While origami-inspired engineering increasingly relies on mechanics-based computational tools to design deployable structures, most existing approaches remain optimized for linear creases or simplified rigid kinematics. Modeling the structural behavior of non-rigid, curved-crease origami represents a significant challenge, as standard finite element methods struggle with complex meshing restrictions, the ill-conditioning of penalty-based hinge constraints, and the artificial stiffening induced by nonlinear plate theories. To overcome these limitations, we present a novel meshless Reissner–Mindlin plate framework, based on the Reproducing Kernel Particle Method (RKPM), that employs high-order polynomial approximations and an exact analytical geometric tangent stiffness formulation. Crucially, rather than relying on traditional penalty-based hinges, we mathematically reduce the complex 3D curved fold kinematics into exact linear equality constraints. This rigorous decoupling of the fold geometry from the spatial discretization allows the discontinuous kinematics to be seamlessly processed by any standard constrained optimization software. We demonstrate that this framework successfully captures the severe nonlinear membrane-bending coupling, doubly-curved equilibrium states, and complex snap-through buckling phenomena inherent to large-deformation curved origami, effectively overcoming the global artificial stiffening that plagues standard formulations.

Determining the mechano-structural relations in biological materials with hierarchical structure is crucial to understanding natural optimization strategies and designing functional bioinspired composites. However, measuring the nanoscale mechanics and dynamic response is challenging when the specimen geometry and loading environment are physiologically complex. To overcome this challenge, we develop a combination of synchrotron X-ray diffraction testing and analytical modelling to explore the mechano-structural changes during bending loads on stomatopod cuticle. Stomatopod cuticle is an example of a hierarchical biomaterial optimized for high impact and bending resistance. Using models for large deformations of elastic continua, we measure cuticle strains from macroscopic deformations and combine diffraction-based fibril strains with stresses to quantify the local elastic moduli and nanoscale strain concentration factors, which are found to vary across cuticle sub-regions and under different flexion loading modes. This approach has the advantage of identifying constituent biomaterial properties and mechanisms in situ and is also suitable for studying time-dependent changes, such as concurrent strains of the nanofibrous phase that occur during physiological loading.

The pyroresistive response of conductive polymer composites (CPCs) has attracted much interest because of its potential applications in many electronic devices requiring a significant responsiveness to changes in external physical parameters such as temperature or electric fields. Although extensive research has been conducted to study how the properties of the polymeric matrix and conductive fillers affect the positive temperature coefficient pyroresistive effect, the understanding of the microscopic mechanism governing such a phenomenon is still incomplete. In particular, to date, there is little body of theoretical research devoted to investigating the effect of the polymer thermal expansion on the electrical connectivity of the conductive phase. Here, we present the results of simulations of model CPCs in which rigid conductive fillers are dispersed in an insulating amorphous matrix. By employing a meshless algorithm to analyze the thermoelastic response of the system, we couple the computed strain field to the electrical connectedness of the percolating conductive particles. We show that the electrical conductivity responds to the local strains that are generated by the mismatch between the thermal expansion of the polymeric and conductive phases and that the conductor-insulator transition is caused by a sudden and global disconnection of the electrical contacts forming the percolating network.

Crop genetic engineering for better root systems can offer practical solutions for food security and carbon sequestration; however, soil layers prevent the direct visualization of plant roots, thus posing a challenge to effective phenotyping. Here, we demonstrate an original device with a distributed fiber-optic sensor for fully automated, real-time monitoring of underground root development. We show that spatially encoding an optical fiber with a flexible and durable polymer film in a spiral pattern can significantly enhance sensor detection. After signal processing, the resulting device can detect the penetration of a submillimeter-diameter object in the soil, indicating more than a magnitude higher spatiotemporal resolution than previously reported with underground monitoring techniques. Additionally, we also developed computational models to visualize the roots of tuber crops and monocotyledons and then applied them to radish and rice to compare the results with those of X-ray computed tomography. The device’s groundbreaking sensitivity and spatiotemporal resolution enable seamless and laborless phenotyping of root systems that are otherwise invisible underground.

