Windows are critical components for maintaining the functionality of space stations in the demanding environment of Low Earth Orbit (LEO). This article considers borosilicate glass (BSG) as a compelling novel material for multi-pane fenestration, evaluating its potential to outperform traditional options like fused silica (FS). By specializing our previously-established methodological framework, we evaluate BSG in its capacity to provide greater radiation shielding than FS, in addition to its superior cost-to-performance ratio. Our analysis models the effects of electromagnetic waves on a three-pane window, analogous to that of the ISS Cupola, in hybrid configurations combining BSG and acrylic glass. We simulate the system's response to solar and terrestrial radiation to assess its transient thermal state and optical properties under two extreme LEO scenarios, corresponding to maximum thermal cycling or peak heating. Beyond the specific parameters of this study, the collective material properties of BSG suggest a robust foundation for achieving superior performance for space glazing. (c) 2026 The Author(s). Published by Elsevier B.V. on behalf of COSPAR. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).

A first experimental assessment of a novel, metal-free orthogonal connection system for laminated glass plates, which uses in-situ injected mortar layers and structural silicone, is presented. The system features a horizontal glass element slotted into a vertical pane, with mortar blocks acting as compression wedges while silicone is utilized to resist sliding forces. Through combined push-out and bending tests, we established the joint performance across ultimate limit states, including accidental glass fracture. Key findings are: near-linear moment-rotation until peak load; exceptional rotational capacity, exceeding 10 degrees; high post-peak ductility, with ultimate failure occurring at 3.4 to 4.3 times the peak rotation; controlled stiffness reduction due to sequential mortar cracking, preventing catastrophic failure even under large deformations. We interpret this behaviour using a simple mechanical model that treats the mortar blocks as compression-only springs and employs an overall energy-based criterion for crack propagation. Although primarily designed for glass staircases, where load-bearing parallel stringers rely on these joints for lateral stability, buckling restraint, and handrail load transfer, the system's strength, ductility, and minimal visual impact make it highly promising for a wider range of transparent architectural applications.

Space windows require transparent materials with superior mechanical, thermal and optical properties. While fused silica has been the traditional choice, acrylic glass is now favored in spacecraft for its cost-effectiveness and radiation shielding capacity, achieved due to radiation absorption. However, this can cause heating, with risks for material integrity especially in space stations at low Earth orbit (LEO), where radiation exposure is more severe than in spacecraft. We investigate the thermal and optical performance of multilayer panels operating in LEO, comparing packages with fused silica, acrylic glass or a combination of both. Using established material properties and a detailed energy transfer model, we calculate temperature distribution under extreme orbital conditions, similar to those on the Cupola of the International Space Station. Two key scenarios are analyzed, considering variations in solar, albedo, and Earth infrared radiation, as well as internal temperature control. The window transmissivity, when calculated within the visible spectrum of sunlight, determines the optical transparency. Our findings identify potential issues with acrylic glass when used in LEO, caused by high radiation absorption. More broadly, our methods permit the evaluation of alternative transparent materials for future applications, contributing to the development of space windows for long-term missions.

Although individual carbon nanotubes (CNTs) possess extraordinary mechanical properties, the macroscopic axial stiffness of assembled fibers, obtained through spinning, falls significantly short of theoretical expectations due to suboptimal load transfer between CNTs. We develop a first-principles multiscale analytical model that explicitly accounts for interfacial shear compliance to predict the effective axial stiffness. Assuming the fiber is a 1D array of aligned CNTs merged in a shear-compliant matrix, we variationally derive closed-form solutions for the effective Young’s modulus. A key contribution is the identification of an internal length scale — determined by CNT geometry and stiffness, and interfacial properties — which controls stress transfer efficiency. We establish asymptotic bounds through limiting-case analysis and validate its closed-form expressions against both simulated and experimental data for various fiber architectures. The model allows to interpret effective fiber properties from full-field micromechanical simulations for systems with well-characterized inputs. When applied to experimental data, the model enables back-calculation of interfacial shear stiffness for aligned CNT fibers. It correctly captures the asymptotic approach to the rule-of-mixtures upper bound for long CNTs and the steep reduction in stiffness for short CNTs. This quantitative agreement confirms the model utility in extracting interfacial properties from macroscopic tests and enables reliable performance prediction and inverse design.

