer molds produced by TPL have been filled with metal through electrodeposition [10], it is a complex two-step process that increases fabrication difficulty, particularly when printing on nonplanar or arbitrary surfaces. Electrohydrodynamic redox printing (EHD-RP) has been developed for single-step direct metal writing [11,12]. Nevertheless, EHD-RP can only write 2.5D architectures with simple geometry.

Recently, the localized electrodeposition in liquid (LEL) method has emerged as a promising alternative for the one-step fabrication of 3D metallic microarchitectures on (non planar) conductive substrates [13–15]. This approach simplifies the process, enabling rapid and precise additive manufacturing of metallic structures – in particular copper – with consistent morphology and microstructure. Single-step fabrication using LEL reduces the complexity and difficulty of the production process compared to TPL, enabling fast and direct 3D printing of metallic microarchitectures. Furthermore, compared to the simple 2.5D geometries reported in literature using EHD-RP [11], LEL enables fabrication of complex, arbitrary 3D geometries. The LEL system utilizes a hollow atomic force microscope (AFM) cantilever for the local delivery of metal ions that are reduced to metal in a confined volume, i.e., a voxel. Through precise control of the electrodeposition parameters, the technique prints honeycomb micro-lattices with a minimum wall thickness as small as ~2 µm. Operating in a voxel-by-voxel and layer-by-layer manner, LEL produces complex 3D architecture at the micro-to-meso scale range [14]. Therefore, LEL enables the fabrication of miniaturized honeycomb architectures as localized packaging or impact-protection structures for MEMS and microelectronic devices.

In this study, we utilized the LEL technique to fabricate microscale copper honeycomb architectures for the first time. The copper micro-honeycombs were printed with a steady deposition rate of approximately 0.6 µm/s, yielding a high-quality surface finish. The fabricated micro-honeycombs were compressed *in situ* at both quasi-static and high strain rates in a scanning electron microscope (SEM). The microstructure of the as-fabricated and deformed honeycombs was characterized using SEM and transmission electron microscopy (TEM)-based analytical techniques to elucidate the microstructure and the rate-dependent deformation mechanism. Through these investigations, we established the microstructure-dynamic property relationships for the copper micro-honeycombs. The micro-honeycomb architectures showed extraordinary energy absorption capacity under loading at different strain rates, two orders of magnitude higher than macroscale metal honeycombs. This work exemplifies the potential of the LEL technique as a versatile platform to provide localized and site-specific MEMS packaging and impact protection under extreme loading conditions.

## 2. Materials and methods

### 2.1. 3D printing of micro-honeycomb

The copper micro-honeycombs were fabricated using the LEL technique via localized force-controlled electrodeposition using the CERES system (Exaddon AG, Glattbrugg, Switzerland). The schematic illustration of the fabrication process is shown in Fig. 1. Electrolytes with copper ions are pushed through a hollow AFM cantilever with a 300-nm-diameter aperture at its tip. The cantilever, including its tip, is immersed in a supporting conductive electrolyte solution with 0.5 M $H_2SO_4$ and 0.5 mM HCl that is contained in a three-electrode electrochemical cell. The electrolyte, which is ejected out of the tip, is made of 800 mM $CuSO_4$, dissolved in the chamber solution.

The electrolyte in the AFM cantilever's reservoir was ejected out of the tip using a precisely controlled air pressure of 7–15 mbar. The cantilever's tip was moved to a predefined location to electrodeposit a copper voxel on a copper-coated silicon substrate, which acts as the working electrode. The honeycomb architecture was converted into a print file with the coordinates of the voxels so that the system could build the architecture voxel by voxel. The laser is deflected by the

<figure><img src="image_4.png" /><figcaption>Fig. 1. Schematic illustration of the setup for LEL technique. CE stands for counter electrode. RE stands for reference electrode. WE stands for working electrode.</figcaption></figure>

cantilever, and the movement of the cantilever can be captured by the laser signal. When the laser signal reaches the predefined threshold caused by the vertical deflection induced by the voxel growth, a voxel is formed, and the cantilever would be moved by the servo-controlled stages to the next coordinate to print the next voxel. The applied potential for the electrodeposition was chosen as –0.5 V.