Echinoderms, such as sea cucumbers, have the remarkable property of changing the stiffness of their dermis according to the surrounding chemical environments. When sea cucumber dermal specimens are constantly strained, stress decays exponentially with time. Such stress relaxation is a hallmark of visco-elastic mechanical behavior. In this paper, in contrast, we attempted to interpret stress relaxation from the chemoelasticity viewpoint. We used a finite element model for the microstructure of the sea cucumber dermis. We varied stiffness over time and framed such changes against the first-order reactions of the interfibrillar matrix. Within this hypothetical scenario, we found that stress relaxation would then occur primarily due to fast crosslink splitting between the chains and a much slower macro-chain scission, with characteristic reaction times compatible with relaxation times measured experimentally. A byproduct of the model is that the concentration of undamaged macro-chains in the softened state is low, less than 10%, which tallies with physical intuition. Although this study is far from being conclusive, we believe it opens an alternative route worthy of further investigation.

Mixing processes are commonly used to handle powders and grains in several industrial fields, and their performance has been subjected to extensive study. However, research is limited on underwater mixing in novel deep-sea mining applications. Consequently, we adopt a discrete element method (DEM) enhanced by a lubrication model to investigate the underwater mixing process. We focus on the effect of microscopic material parameters on macroscopic mechanical responses in this study. Variations in macroscopic responses are small among DEM samples with a well-controlled initial density; the largest coefficient of variation (cv) is less than 1.4% in normalized forces on the sidewall, and the values of cv are less than 1.0% for other macroscopic responses. A comprehensive parametric study is conducted for elastic moduli and for dissipative parameters. Elastic moduli exhibited a negligible influence, and the effects of dissipative parameters ranged from most significant to most negligible in the order of coefficient of rolling friction, coefficient of friction, coefficient of restitution, and fluid viscosity. We further discuss the network connectivity of force chains and shear-induced size segregation; it was found that an increase in rolling friction increases the connectivity of particles in principal stress chains, which increases the mixing resistance. Size segregation is monitored for DEM samples with particles that initially follow a uniform size distribution: an increase in friction is observed to enhance the segregation and an increase in fluid viscosity to alleviate it. The findings in this paper can advance the understanding of the dynamics of underwater mixing and offer insights for designing mixing systems for granular materials with large variations in material properties.

A novel one-step Roll & Press process for fabricating capacitors with embedded electrodes and with highly reversible polar nanostructures and superior energy storage performance (energy density: 50 J cm−1; efficiency: 80%).

A wide range of modern and advanced structural applications includes self-folding materials and origami metamaterials. Simulation tools capable of modelling creases in continuum media have become desirable to keep up with such technological advancements. We present an approach to simulate folding as sharp discontinuities in the Euler rotations of nonlinear plates. We used large deformations and large rotations within a first-order shear plate theory. The novel finding is a set of constraints that the rotation jumps must satisfy on a crease. We used a meshfree method to implement such conditions and check their effectiveness. We verified the numerical solutions against available analytical and semi-analytical solutions. We show that the proposed idea works well also for more complicated configurations, such as rigid origami motions with multiple folding lines and crumpled sheets with random creases.

Mutable connective tissues of the sea cucumbers' dermis can assume three different mechanical states (soft, standard and stiff) according to the chemical changes in the water. There is broad consensus that variable cross-linking of the extracellular matrix is responsible for such changes. This paper uses Small-angle X-ray Scattering (SAXS) measurements, a micromechanical viscoelastic model, and a molecular extended reptation theory to look for other causes beyond cross-linking. We conclude that in potassium-ions enriched seawater, the interfibrillar matrix stiffens due to increased cross-linking, but this must also imply macromolecular chain scission change in molecular weight and increased friction between the chains. In softening water solution (calcium-ions deprived seawater), the interfibrillar matrix softens because of decreased cross-linking, and simultaneously macromolecules chain recombine and friction between the chains decreases. These findings allow us to conclude that the zero-shear viscosity increases more than five times during stiffening and reduces to 3% of its standard value during softening. Also, we find that the fibril strains measured through SAXS seem to suggest that, in reference conditions, the interfibrillar matrix (artificial sea water) behaves similarly to a covalently cross-linked gel; instead, during softening and stiffening, it appears that the matrix shows stress relaxation akin to an ionic cross-linked gel.