We evaluate an in-house implementation of a Nondominated Sorting Genetic Algorithm II (NSGA-II) for stiffness and cost efficiency multi-objective structural optimization of laminated glass under wind and self-weight, considering accidental partial breakage according to safety standards. Variables include glass thermal/chemical treatments and thickness, and interlayer types, encoded in a binary representation subjected to mutations. Load duration affects glass strength and shear coupling of the glass plies; the “Enhanced Effective Thickness” (EET) method is the reduced order calculation model. Structural verification are handled as constraints through the Compliance Score technique, influencing selection probability via penalty functions. Dynamically changing mutation probabilities are explored to prevent premature convergence to a single part of the Pareto front. The “Technique for Order of Preference by Similarity to Ideal Solution” (TOPSIS) is discussed for selecting the best solution within the Pareto set based on design inputs. The worked problem allows evaluation of all configurations and calculation of the true Pareto set via pairwise comparison, serving as a benchmark for assessing algorithm efficiency based on population size and mutation probability type (fixed or dynamically changing). Findings confirm the great potential of genetic algorithms in multi-objective structural optimization of laminated glass.

Thermal analyses of space station windows in Low Earth Orbit (LEO) are usually focused on a specific orbiting scenario, namely the one with the longest eclipse duration and the greatest temporal fluctuation in solar radiation, that is typically considered the most critical for satellites. However, for windows made of materials such as acrylic glass, whose mechanical properties are sensitive to temperature, alternative orbital configurations can lead to significantly higher heating than previously estimated. In particular, this study identifies a critical condition, occurring when the orbit plane is highly inclined with respect to the Sun rays, so that one surface is exposed to prolonged and intense radiation. Here, it is demonstrated that, under this scenario, the Sun-facing surface may reach temperatures above the glass transition point, risking material degradation and structural failure, while the opposite surface experiences low temperatures, potentially leading to embrittlement. These findings emphasize the need to evaluate transient thermal behavior under diverse orbital geometries when designing large windows for future space stations. The results highlight key trade-offs between material properties, glazing dimensions, and orbital parameters to ensure safety and performance

The growing interest in space exploration, not least for tourism purposes, requires comfortable and visually engaging accommodations in orbiting stations, with large windows to observe the Earth and the cosmos. While seemingly simple, these elements are complex engineering feats, of paramount importance to enhance both the functionality and the human experience of space missions. Designing space windows requires addressing a unique set of engineering demands to ensure safety, durability, and performance under the extreme space conditions. The key requirement is the capacity to withstand the pressure differential between the station’s interior and the vacuum of space, about two order of magnitude higher than in terrestrial applications, without excessive deformation or failure. Furthermore, the glazing is particularly vulnerable to the temperature variations, from the intense heat of direct sunlight to the extreme cold of space, generating cyclically-varying thermal stress that can damage the materials. Finally, space windows must be designed to handle impacts from space debris traveling at high velocities. Other requirements are resilience, high fracture toughness, high endurance limit and lightweight. For these reasons, space glazing are usually composed of several layers, to provide: radiation/thermal shield (multiple plies, vacuum insulated); structural capacity (redundant pressure panes); protection against debris (external pane) and from scratch (internal sacrificial layer). The state of the art in space glazing is represented by the Cupola of the International Space Station (ISS), made of fused silica monolithic flat panels. To address the unique challenges of the space environment, it is not possible to transfer to this context the glazing technology used for terrestrial applications, and innovative transparent composite are necessary. With reference to the windows of the ISS Cupola, taken as paradigmatic examples, we discuss the design, conception, and modeling of high-performance transparent unitized cells for large spacecraft and space station windows, based on operational thermal, optical, and structural requirements.