### 2.2. *In situ* mechanical testing

Micro-compression testing was carried out within a Philips XL30 FE-SEM (Philips Electron Optics B.V., Netherlands), utilizing an Alemnis *in situ* nanoindenter (Alemnis AG, Thun, Switzerland) with a 60-µm flat punch diamond tip. The honeycombs were fabricated to undergo uniaxial compression in the out-of-plane direction to achieve the highest energy absorption [16]. The applied strain rates varied from 0.001 to $0.1 \text{ s}^{-1}$ using the standard Alemnis assembly and extended up to $110 \text{ s}^{-1}$ with the high-dynamic module. Additional technical specifications for this testing system are mentioned elsewhere [17,18]. To ensure accuracy, the raw force-displacement curves were adjusted for instrument compliance and corrected for elastic sink-in effects using Sneddon's method [19]. Yield points were determined by offsetting the linear elastic fit of the load curve by 2 % along the strain axis.

### 2.3. Microstructure characterization

Micrographs of the as-fabricated and deformed microstructure were conducted with a Hitachi S4800 SEM (Hitachi High-Tech, Tokyo, Japan) with an acceleration voltage of 1 kV. Cross-sections of the cell wall of micro-honeycombs were milled along the out-of-plane direction using a Zeiss Auriga (Carl Zeiss AG, Jena, Germany) focused ion beam (FIB). Thin foil lift-out was conducted in a TESCAN LYRA (Tescan, Bruno, Czech Republic) FIB. Microstructure analysis of pristine and deformed structures was performed in a probe-corrected Themis 200 G3 (Thermo Fischer Scientific, Eindhoven, Netherlands) transmission electron microscope (TEM) operating at 200 kV. Scanning precession electron diffraction (SPED) was performed using a DigiSTAR NanoMEGAS (NanoMEGAS SPRL) in the same aberration-corrected TEM, employing a 2 or 3 nm step size to generate high spatial resolution inverse pole figure (IPF) maps. Measurements at two different locations were performed within each lamella. The data was converted into ANG files containing the recorded Euler angles for all the scanned points. The orientation and grain sizes were analyzed using TSL OIM Analysis software (EDAX, Pleasanton, CA, USA). The grains were defined with a misorientation angle of more than 5 degrees, and the twins are integrated into the parent grain for grain size calculation. The analysis was done using a weighted average to combine the two datasets. The grain area is the integration of all the pixels within the grain. The grain size was calculated by determining the area of a grain and then assuming the grain is a
circle and calculating the diameter of the circle. For the cross-section generated during liftout, energy-dispersive X-ray spectroscopy (EDS) elemental mapping was carried out using an Oxford Ultim Max 65 detector (Oxford Instruments NanoAnalysis, High Wycombe, United Kingdom) with an accelerating voltage of 20 kV, a dwell time of 0.8 ms, and a resolution of 1024x1024 pixels. The EDS analysis was performed using Aztec v6.0 (Oxford Instruments NanoAnalysis, High Wycombe, United Kingdom) software. Electron backscattered diffraction (EBSD) of the cross-section during liftout was performed using an Oxford Symmetry EBSD camera (Oxford Instruments NanoAnalysis, High Wycombe, United Kingdom) at an accelerating voltage of 20 kV with data analysis using HKL Tango and Mambo v.5.12 (Oxford Instruments NanoAnalysis, High Wycombe, United Kingdom).

# 3. Results and discussion

## 3.1. 3D-printed micro-honeycomb architecture

The SEM micrographs of the copper micro-honeycomb architecture fabricated by LEL are shown in Figs. 2a and b. The honeycomb architecture consists of eight hexagon cells (Fig. 2b) standing on the Si-wafer substrate coated with titanium and copper. The height of the cell of the micro-honeycomb architecture is 30 µm, and the cell wall thickness is ~2.5 µm. Fig. S1 (supplementary materials) reveals the microstructure of the cell wall milled by FIB. The micrographs show that the cell wall has an ultrafine-grained (UFG) microstructure. Moreover, a thin layer coating with a thickness of around 350 nm around the cell wall is observed (Fig. S1d, supplementary materials). To better characterize the microstructure, a lamella of the cell wall was lifted out, and the location of the liftout is indicated in Fig. 2b. TEM-SPED was carried out to map the orientation of the grains (Fig. 2c). The average grain size obtained from the SPED analysis was 84.7 ± 114.3 nm, exhibiting an ultrafine-grained (UFG) microstructure.