Recent studies have shown that root system architecture determines crop resilience and productivity. However, roots grow invisibly underground and are notoriously difficult to track. Root visualization requires digging, which is time-consuming and destructive. The lack of real-time non-invasive underground imaging methods has made it challenging to study this vital organ. Here, we report a method for imaging underground root system using the distributed fiber optic sensor. device named "Fiber-RADGET". By formulating an optical fiber into spiral polytetrafluoroethylene film, the sensor device named Fiber-RADGET detects and monitors geophysical strain generated by root development. Agricultural technology is increasingly becoming automated with seamless feedback through Internet-of-Things remote sensors. The device highlighted here represents a significant addition to the repertoire of tools that next-generation agriculturalists can use for data-driven automation.

In the non-dissipative regime, the potential energy is the difference between the strain energy of the deforming solid and the work done by the external forces. For configuration-dependent external forces, whose direction is perpendicular to the deformed shape, we obtain a simple formula for the strain energy release rate of peeled strips experiencing large deformations and prove rigorously that the same formula applies for external forces having fixed direction. We then apply Griffith's criterion for fracture to calculate critical loads for two cases: peeling produced by a uniform follower pressure distributed along the flexible strip and peeling produced by a localized follower shear force applied at the edge of the strip. We found that for these loads, the critical pressure for peeling follows approximately qc∼ΓL−1, where Γ is the solid–solid interface energy and L is the initial peeling length; for the shear force, the corresponding critical value instead follows Q0c∼Γ, independently of the initial length. These formulas are, unexpectedly, independent of the bending stiffness EI of the strips and differ from the ones predicted for small deformations, i.e. qc∝L−2EIΓ and Q0c∝L−1EIΓ. We apply our results to predict the critical hydrodynamic load necessary to exfoliate graphene sheets from graphite, a fluid–structure interaction problem where the load is of the follower type. We find that a follower load peeling model gives significantly improved predictions than fixed load peeling. For the same Γ, L and b, the critical hydrodynamic follower load is always lower than the one with fixed forces: approximately half for the case with uniform pressure, and one third for the case with shear force.

Using an analytical solution of the Euler’s Elastica, we stumbled upon peculiar shapes of a cantilever beam subject to a large value of shear follower force at the free end. Intrigued by whether such shapes existed or not, we set out to realise an experimental apparatus to validate our predictions. Attaining such system, in reality, is not at all a trivial task. Indeed, it has represented an experimental challenge for decades, due to the emergence of unstable configurations. After various attempts, we were finally able to conceive and realise a device capable of generating a transverse follower force to the beam via air-thrust. We compared the measurement of the forces and the deformation of the beam obtained experimentally with the analytical solution of the Euler’s Elastica in dimensionless form. Since the experiments are quasi-static, the aerodynamic effect induced by the air flow are negligible; this is confirmed by the agreement between the experimental results and both theoretical and numerical predictions. During the experiments, we observed a high susceptibility to perturbations around a dimensionless load of 41.15. We used finite element simulations with an explicit time integration scheme to carry out a stability analysis. Our analysis confirmed the appearance of an unstable configuration for a load of 40.5. Therefore, by carefully tuning the apparatus, we could reach load values higher than the unstable load, at around 120. For such levels of forces, the solution of the Elastica prescribes hook-like shapes that we show experimentally in this paper. These results can find several applications, for instance, the design of soft-actuators, the realisation of more efficient drilling pipes for underwater, or underground, well or the design of biomedical equipment, such as catheters.

