Additively Manufactured Dual‐Faced Structured Fabric for Shape‐Adaptive Protection

Abstract Fabric‐based materials have demonstrated promise for high‐performance wearable applications but are currently restricted by their deficient mechanical properties. Here, this work leverages the design freedom offered by additive manufacturing and a novel interlocking pattern to for the first time fabricate a dual‐faced chain mail structure consisting of 3D re‐entrant unit cells. The flexible structured fabric demonstrates high specific energy absorption and specific strength of up to 1530 J kg−1 and 5900 Nm kg−1, respectively, together with an excellent recovery ratio of ≈80%, thereby overcoming the strength–recoverability trade‐off. The designed dual‐faced structured fabric compares favorably against a wide range of materials proposed for wearable applications, attributed to the synergetic strengthening of the energy‐absorbing re‐entrant unit cells and their unique topological interlocking. This work advocates the combined design of energy‐absorbing unit cells and their interlocking to extend the application prospects of fabric‐based materials to shape‐adaptive protection.

Both structured fabrics exhibited hysteresis during their deformation which might be attributed to the friction between the struts of adjacent unit cells, as well as the accumulated plastic deformation of the base material, especially at the structural joints.
For the dual-faced structured fabric, the hysteresis loop shrinks during the first two cycles and remains almost unchanged from the third cycle onwards, indicating that the cyclic response stabilizes after approximately three cycles ( Figure S3a). This result reveals that the accumulation of plastic deformation occurs mainly in the first two cycles and after that, mainly elastic deformation occurs. For the octahedral structured fabric, however, the hysteresis loop keeps shrinking during the entire cyclic compression test, which is not only related to the accumulation of plastic deformation, but also to the gradual failure of vacuum confining pressure with the increase in the number of cycles. For the dual-faced structured fabric, the vacuum confining pressure is preserved after 30 compression cycles ( Figure S3c).
The failure of the vacuum confining pressure is attributed to the puncturing of the enveloping film by the sharp corners of the octahedral structured fabric (Figure S3d).
In addition, the energy loss coefficients of the dual-faced and octahedral structured fabrics were stable at about 38% and 44%, respectively, during cyclic compression (see Methods). Moreover, the energy loss coefficient of the dual-faced structured fabric is as low as that of three-dimensional (3D) thermoplastic polyurethane (TPU) lattice foam [2]. This finding shows that the dual-faced structured fabric has excellent energy restoration and longlasting performance under long-term cyclic loading.   Figure   S4). However, the central part is close to the neutral axis of the structured fabric, thus remaining stress-free. As for the lower part, since the structured fabric is a chain mail structure consisting of three-dimensional re-entrant unit cells, they are not in contact across the lower part for small displacement, as shown in "II" of Figure S4. The interlocking between the adjacent unit cells will only be evident when the structured fabric experiences large deformation. Therefore, the lower part is stress-free at the linear elastic stage (small displacement) and may be subjected to tensile stress only under large deformation (large displacement).
The bending moment contributed by the plane contact region B 1 M is calculated by where B 1 y is the radial distance of a certain point in the plane contact region relative to the neutral axis. b and h are the width and height of the infinitesimal segment, and is the thickness of the region corresponding to plane contact (upper half of Figure 3e in the manuscript).
The effective Young's moduli of the plane contact region, point contact region, and enveloping film are referred to as E c1, E c2 , and E t , respectively. The B c1  can be calculated by where the corresponding compression strain B c1  can be calculated by where  is the curvature radius of the infinitesimal segment and B 1 y is the radial distance of a certain point in the region relative to the neutral axis.
The substitution of Eqs. (4) and (5) The second moment of area for the plane contact region B z1 I is expressed as Thus, Eq. (6) can be simplified to Similarly, the bending moment contributed by the point contact region can be expressed where B z2 I is the second moment of area of the point contact region relative to the neutral axis, which can be expressed as where B 2 y is the radial distance of a certain point in the point contact region relative to the neutral axis.
The bending moment contributed by the enveloping film can be expressed as where B z3 I is the second moment of area of the enveloping film relative to the neutral axis, which is expressed as where B 3 y is the radial distance of a certain point in the enveloping film relative to the neutral axis and m is the thickness of the enveloping film.
By substituting Eqs. (8), (9), and (11) into Eq. (2), the bending moment acting on an infinitesimal segment in the case of loading the bottom surface is derived as Similarly, for the case of loading the top surface, as shown in the lower half of Figure 3e in the manuscript, the bending moment in an infinitesimal segment is given by where T 1 M can be expressed as where T z1 I is the second moment of area of the region relative to the neutral axis. T z1 I can be expressed as where T 1 y is the radial distance of a certain point in the plane contact region relative to the neutral axis.
The bending moment contributed by the point contact region can be expressed as where T z2 I is the second moment of area of the point contact region relative to the neutral axis, which is expressed as where T 2 y is the radial distance of a certain point in the point contact region relative to the neutral axis.
The bending moment contributed by the enveloping film can be expressed as where T z3 I is the second moment of area of the enveloping film relative to the neutral axis. T z3 I can be expressed as where T 3 y is the radial distance of a certain point in the enveloping film relative to the neutral axis.
By substituting Eqs. (15), (17), and (19) into Eq. (14), the bending moment acting on an infinitesimal segment in the case of loading the top surface is derived as By combining Eqs.
By substituting Eqs. (16) and (18) into Eq. (23), and taking b, h, and  as 50, 13, and 0.3 mm, respectively, the following result can be obtained: Note that the effective Young's modulus of the plane contact region E c1 is larger than that of the point contact region E c2 . Thus, it is shown that T M is greater than B M .