The lamella was also characterized using TEM (Figs. 2d and 2e). A large number of lath-like twins formed within the microstructure. The

width of the twins ranges from a few nanometers to roughly 50 nm (Fig. 2d). Moreover, high-resolution TEM images (Fig. 2e) of the twins were also obtained. The twins are confirmed by the indexed diffraction pattern in Fig. 2f. The symmetric atomic layers in the twins can be clearly observed [15].

## 3.2. In situ compression tests of the micro-honeycomb architectures

The fabricated micro-honeycomb architectures were in situ deformed at both quasi-static and high strain rates inside the SEM. The honeycombs were compressed in the out-of-plane direction over five orders of magnitude in strain rate ($\dot{\epsilon}$) from 0.001 $s^{-1}$ to 110 $s^{-1}$. For quasi-static deformation with a strain rate of less than 1 $s^{-1}$, load and displacement were recorded using a strain gauge-based load cell and displacement sensor, respectively. For high strain rate testing, load and displacement were recorded using a piezoelectric load cell and a strain gauge-based displacement sensor, respectively. The undeformed and deformed honeycomb architectures were characterized using SEM, as shown in Fig. 3. The honeycomb cells were deformed with height reduction until a strain of more than 40 %. The buckling of the cell walls can be observed in all deformed images recorded after deformation. Such elastoplastic buckling accommodates the plastic strain once the stress exceeds the yield stress of the honeycombs [16].

In the SEM micrograph, the tear and delamination of a thin layer covering the cell wall can be seen in all deformed honeycomb architectures. To identify the composition of the thin-layer coating, elemental mapping was performed using energy dispersive X-ray spectroscopy for the cross-section of the cell wall from a honeycomb architecture deformed with $\dot{\epsilon}$ = 110 $s^{-1}$. The micrograph of the cross-section milled by FIB and the element distribution are shown in Fig. S2 (supplementary materials). The elemental maps reveal that the main elements of the thin coating layer are C and O. The copper signal comes from the honeycomb architecture and the copper coating on the Si wafer substrate. The Si signal comes from the redeposition during the FIB milling process. Based on the observation, we believe the thin layer coating formed after the

<figure><img src="image_5.png" /><figcaption>Fig. 2. SEM micrographs of the 3D printed copper micro-honeycomb architecture a) side view and b) top view (the location where the lamella lifted out is marked by red dashed rectangle), c) orientation mapping of the cell wall of the micro-honeycomb architecture with inverse pole figure (IPF) at the corner denoting the orientations, d) bright-field (BF) TEM image of the lamella, e) BF high-resolution TEM image of the twins, f) selected area diffraction of the twin region in d). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** SEM micrographs of a) quasi-static deformed micro-honeycomb architectures with $\dot{e} = 0.001 \text{ s}^{-1}$, b) micro-honeycomb deformed at high strain rate with $\dot{e} = 110 \text{ s}^{-1}$.</figcaption></figure>

printing process. We believe that the polymeric layer could come from impurities in the solvent that was used for cleaning processes. After deformation, cracking and delamination of the polymeric layer were observed. The adhesion between the polymer and the copper cell is not strong enough to accommodate the plastic deformation of the micro-honeycomb cell. However, even though the interface between the polymer and the metal cell is weak, a minor contribution is expected to the deformation of the whole architecture from the polymer layer. In a study [20] of the tensile behavior of penta-twinned silver nanowires coated with polyvinylpyrrolidone polymer layers and amorphous carbon, the estimated contribution from the coating is up to 11 % where the coating well adhered to the nanowires during deformation. In the current study, the ratio of metal/polymer is 6.5, a bit larger than the nanowire case, which has a metal/polymer ratio of around 6. Furthermore, the delamination of the polymer layer after deformation indicates a weak adhesion between the copper micro-honeycomb and the polymer layer, unlike the silver nanowire mentioned above. Therefore, we estimate that the contribution of the polymer layer to the plastic deformation would be much smaller than in the silver nanowire case.