Metabolic bone diseases have an impact on the multi-scale structure of bone and its mechanical properties. This study aims to conduct quantitative analysis of the link between specific material-level changes and mechanical alterations of bone tissue. We combine several scanning probe methods with an analytical multiscale model to investigate these links in a mouse model (Crh−120∕+) with endogenous steroid production. Experimental results from our prior study are used, which showed significant changes in spatial maps of nano-scale orientation, mineralization, and microporosity in Crh−120∕+ mice bone. An analytical composite/continuum mechanical model is incorporated with these experimental parameters to predict the progressive reduction in elastic moduli. The largest fractional reduction in elastic modulus is found to arise from incorporation of microscale porosity, followed by the reduced nanoscale degree of orientation. Our work provides both insights into the altered structure-performance relations and a systematic analytical framework for linking scanning micro- and nanoprobe experimental data on hierarchical structural materials to macroscopic biomechanical outcomes.

Soft biological tissues have a hierarchical architecture from the molecular to the macroscale, with structure–function relations at each level crucial for function. In developing new soft biomaterials for medical applications, understanding, and emulating these mechanisms will provide essential guidance. In this chapter we review how time- and position-resolved synchrotron small-angle X-ray scattering (SAXS) combined with multiscale mechanical modelling can illuminate such small-scale mechanisms, using the examples of articular cartilage and the mutable connective tissue of echinoderms. In articular cartilage, SAXS reveals a gradient in fibrillar-level pre-strain, which is suppressed either by physiological static loading or by enzymatic modifications mimicking ageing, and modelling of the fibril/proteoglycan network shows that the pre-strain reflects the local internal swelling pressure. In mutable connective tissue, our results show that interfibrillar stiffening and de-stiffening enable its rapid alterations in mechanical properties, whose kinetics can be captured by analytical modelling of the structure. The combination of multiscale modelling and in situ SAXS thus shows potential in investigating and elucidating the mechanisms enabling function in both natural tissues as well as in new soft biomaterials mimicking their structure.

We report the full analytical solution of the large deformations of a cantilevered elastica loaded by a uniformly distributed follower pressure. We consider an unshearable, inextensible and linear elastic rod. We obtain a spatial nonlinear differential equation in the curvatures, analogous to the undamped Duffing oscillator with a constant driving force. We solve such differential equation, obtaining the curvature, although in implicit form, for arbitrarily large values of the load. We are then able to obtain the rotations owing to a change of variables from the curvilinear abscissa to the curvature. This step is somewhat mandatory due to the implicit nature of the solution. Finally, with the same change of variables, it is possible to obtain a closed-form solution for the deformation in Cartesian coordinates. The solutions show that the rod deforms into drop-like shapes. The number of drops is equal to the number of spatial periods of the solution, which goes with q∗1/3, with q∗ a dimensionless load normalised to the bending stiffness. Interestingly, we find that for q∗⩾3094.2, the number of drop-like shapes does not increase, but remains three.

Micromechanics of liquid-phase exfoliation of a layered 2D material: A hydrodynamic peeling model

The fabrication of multifunctional materials that interface with living environments is a problem of great interest. A variety of structural design concepts have been integrated with functional materials to form biodevices and surfaces for health monitoring. In particular, approaches based on kirigami-inspired cuts can engineer flexibility in materials through the creation of patterned defects. Here, the fabrication of a biodegradable and biofunctional "silk kirigami" material is demonstrated. Mechanically flexible, free-standing, optically transparent, large-area biomaterial sheets with precisely defined and computationally designed microscale cuts can be formed using a single-step photolithographic process. Using modeling techniques, it is shown how cuts can generate remarkable "self-shielding" leading to engineered elastic behavior and deformation. As composites with conducting polymers, flexible, intrinsically electroactive sheets can be formed. Importantly, the silk kirigami sheets are biocompatible, can serve as substrates for cell culture, and be proteolytically resorbed. The unique properties of silk kirigami suggest a host of applications as transient, "green", functional biointerfaces, and flexible bioelectronics.