Calculating the temperatures of windows of space stations in Low Earth Orbit (LEO) is crucial for ensuring their structural integrity. We present a comprehensive thermal analysis that considers direct solar radiation, Earth’s albedo effect, infrared radiation from the Earth and convective heat exchange with the internal environment. The thermal balance equation incorporates the time variation of these contributions due to orbital motion for windows with different orientations, to determine the temperature of the materials, factoring in key parameters such as absorptivity, transmissivity, reflectivity, and their dependence on the radiation wavelength spectrum. Referring to the conditions of the Cupola of the International Space Station as a paradigmatic example, we compare the thermal performance of two common window materials: fused silica and acrylic glass. Our results indicate that the higher transmissivity of fused silica makes it insensitive to solar and albedo radiation, reducing temperature values and their dependence on plate thickness and exposure variability due to orbital motion. In contrast, the higher absorptivity of acrylic glass results in much higher temperatures, proportional to the thickness, with a cyclical dependence on the orbital period. This analysis provides insights for the design and selection of window materials in space station construction, ensuring their durability and functionality in the conditions of LEO.

Most standards reduce the design strength of glass through a modification coefficient that accounts for static fatigue caused by subcritical propagation of surface cracks. For wind pressures on glass plates, the coefficient is derived assuming nominal durations of maximum wind gusts or cumulative winds, which are defined based on tradition and practice. Here we derive closed-form expressions for the modification coefficient using a fracture mechanics approach which incorporates the time histories of wind velocity or their probabilistic distributions. The coefficient depends on the duration of the action and becomes constant for typical design lives. A consistent nominal duration is then defined by referring to a wind with fixed reference velocity which produces the same damage of the actual action. The approach, applicable to the European context, has been applied to data recorded in Italy. The results are compared with prescriptions from various standards showing that they are in general non-conservative.

We present a one-dimensional viscoelastic finite element model for laminated glass, employing fractional calculus to effectively capture the shear-coupling behavior of the polymeric viscoelastic interlayer between glass plies. The polymer relaxation curve is approximated using four power-law branches, which are sufficient to represent both the short-and long-term responses of most commercial materials. This ensures that Boltzmann's integral aligns with Caputo's definition of a fractional time derivative. The spatial FE discretization is incorporated into the weak formulation of the dynamic viscoelastic problem derived from Hamilton's principle. Time integration is performed using finite differences, with fractional derivatives approximated through the L1 formula. This allows to use a variable time-step, progressing in logarithmic scale, to balance the representation across the different power-law branches of the relaxation curve. The model is validated through four-point bending experiments on laminated glass specimens, involving loading at various strain rates and relaxation tests at different temperatures. Comparisons between experimental results and model predictions show strong agreement across a wide range of loading conditions, time scales, and temperatures. This demonstrates the model's ability to accurately simulate the coupled viscoelastic response of laminated glass under bending loads, establishing it as a valuable tool for structural analysis and design in building engineering.

A Mobius kaleidocycle is a closed kinematic chain of n >= 7 identical links connected by revolute joints, forming a linkage with the nonorientable topology of a Mobius band. If its joints are set at a critical, n-dependent twist angle - the smallest that allows closure without forcing - then, despite formally having n-6 internal degrees of freedom, the linkage admits only a single one: a reversible, periodic everting motion. Focusing on the case n = 7, we determine the kinematic matrix via the Denavit-Hartenberg construction, under closure and congruence constraints. A geometric mechanism arises alongside the topological one due to a matrix-rank deficiency, accompanied by a corresponding state of self-stress. The geometric mechanism is infinitesimal and stiffened by self-stress, while eversion is enabled by the finite mechanism. Using a variational argument, we confirm that the sum of squared joint rotations remains constant throughout eversion. We further categorize the states of self-stress, identifying conserved quantities - including the sum of twisting moments raised to any positive integer power lambda >= 1 - which enable estimates of self-stresses in moderately incongruent linkages requiring elastic forcing to close.