The stress-strain signatures of honeycomb deformation at different strain rates are shown in Fig. 4a. The engineering stress was calculated using the force divided by the area of the eight hexagon cells from the top view. The engineering strain was calculated using the height reduction. The quasi-static compression tests until a strain rate of $1 \text{ s}^{-1}$

were conducted in true-displacement control using a PID-based feedback loop; thus, the strain could be controlled precisely. However, for high strain rate testing (larger than $1 \text{ s}^{-1}$), the compression was conducted in open loop yet under intrinsic displacement control (higher stiffness components compared to the sample). Therefore, precise control of the strain was not possible, resulting in differences in strain levels between the copper micro-honeycombs deformed at quasi-static and high strain rates. The stress-strain curves for the deformation of the honeycomb cells are similar, containing both elastic and plastic regimes at all the strain rates. Within the elastic regime, stress increases linearly with increasing strain. With continuing increasing stress, the honeycomb cells deform plastically after reaching the yield point. The stress steadily increases to the peak stress and then drops a bit to a near-constant plateau. The high plateau stresses with slight drops from peak stress illustrate that progressive plastic collapse dominates in the plastic regime for deformation of the micro-honeycombs at all tested strain rates, resulting from the high relative density (0.6) of the micro-honeycombs [3,16]. The overall deformation behavior of the micro-honeycombs resembles a near-perfect plastic response as a result of the combination of geometry and high relative density. The stress will then again increase after reaching more than 40 % strain. At this high strain, the increase in stress was caused by the densification of the honeycomb architecture [16]. During the densification regime, the collapsed cell wall acts as a non-linear spring and resists further

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** A) representative engineering stress-strain curves of 3D printed micro-honeycombs compressed at strain rates from $0.001 \text{ s}^{-1}$ to $110 \text{ s}^{-1}$, and b) plot of yield stress versus strain rate for all tests. It should be noted that at least two tests were conducted for each strain rate.</figcaption></figure>
deformation.

The yield stress as a function of testing strain rate is shown in Fig. 4b. The yield stress is defined as the stress of the offset yield point at a plastic strain of 2 %. Here, we choose a 2 % offset strain instead of the classical 0.2 % offset strain to avoid errors in yield determination arising from heterogeneous deformation systematically [21]. It can be clearly seen that with increasing strain rate, the yield stress also increases. The strain rate sensitivity *m* was calculated using the formula below:

$$m = \frac{\partial \ln \sigma}{\partial \ln \dot{\epsilon}} \qquad (1)$$

The calculated *m* value is 0.035 ± 0.002, and the strain rate sensitivity doesn't change throughout the tested strain rates. Therefore, we hypothesize that the deformation mechanism also doesn't change with increasing the strain rate to 110 s⁻¹. Nevertheless, there is no significant difference in the yield stress for deformation at strain rates of 56.8 s⁻¹ and 110 s⁻¹. In the previous study [15] on compression of ultrafine-grained (UFG) micro-pillar fabricated using LEL technique at both quasi-static and high strain rates, the yield stress saturated at the strain rate of 0.1 s⁻¹. But the average grain size of the UFG micro-pillar tested in the previous study was 170 nm, which is comparatively larger than the micro-honeycombs. Moreover, the micro-honeycomb is a hollow architecture compared to the fully dense micropillar. As such, it can be hypothesized that the combined microstructure and geometry effect could cause the saturation of the yield stress to occur at a higher strain rate than in the micropillars. Confirmation of this would require

experimental tests of the micro honeycombs at strain rates beyond 110 s⁻¹, which is left for future work.

The honeycomb cells deformed at $\dot{\epsilon} = 0.001 s^{-1}$ and $\dot{\epsilon} = 110 s^{-1}$ were chosen for post-test microstructural evaluation, specifically to study the deformation behavior at strain rate extremes, with both samples deformed to a strain level of ~ 45 %. (Supplementary Video 2 and Video 3). The locations of lamellae that were lifted out and thinned down to electron transparency are marked in the SEM micrographs (Figs. 5a and e). Both lamellae were imaged in TEM. The orientation mappings were carried out using SPED and are shown in Figs. 5b and f.