Section 4. Compression responses of the different structured fabrics
Seven structured fabrics, constructed using different unit cells or topological interlocking, were designed. Their physical features, including the configuration, strut diameter, strut length, and apparent density, are presented in Table S1.  Figure S7. Deformed structured fabrics after the application of 70% compression strain.  can be more easily overcome. However, at a higher vacuum confining pressure, a stronger jamming effect between interlocked unit cells is introduced. Thus, the frictional drag in the point contact region on the bottom surface will increase to be close to that in the plane contact region on the top surface due to a more substantial jamming effect, resulting in minor differences between them. Therefore, the difference in the specific bending modulus of the bottom and top surfaces should be much smaller at a higher vacuum confining pressure of 90 kPa. Alumina hollow lattice -9.6 0.44 [3,9] Hybrid hollow lattice -100 0.36 [3,10] Polymeric BCC lattice -330 0.40 [11,12] -317 0.70 [11,12] -235 0.56 [11,12] NiP multiscale lattice -23.7 0.09 [3,13] CNT/PA12 SC-12H lattice -88.74 0.219 [8] CNT/PA12 pyramidal lattice -72.19 0.80 [8] CNT/PA12 honeycomb lattice -142.54 0.82 [8] Tough polymeric re-entrant lattice -370 0.59 [14] TiN octahedral hollow lattice -90.7 0.09 [3,15] Ni BCC lattice -69.5 0.17 [3,4] -23.8 0.02 [3,4] * Present work Section 7. Performance evaluation of materials reported for wearable applications Table S5 shows a performance comparison of the presently designed dual-faced structure against four other types of materials proposed for wearable applications. As far as possible, scorings are given based on relative performance. When a scoring cannot be given on a quantitative basis, we have attempted to give a reasonable score based on rational interpretation.  [16] Jammed sheet [17] Unjammed sheet [17] Medicinal plaster [18] Specific bending modulus

Section 8. Mechanical properties of MJF-printed PA12 bulk material
A preloading of around 5 N was set for all MJF-printed PA12 tensile specimens at horizontal build orientation. Uniaxial tensile tests with a displacement rate of 10 mm/min were performed on the tensile specimens. The uniaxial tensile test results of the tensile specimens are shown in Figure S9 and Table S6. As observed, the stressstrain curves for the three samples closely overlap. The Young's modulus, ultimate tensile strength and elongation at break are 1404 MPa, 47.7 MPa and 20.7%, respectively. The mechanical properties of the MJF-printed PA12 bulk material obtained here are similar to those reported in previous studies [19,20].  Note that defects are inevitable during the printing process, and our group has previously carried out a related study on the effect of void defects on the mechanical properties of the MJF-printed PA12 bulk material based on uniaxial tensile tests [21].
The results reveal that the expansion and coalescence of voids lead to crack initiation and propagation in the bulk material during uniaxial tensile deformation. In addition, our previous work has indicated that the porosity of MJF-printed bulk material can be decreased by optimizing the printing parameters, such as the build direction, power input, layer thickness, etc. [22]. Given the structural complexity of the dualfaced structured fabric, the effect of defects on the overall performance of the protection system has not been studied in the present work, but will be carried out as part of future work.