We discuss a probabilistic methodology to align theoretical strength predictions with experimental results, by establishing quantitative relationships between failure probabilities and applied test loads. This enables reliable safety margin verification for structural designs even when only limited experimental data is available on full-scale prototypes. The methodology is demonstrated through the case study of a structural bolted joints connecting large, non-standard four-ply laminated heat-tempered glass plates. The research combines experimental testing with a theoretical interpretation grounded in probabilistic mechanics. Observing that the expected strength of the joint, derived from semi-probabilistic design, is much lower than the actual test results, our study examines how key factors, primarily lamination effects on redundancy and statistical interference between intrinsic glass strength and heat-induced surface prestress (tempering), can influence structural capacity. While the application is specific, the underlying approach remains applicable to other structural systems. The analysis demonstrates that accounting for the statistical interaction of multiple variables, overlooked in semi-probabilistic methods, can lead to strength predictions up to 125% higher than those obtained through the semi-probabilistic approach, in agreement with experimental findings. This improved approach forms the basis for enhanced verification methodologies, promoting optimized material utilization and mitigating excessive conservatism in structural glass design.

Propaedeutical to a better understanding of the mechanics of cables, with potential applications in material science and biology, tensile tests were performed on two-ply yarns made of rubber rods, manufactured by transforming the twist on two adjacent straight rods into tortuosity for the resulting double-helix shape. Modeling of the yarn as a pair of Kirchhoff rods in reciprocal contact, fails to provide results in agreement with experiments, especially when the helix slope angle α tends to π/4, representing the geometric limit for material interpenetration. This discrepancy could not be justified by considering the viscosity of the rods, their cross-sectional distortion, or cohesive/frictional contact. Our contribution starts from the experimental observation that the rods are in an eigenstress state already in the reference balanced configuration. This is characterized by a high twist, dictated by the ratio between torsional and bending rod stiffness, which increases as α decreases, growing unboundedly as α→π/4. Experiments confirm that twisting can significantly increase the tensile stiffness of straight rubber rods, in agreement with non-linear elasticity theory. Tensile tests on the yarns can be reproduced excellently only if the twist-induced stiffening is considered.

A viscoelastic description via fractional calculus is used to theoretically determine the time-varying stress state in single-curvature cold-bent laminated glass. This approach is proven effective when the relaxation function of the polymeric interlayer can be approximated by branches of power laws, as in most commercial materials. Solutions are obtained numerically by approximating the fractional time derivatives with the L1 formula. This conveniently allows to use a variable time step for a phenomenon characterized by two time-scales, corresponding to the loading process and the long-term relaxation. A parametric analysis shows the effects of polymer type, interlayer thickness, deformation history and operating temperature. A comparison is made with the results from the quasi-elastic approximation, which neglects the memory effect of viscoelasticity, showing that, since the interlayer strain is kept constant in the long term, it provides accurate results in term of peak and asymptotic stresses in glass, although the early stages of the deformation history give rise to differences when the structure is far from the layered or monolithic limits. This study can be useful for the optimization of the cold-bending process.

We propose a weak form of the transient heat equations for solid bodies, as a time-dependent spatial variation of the heat displacement vector field, whose time derivative is the heat flux. This develops the variational principle originally proposed by Biot, inasmuch Fourier’s law is embedded as a holonomic constraint, while energy conservation results from the variation (the vice-versa from Biot). This is a neat formulation because only the heat displacement appears in the variational equations, whereas Biot’s form also involved the unknown temperature field: Fourier’s law is used only a posteriori to recover the temperature. Since the heat displacement is generally more regular than the temperature field, it represents a natural variable in problems with material inhomogeneities, uneven radiation, thermal shocks. The three-dimensional analytical set-up is presented in comparison with Biot’s, for boundary conditions accounting for radiation and convection. A mechanical analogy with the equilibrium of an elastic bar with viscous constraints is suggested for the one-dimensional case. The variational equations are implemented in a finite element code. Numerical experiments on benchmark problems, involving high temperature gradients, confirm the efficiency of the proposed approach in many structural problems.

