A micro-architectured material as a pressure vessel for green mobility

The transition to green mobility heightens the need for pressure vessels for hydrogen that are lightweight, safe (favoring leak-before-break), and spatially conformable. Traditional pressure vessels, often spherical or cylindrical, can fail catastrophically, especially when thick-walled, despite advances and regulation. The hypothesis here is that a TPMS-based shellular, uniquely stretching-dominated even at ultralow densities, can function as a pressure vessel, efficiently sustaining internal pressure by biaxial tensile stresses. The study aims to determine whether shellular architectures can provide higher efficiency (internal energy capacity per unit vessel mass) than conventional vessels and under what design parameters (TPMS type, cell size/count, cold stretching, single vs. double chamber) this superiority is realized.

Prior work (Kolesnikova et al., 2019) measured critical internal pressures for small P-surfaced shellulars (Ni-P, Cu, silica), finding ductile Cu shellulars exhibited the highest resistance, comparable to cylindrical vessels at similar t/D despite micro-scale shells and imperfections. However, their internal volume per total weight was roughly half that of cylindrical vessels, questioning practicality. Classical safety concepts such as leak-before-break in thin-walled vessels inform design goals. Conventional shapes (spherical, cylindrical) are widely used but limit spatial conformability. Other micro-architectures (microlattice, nanolattice, metamaterials) rely on thin foils over templates but are bending-dominated and unsuited for pressure containment despite large interfacial areas. TPMS variants (P, D, F-RD) are reported to offer varied permeability, strength, and surface area characteristics relevant to pressure vessel performance.

- Finite element modeling: TPMS shellulars (P, D, F-RD) were generated (Surface Evolver), re-meshed with quadratic shell elements (HyperMesh), and analyzed in Abaqus. Constitutive model: E=100 GPa, ν=0.3, σ0=120 MPa, perfectly plastic, no hardening. Pressure was increased in 1% increments of expected yield. - Cold stretching: Excess internal pressure was applied until >85% surface area yielded (max equivalent plastic strain ~8.6%); pressure was released to obtain cold-stretched geometries with reduced residual stresses and more uniform stress distributions. Cold stretching increased yield pressure by ~3× across TPMS types. - TPMS selection: Comparative FEA of cold-stretched P, D, F-RD shellulars evaluated internal pressure resistance and internal volume per total weight. The cold-stretched P-surface performed best and was selected for further study. - Yield pressure relation: For cold-stretched P-shellulars, normalized yield pressure P0/σ0 was fit versus relative thickness t/D: P0/σ0 = 1.357 × (t/D)^0.9358. - Efficiency metric: Defined efficiency of pressure vessel (EPV) = (P0 Vin) / (P0 f Vs / At), where Vin is internal gas volume, Vs solid volume, At shell area, and f=0.5 volume fraction per sub-volume. EPV reflects maximum permissible internal energy for given vessel material volume and strength. - Cell size/count and sealing: Practical vessels include hemispherical sealing caps at openings. For fixed Vin and yield pressure (e.g., P0 = 0.01 σ0), parametric models ranged from single cell to N×N×N cells (e.g., 3×3×3, 9×9×9, 100×100×100), adjusting D and t to keep t/D consistent with target P0. - Single- vs double-chamber: Double-chambered designs use both TPMS sub-volumes, adding sealing at necks to create a second chamber (further increasing effective internal volume). Closed-form EPV expressions were derived for single- and double-chambered P-shellulars as functions of N for fixed Vin and P0. - Experimental validation: Copper P-shellular specimens (D=5 mm cell size, t=4–110 µm, 3×3×3 cells) were fabricated via 3D-printed PVA molds, PMMA templates, surface treatment (including Han’s treatment), electroless copper plating, template removal, and annealing at 260 °C for 3 h. Single- and double-chamber variants were sealed (PDMS; glycerol solution) and tested under internal hydraulic pressure using an Instron 8872 setup with a syringe-driven plunger at 0.01 mm/s. Yield pressures were obtained by dividing load at yield by plunger cross-sectional area. Tensile and surface roughness tests characterized Cu foil properties and shell quality. Cold-stretching effects were evaluated by pre-pressurization and re-testing.