As bone is used in a dynamic mechanical environment, understanding the structural origins of its time-dependent mechanical behaviour - and the alterations in metabolic bone disease - is of interest. However, at the scale of the mineralized fibrillar matrix (nanometre-level), the nature of the strain-rate dependent mechanics is incompletely understood. Here, we investigate the fibrillar- and mineral-deformation behaviour in a murine model of Cushing's syndrome, used to understand steroid induced osteoporosis, using synchrotron small- and wide-angle scattering/diffraction combined with in situ tensile testing at three strain rates ranging from 10-4 to 10-1 s-1. We find that the effective fibril- and mineral-modulus and fibrillar-reorientation show no significant increase with strain-rate in osteoporotic bone, but increase significantly in normal (wild-type) bone. By applying a fibril-lamellar two-level structural model of bone matrix deformation to fit the results, we obtain indications that altered collagen-mineral interactions at the nanoscale - along with altered fibrillar orientation distributions - may be the underlying reason for this altered strain-rate sensitivity. Our results suggest that an altered strain-rate sensitivity of the bone matrix in osteoporosis may be one of the contributing factors to reduced mechanical competence in such metabolic bone disorders, and that increasing this sensitivity may improve biomechanical performance.

Flexible and controllable self-regulating heating devices with positive temperature coefficient (PTC) behaviour are potentially excellent candidates in applications like healthcare, soft robotics, artificial skin and wearable electronics. Although extensive studies have been carried out in this field to understand the mechanism of PTC effect, rather limited conclusions have been reached. Many controversies remain on the dominating factors that influence the PTC performance of composites, hence limiting their design and broader applications. Herein, we propose a systematic study to explore the PTC phenomenon and the underlying mechanism, from a conductive network viewpoint, taking account of both conductive fillers and polymer matrices. Three representative conductive fillers with distinct dimensions and shapes (0D silver coated glass spheres, 1D carbon nanotubes and 2D graphene nanoplatelets), in combination with three different polymer matrices (high density polyethylene, thermoplastic polyurethane and polycarbonate) were selected to elucidate the effect of the "robustness" of different conductive networks on PTC behaviour in conductive polymer composites (CPCs). The desired conductive network can be obtained by selecting preferentially larger filler size, lower filler aspect ratio and/or selective distribution of filler (e.g. in the amorphous region of semi-crystalline polymers). The highest PTC intensity was observed around the "critical" percolation threshold, in correspondence of networks with the lowest number of inter-particle contacts. This study can serve as a guideline in the selection of the most appropriate conductive filler and polymer matrix for various self-regulating heating requirements and final applications.

Structural and associated biomechanical gradients within biological tissues are important for tissue functionality and preventing damaging interfacial stress concentrations. Articular cartilage possesses an inhomogeneous structure throughout its thickness, driving the associated variation in the biomechanical strain profile within the tissue under physiological compressive loading. However, little is known experimentally about the nanostructural mechanical role of the collagen fibrils and how this varies with depth. Utilising a high-brilliance synchrotron X-ray source, we have measured the depth-wise nanostructural parameters of the collagen network in terms of the periodic fibrillar banding (D-period) and associated parameters. We show that there is a depth dependent variation in D-period reflecting the pre-strain and concurrent with changes in the level of intrafibrillar order. Further, prolonged static compression leads to fibrillar changes mirroring those caused by removal of extrafibrillar proteoglycans (as may occur in aging or disease). We suggest that fibrillar D-period is a sensitive indicator of localised changes to the mechanical environment at the nanoscale in soft connective tissues. STATEMENT OF SIGNIFICANCE: Collagen plays a significant role in both the structural and mechanical integrity of articular cartilage, allowing the tissue to withstand highly repetitive loading. However, the fibrillar mechanics of the collagen network in cartilage are not clear. Here we find that cartilage has a spatial gradient in the nanostructural collagen fibril pre-strain, with an increase in the fibrillar pre-strain with depth. Further, the fibrillar gradient changes similarly under compression when compared to an enzymatically degraded tissue which mimics age-related changes. Given that the fibrils potentially have a finite capacity to mechanically respond and alter their configuration, these findings are significant in understanding how collagen may alter in structure and gradient in diseased cartilage, and in informing the design of cartilage replacements.