In order to demonstrate the wide range of inelastic non-linear tensile responses observed in structured fibers of various types, an ideal phenomenological model (Gedankenmodell) is theoretically analyzed, prototyped and tested. This consists in a rod made of a regular ensemble of sticks in a brickwork -like three-dimensional grid, hooped by elastic bands. The stick lateral faces are wavy surfaces in cohesive -frictional contact; their relative sliding induces a transversal expansion opposed by the bands, providing shear -slip constitutive laws that mimic the complex interaction forces in fibers composed of adherent fibrils. The macroscopic response of the rod to uniaxial loading is theoretically modeled in the framework of generalized standard materials. Experiments conducted on 3D -printed prototypes confirm the theoretical approach. As an example, the Gedankenmodell is applied to the tensile response of Carbon NanoTube (CNT) fibers, composed of CNTs laterally bonded via a spinning process. The model phenomenologically reproduces the tensile response of dry -spun, aerogel-spun and wet -spun CNT fibers, specifically the onset of a yield point, elastic unloading-reloading and inelastic aftereffects. This approach interprets the adhesion of the CNTs within the broad paradigm of cohesive -frictional adherence, combined with conservative forces of attraction.

The overall heating of satellites operating in low orbit, essentially due to direct radiation from the sun and terrestrial albedo, and the planetary radiation, is well studied, but little is found specifically on transparent plates used for windowing spacecrafts. The most historic material of choice is fused silica, as in the cupola of the International Space Station; more recently, acrylic glass is being used, but its refractive properties are poorly documented. Starting from Maxwell’s laws, the effects of electromagnetic waves incident on multilayer windows composed of panes of fused silica or acrylic glass, or a composition of these, are analyzed. Using data of refractive index from the literature, which however are incomplete and sometimes contradictory, the problem is addressed by distinguishing the frequency of the radiation, because this affects the transmissibility and absorption of each material; moreover, the frequency content of the radiation of the solar and terrestrial albedo is different from that of the planet. Worked examples show that fused silica allows most radiation to pass directly through; absorption occurs in such a thin surface layer that it can be modeled as a boundary condition. Acrylic glass, on the other hand, is characterized by absorption depending on the thickness; this can potentially increase its temperature, posing a problem since the mechanical properties decay at temperatures above 100 °C. This study represents a key step to analyze the thermal problem for space windows, of considerable interest since glazing can fail due to thermal shocks, constrained thermal variations, or temperature concentrations.

Consider a linear elastic infinite disk, a sector of which, of arbitrary opening angle 2 beta, is subjected to a uniform temperature increase Delta T with respect to the complementary portion. An analytical solution is sought, imagining that the disk is first cut along the interface with the heated sector, now free to expand; then the two parts are re-joined and the thermal mismatch is annihilated by arrays of glide dislocations, distributed along the interfaces. A sequence of approximate solutions is found as the length of the arrays of reconciling dislocations is increased, characterized by a logarithmic stress singularity at the sector tip. However, modulo the particular case 2 beta=pi, the stress grows unboundedly when the length of the dislocation arrays tends to infinity. This is in agreement with the predictions from dimensional analysis, because for the infinite disk problem there is no internal length scale. If the disk is finite in size, its radius R represents an additional length scale enriching the class of solutions, but the analytical treatment results much more complicated. Therefore, we propose to correlate the solution of this problem with that of an infinite disk for which the length of the arrays of reconciling dislocations is finite and depends upon R. An excellent agreement with numerical experiments in abaqus is thus found. An approach of this type can be useful in many engineering problems for which the limit condition of infinite body, though leading to analytic simplifications, could imply spurious results.

Numerical approaches are elaborated to calculate the rheological response of laminated glass beams, whose viscoelastic interlayer is modeled via fractional calculus. This mathematical description is very effective when the relaxation function of the polymer can be expressed by continuously connected branches of power laws, as is the case for most materials used to laminate glass. The classical approach uses the Gr & uuml;nwald-Letnikov approximation of fractional derivatives, but it requires constant time-steps, which would become very large to reasonably cover the entire observation time, thus losing accuracy. The use of the L1 algorithm with increasing time-steps is proposed, which is well suited to the power law character of the relaxation function. This allows to follow the long-term creep response, providing a better approximation when needed. The method is implemented for beams laminated with viscoelastic interlayers whose relaxation is described by four branches of power laws, to cover most practical cases. Numerical experiments show their advantages over the Grunwald-Letnikov approach for characterizing the long-term structural response.