- Cold-stretching improved stress uniformity and tripled yield pressure in TPMS shellulars. The P-surface was optimal among P, D, and F-RD variants for pressure resistance and efficiency. - Yield pressure law for cold-stretched P-shellulars: P0/σ0 = 1.357 × (t/D)^0.9358. - Conventional benchmarks: EPV for cylindrical and spherical vessels are constant at 5/12 ≈ 0.417 and 2/3 ≈ 0.667, respectively (independent of pressure/material strength). - Single-chambered P-shellulars: Derived EPV(N) = 0.475 × (8N + π)/(9.36N + 3π). EPV increases with N but has an upper limit ≈0.406, below the cylindrical benchmark (0.417). Example: N=100 (one million cells), D=10 mm, t=54 µm at P0=0.01σ0 and fixed Vin yields EPV≈0.39 (~94% of cylindrical, ~59% of spherical). - Double-chambered P-shellulars: EPV(N) = 0.475 × 8[(1 + (π/(4N^2))^1/2) + π(1 + (1/N^2))^1/2] / [9.36N + 3π(1 + (1/N^2))^1/2]. EPV rises rapidly with N; exceeds cylindrical at N≈4 and equals spherical at N≈14. For N=100 (D=10 mm, t=54 µm), EPV≈0.79, i.e., 188% of cylindrical and 119% of spherical EPVs. - Experiments: Load–displacement curves showed (i) initial nonlinearity and extended plastic flow pre-cold-stretching and (ii) linear response with clear yield after cold-stretching. Measured yield pressures for both single- and double-chambered Cu P-shellulars aligned with the FEA-based relation (Eq. 1), with the upper bound formed by cold-stretched specimens. Data at very low t (≈4 µm) were limited by plating roughness (peak-to-valley ≤4 µm), preventing reliable t/D < 8×10^−3 measurements. - Double-chamber robustness and role of interior frame: FEA showed the interior frame constrains the outer shell; removal of interior layers altered stress distributions, but many interior defects (e.g., 5.30% area missing) did not affect outer shell stresses. Double-chambered specimens had higher successful cold-stretching and performance rates (25%) than single-chambered (19%), indicating defect tolerance in the interior frame. - Feasibility beyond spherical: Analysis of area, thickness, and solid volume vs N showed total solid volume/mass of double-chambered shellulars drops below that of spherical vessels by N≈15 and converges lower, explaining EPV superiority at sufficient N.

The study demonstrates that TPMS-based (P-surface) shellular vessels can be engineered to sustain internal pressure via biaxial tension, leveraging cold stretching to homogenize stresses and raise yield pressures. While single-chambered designs approach but do not surpass conventional cylinders in EPV, activating both sub-volumes (double-chamber) and increasing cell count enable EPV to exceed even spherical vessels at practical N. The mechanism involves rapid decrease of required shell thickness with N and efficient use of added interior frame area without proportional mass penalty, yielding lower total solid volume at constant pressure capacity and internal volume. Experiments on Cu P-shellulars validate the FEA-derived yield law (Eq. 1), supporting the accuracy of EPV predictions. The interior frame primarily stabilizes the outer shell; because both chambers are pressurized, the interior frame sees lower differential stresses and tolerates defects, which eases manufacturing constraints. Collectively, these results address the central question by showing when and how a shellular vessel can outperform conventional shapes, with implications for safer leak-before-break designs, spatial conformability, and multifunctional interfaces (heat/mass transfer) in hydrogen mobility and related applications.

This work introduces and validates a TPMS shellular (P-surface) as a pressure vessel architecture. Numerically and experimentally, cold-stretched shellulars obey a yield-pressure relation tied to relative thickness, enabling scaling to many small cells. A new efficiency metric (EPV) shows single-chambered shellulars approach conventional cylinders, whereas double-chambered designs with sufficient cell count (N≥14) surpass spherical vessels, reaching EPV≈0.79 at N=100. The concept offers key advantages: flexible overall shape, inherent leak-before-break due to thin shells and many cells, potential reinforcement by 2D materials, and multifunctionality via large interfacial area. Future work should focus on scaling fabrication (e.g., modular quadrilateral shell welding, robotic assembly), optimizing sealing strategies, exploring alternative TPMS geometries and materials (including composites and 2D coatings), refining models to include hardening and defects, and integrating thermal/catalytic membranes for combined storage–exchange devices.

- Experimental shell thickness lower bound (~4 µm) limited by electroless plating roughness (peak-to-valley ≤4 µm), restricting t/D < 8×10^−3 data. Some specimens failed during cold stretching due to surface roughness/non-uniformity. - FEA assumed perfectly plastic material (no hardening) and idealized geometry; manufacturing defects and residual stresses may alter performance. - Validation focused on P-surface TPMS and Cu foils; generalization to other materials/TPMS types requires further testing. - EPV comparisons used fixed Vin and P0 (e.g., 0.01σ0) and hemispherical sealing caps; different operating pressures, materials, or sealing designs could shift thresholds. - Large-scale fabrication remains technically challenging (complex 3D welding paths), although interior frame defect tolerance may alleviate some constraints.