To better understand the deformation mechanism, TEM characterization was conducted for the lamellae lifted out from the honeycomb cell deformed at both $\dot{\epsilon} = 0.001 s^{-1}$ and $\dot{\epsilon} = 110 s^{-1}$. The ultrafine-grained structure and dislocation structures can be found in both lamellae, as shown in Figs. 5c and g. For the honeycomb cell deformed at $\dot{\epsilon} = 0.001 s^{-1}$, twinning lathes can be observed. Besides, it can be seen that a large density of dislocations was identified inside the grains and twins. The twin boundaries interact with each other, forming interlocks which were characterized by high-resolution (HR) TEM and shown in Fig. 5d [22]. Such interlocks could pin the motion of dislocations, aiding stable hardening in the plastic regime. A large number of twins and dislocations are also observed in the micro-honeycomb deformed at 110 s⁻¹ (Fig. 5g). Furthermore, the HR-TEM analysis also revealed nanotwins with a thickness of around 30 atomic layers, formed after deformation (Fig. 5h).

The average grain sizes, boundary density, and twin fraction were

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** A) e) SEM images of the micro-honeycombs after deformation with the location of the lamella lifted out from the cell wall marked by the blue rectangle, b) f) orientation mapping of the areas within the lamellae of the micro-honeycombs lifted out from the location marked in the micrographs, c) g) BF-TEM images of areas on the lamellae, d) high-resolution TEM image of a region with interlocking twins, h) high-resolution TEM image of the nanotwins. The atomic planes are marked by red lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

**Table 1**

Average grain size and boundary density in each of the lamella lifted out from the undeformed and deformed honeycomb cells.

<table><thead><tr><th></th><th>Average grain size (nm)</th><th>Boundary density (µm<sup>-1</sup>)</th><th>Twin fraction (%)</th></tr></thead><tbody><tr><td>As-fabricated</td><td>84.7 ± 114.3</td><td>49.81</td><td>45.4</td></tr><tr><td>ε̇ = 0.001 s<sup>-1</sup></td><td>66.6 ± 89.6</td><td>68.87</td><td>44.0</td></tr><tr><td>ε̇ = 110 s<sup>-1</sup></td><td>53.0 ± 53.6</td><td>86.00</td><td>45.9</td></tr></tbody></table>
extracted from the TEM-SPED analysis and listed in Table 1. The average grain size decreases after both quasi-static and high strain rate deformation. High strain rate deformation results in finer grains compared to quasi-static deformation. Besides, the boundary density increases after deformation. Both the average grain size and the boundary density indicate that possible grain refinement has occurred. The grain size distribution is plotted in Fig. S3 (supplementary materials). The distribution is skewed towards the small grain size. One reason possibly causing the skewed distribution is that the small grain size and step size for the SPED scan cause under-sampling of the grains in the mis-indexed points, even though a cut-off of a minimum of 3 pixels was set. The other reason could be that the grains cut by the edge of the map might bias the distribution towards the smaller grain size. Moreover, at the location where the cell wall buckles, the grain size is larger than in other regions on the cell wall (Fig. S4, supplementary materials). It is hypothesized that the high localized strain at the buckling point of the cell wall results in high stored energy and leads to local static recrystallization in the region around the buckling point, relieving the stress [23]. However, the region where the SPED was performed on the cell wall could not be determined precisely after the lamella thinning. Therefore, there may be discrepancies in the grain size estimated by the SPED analysis. The calculation of the twin fraction is the area of all of the twins divided by the sum of the areas of all of the grains. No significant change was observed for the deformed and undeformed regions. However, nanotwin formation has been captured in the high strain rate deformed micro-honeycomb (Fig. 5h). Those nanotwins with tens of atomic layers may not be captured during SPED. The effective probe size in the SPED would be a few nanometers, a similar size to the twin width, and the effective interaction volume would be larger than the probe size. As a result, spatially resolving individual nanotwins would not be possible; as such, it should be noted that the twin fraction could be underestimated in the high strain rate deformed micro-honeycomb. Therefore, nanotwin formation could also be the deformation mechanism for high strain rate deformation.

### 3.3. Energy absorption properties

The original design of the honeycomb architecture was intended to enhance energy absorption during compressive deformation. As such, the energy absorption ability of the micro honeycombs was evaluated. The energy absorption (EA) can be calculated as follows [5]:

$$EA = \int_{0}^{\epsilon_d} \sigma(\epsilon) d\epsilon \qquad (2)$$

where $\sigma(\epsilon)$ is the stress as a function of strain $\epsilon$, $\epsilon_d$ is the strain at the onset of densification.

The specific energy absorption (SEA) is characterized as absorbed energy by an architecture per unit volume, given by [5]:

$$SEA = \frac{EA}{V} \qquad (3)$$

where V is the volume of the architecture. The volume is calculated using the area of the eight hexagon cells from the top view, multiplied by the height of the cell.

The SEA of the honeycomb architecture was calculated for deformation at all tested strain rates. The SEA versus the strain rate $\dot{\epsilon}$ is plotted in Fig. 6a. For comparison, the SEA of octet-truss architectures that deformed at different strain rates from the literature [13] is also plotted in the figure. The SEA for the out-of-plane direction of the honeycomb cell is superior compared to the octet-truss. The SEA for the octet-truss is less than 50 MJ/m³ across all the tested strain rates. Whereas the SEA for honeycomb increases at least four times more compared to the octet-truss at the same strain rate. Moreover, the SEA for the honeycomb cell increases with increasing strain rate. The SEA is 189.9 MJ/m³ at $\dot{\epsilon} = 0.001 s^{-1}$ and increased to 314.5 MJ/m³ at $\dot{\epsilon} = 110 s^{-1}$, which makes the honeycomb a much better energy absorber at high strain rate. The SEA values of the micro-honeycombs (21.1–35.0 kJ/kg) are comparable to those of the porous Ti-6Al-4 V alloy with ammonium carbonate particles sintered using blended elemental powder metallurgy under dynamic compression (1420–1500 s⁻¹) to a strain of 40 % (33–52 kJ/kg) [24]. Furthermore, a metal matrix syntactic foam with CoCrFeMnNi high entropy alloy matrix and alumina cenosphere fillers has an SEA of 242.8 MJ/m³ under compression with 0.001 s⁻¹ up to a strain level of 50 % [25]. Porous materials are known as excellent energy absorbers. The comparable SEA values demonstrate the efficient energy-absorbing properties of the copper micro-honeycombs manufactured using the LEL technique.

The energy absorption efficiency (Ef) is calculated as follows:

$$Ef = \frac{\int_{0}^{\epsilon_d} \sigma(\epsilon) d\epsilon}{\sigma_d} \qquad (4)$$

where $\epsilon_d$ is the strain at the onset of densification, $\sigma_d$ is the stress at $\epsilon_d$.

The energy absorption efficiency versus strain rate is plotted in Fig. 6b. The Ef is rather constant across all tested strain rates. The stress increases with increasing strain rates. Even though the EA increases with increasing strain rate, the Ef stays constant with an efficiency of around 0.38. The energy absorption efficiency describes how the structure

<figure><img src="image_9.png" /><figcaption>Fig. 6. A) specific energy absorption per unit volume versus strain rate is plotted for both the micro-honeycomb in this work (relative density: 0.6) and the octet-truss micro-lattice from literature [13] (relative density: 0.4) for comparison. B) plot of energy absorption efficiency versus strain rate for the micro-honeycomb in this work.</figcaption></figure>
resists the applied load during deformation before reaching densification [16]. The stress-strain curves in Fig. 3a are similar in shape across different strain rates, indicating similar deformation behavior. As a result, Ef shows no significant change at different strain rates.

The SEA of a 3D-printed micro-octet-truss from a recent work was also plotted in Fig. 6a [13]. The octet-truss has a unit-cell length of 15 µm and a strut diameter of 2.5 µm, with unit cells repeating three times along the x, y, and z coordinate axes. Moreover, 5-µm-thick plates were added at the bottom and top of the lattice structure. The SEA of the micro-honeycomb is much higher than the micro-octet-truss throughout the strain rate from 0.001 s⁻¹ to 100 s⁻¹. With increasing the strain rate, the advantage of micro-honeycomb increases. At the strain rate of around 100 s⁻¹, for the same volume, the copper micro-honeycombs can absorb ~6.5 times more energy compared to copper micro-octet-truss lattices with similar microstructure [13]. Moreover, the copper octet-truss micro-lattices have a lower plateau stress compared to the micro-honeycomb in this study. Even though the SEA is lower, the octet-truss micro-lattices with a lower relative density and lower plateau stress are more ideal for protection in direct contact with the sensitive components to mitigate the impact. The micro-honeycombs, on the other hand, with high plateau stress and high SEA, are more suitable as additional protection built around the sensitive components in the MEMS devices to absorb as much energy as possible during the impact event and protect the sensitive component from potential contact with the impact source. Furthermore, the plateau stress can be tuned by changing the design of the micro-architecture fabricated using LEL, depending on the expected loads and conditions, providing an optimized plateau stress that is either high enough to sustain the expected loads without completely collapsing or low enough to evenly distribute the forces with minimum transmission. This also underlines the potential of the LEL technique for fabricating micro-architecture with tunable complex geometries.

The SEA property of the micro-honeycomb is also compared to the macroscale commercial honeycombs that are used in large-scale applications in Table 2. The macroscale commercial honeycombs are primarily fabricated using aluminum or *meta*-aramid materials and are designed for energy absorption with a low relative density (shown in Table 2), ideal for lightweight applications. At quasi-static strain rates, the SEA of the micro-honeycomb is ~40–50 times higher than that of macroscale honeycombs. At high strain rates, the SEA of the micro-honeycomb is two orders of magnitude higher than the macroscale honeycomb made from carbon fiber reinforced plastic (CFRP) embedded in A5052 aluminum. The high SEA for the copper micro-honeycomb is attributed to the high relative density (0.6) compared to the macroscale honeycombs [16]. The high relative density results in the deformation of the micro-honeycombs, which is dominated by progressive plastic collapse. Thus, the plateau stress is close to the yield stress, which is already quite high owing to the smaller-is-stronger effect. However, for the macroscale honeycombs, the dominant deformation mechanism is plastic buckling of the cell wall, resulting in lower plateau stress. Even though the strain at the onset of densification is larger for aluminum macroscale honeycombs, roughly two times as much as that of the

copper micro-honeycombs, the plateau stress of the aluminum honeycomb is just around 0.1–0.2 MPa, which is much smaller than that of the copper micro-honeycombs. Therefore, the copper micro-honeycombs have much higher SEA owing to the intrinsically higher strength, the smaller dimensions, and the higher plateau stress. It should be noted that the macroscale honeycombs are designed for lightweight. Therefore, the relative density is low and often fabricated using materials with low density. Nevertheless, for macroscale applications, the total volume is low. Thus, the relative density is designed to be higher for copper micro-honeycombs to achieve better SEA, where the density of the material itself is not an important factor.

The high SEA of the micro-honeycombs demonstrates the potential for site-specific protection with macroscale precision. The LEL fabrication can be conducted on any electrically conductive surface, such as doped device silicon layers or gold traces. This would allow copper micro-honeycombs to be used as additional protection that is built around sensitive moving regions of MEMS/NEMS devices for high energy absorption during impact, along with traditional packaging, reducing the risk of damage and functionality during harsh applications.

## 4. Conclusion

In this work, we successfully fabricated eight-cell copper micro-honeycomb lattices with a height of 30 µm and cell wall thickness of 2.5 µm using the localized electrodeposition in liquid (LEL) technique. The micro-honeycombs were subjected to *in situ* compression tests under both quasi-static and high strain rate conditions, with strain rates ranging from 0.001 s⁻¹ to 110 s⁻¹. The yield stress increased nominally with increasing strain rate (e).

Detailed microstructural characterization using electron microscopy was performed on the as-fabricated and deformed honeycombs at e = 0.001 s⁻¹ and 110 s⁻¹ to elucidate the underlying deformation mechanisms. Grain refinement was observed for both quasi-static and high strain rate deformation. Furthermore, microstructural features such as interlocking of twin boundaries and nanotwins were identified in the micro-honeycombs tested at e = 0.001 s⁻¹ and at 110 s⁻¹, respectively. These grain refinement and nanotwin formation were attributed to the observed mechanical behavior.

The copper micro-honeycombs demonstrated outstanding energy absorption capability with specific energy absorption (SEA) values ranging from 189.9 MJ/m³ at e = 0.001 s⁻¹ to 314.5 MJ/m³ at e = 110 s⁻¹. Remarkably, these values are up to orders of magnitude higher than those of conventional macroscale honeycombs fabricated from aluminum or *meta*-aramid materials.

Overall, this study establishes the feasibility of using the LEL technique to fabricate high-performance metallic micro-honeycomb architectures. The exceptional energy absorption characteristics of these structures underscore their potential for use as localized packaging and protective components for sensitive features in MEMS/NEMS and microelectronic devices operating under extreme loading conditions.

### CRediT authorship contribution statement

**Kuan Ding:** Writing – review & editing, Writing – original draft, Visualization, Formal analysis. **Manish Jain:** Writing – review & editing, Investigation, Formal analysis, Data curation. **Szilvia Kalácska:** Writing – review & editing, Investigation, Formal analysis, Data curation. **Amit Sharma:** Writing – review & editing, Investigation, Formal analysis, Data curation. **Wabe W. Koelmans:** Writing – review & editing, Investigation. **Patrik Schürch:** Writing – review & editing, Investigation. **Gerhard Dehm:** Writing – review & editing. **Johann Michler:** Supervision, Resources. **Rajaprakash Ramachandramoorthy:** Writing – review & editing, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.

<caption>**Table 2**</caption>

Specific energy absorption properties at different strain rates of macroscale honeycomb in this work and macroscale honeycomb made with different materials from the literature.

<table><thead><tr><th>Honeycomb</th><th>SEA (MJ/m³)</th><th>Strain rate (s⁻¹)</th><th>Relative density</th></tr></thead><tbody><tr><td>Microscale honeycomb</td><td>189.9</td><td>0.001</td><td>0.6</td></tr><tr><td>Macroscale</td><td>314.5</td><td>110</td><td></td></tr><tr><td>CFRP-aluminum[26]</td><td>3.89</td><td>~150 (estimated)</td><td>~0.014</td></tr><tr><td>Macroscale aluminum[27]</td><td>4.14</td><td>~0.01</td><td>~0.016</td></tr><tr><td>Macroscale</td><td>0.85</td><td>0.15</td><td>~0.016</td></tr><tr><td>meta-aramid[28]</td><td>3.43</td><td>&lt;0.001</td><td>~0.109</td></tr></tbody></table>
Declaration of competing interest

The authors declare the following financial interests/personal re-
lationships which may be considered as potential competing interests:
Rajaprakash Ramachandramoorthy reports financial support was pro-
vided by European Research Council. Dr. Johann Michler is a member of
the International Editorial Board of the journal Materials & Design.
Given his role as a member of the International Editorial Board, had no
involvement in the peer review of this article and had no access to in-
formation regarding its peer review. Full responsibility for the editorial
process for this article was delegated to another journal editor. If there
are other authors, they declare that they have no known competing
financial interests or personal relationships that could have appeared to
influence the work reported in this paper.

Acknowledgements

K. Ding and R. Ramachandramoorthy acknowledge the funding from
the European Union (ERC Starting Grant, Project AMMicro, grant no.
101078619). Views and opinions expressed are, however, those of the
authors only and do not necessarily reflect those of the European Union
or the European Research Council. Neither the European Union nor the
granting authority can be held responsible for them.

**Appendix A. Supplementary data**

Supplementary data to this article can be found online at https://doi.
org/10.1016/j.matdes.2025.115090.

Data availability

Data will be made available on request.

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