We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative L 2 -gradient flow of the elastic energy. For any initial curve lying merely in the energy space we show existence and parabolic smoothing of the solution. Applying previous results on long-time existence and proving a constrained Łojasiewicz-Simon gradient inequality we furthermore show convergence to a critical point as time tends to infinity.

Aortic stiffening is an inevitable manifestation of chronological aging, yet the mechano-molecular programs that orchestrate region- and layer-specific adaptations along the length and through the wall of the aorta are incompletely defined. Here, we show that the decline in passive cyclic distensibility is more pronounced in the ascending thoracic aorta (ATA) compared to distal segments of the aorta and that collagen content increases in both the medial and adventitial compartments of the ATA during aging. The single-cell RNA sequencing of aged ATA tissues reveals altered cellular senescence, remodeling, and inflammatory responses accompanied by enrichment of T-lymphocytes and rarefaction of vascular smooth muscle cells, compared to young samples. T lymphocyte clusters accumulate in the adventitia, while the activation of mechanosensitive Piezo-1 enhances vasoconstriction and contributes to the overall functional decline of ATA tissues. These results portray the immuno-mechanical aging of the ATA as a process that culminates in a stiffer conduit permissive to the accrual of multi-gerogenic signals priming to disease development.

A hydrostatic skeleton allows a soft body to transmit muscular force via internal pressure. A human\'s tongue, an octopus\' arm and a nematode\'s body illustrate the pervasive presence of hydrostatic skeletons among animals, which has inspired the design of soft engineered actuators. However, there is a need for a theoretical basis for understanding how hydrostatic skeletons apply mechanical work. We therefore modeled the shape change and mechanics of natural and engineered hydrostatic skeletons to determine their mechanical advantage (MA) and displacement advantage (DA). These models apply to a variety of biological structures, but we explicitly consider the tube feet of a sea star and the body segments of an earthworm, and contrast them with a hydraulic press and a McKibben actuator. A helical winding of stiff, elastic fibers around these soft actuators plays a critical role in their mechanics by maintaining a cylindrical shape, distributing forces throughout the structure and storing elastic energy. In contrast to a single-joint lever system, soft hydrostats exhibit variable gearing with changes in MA generated by deformation in the skeleton. We found that this gearing is affected by the transmission efficiency of mechanical work (MA×DA) or, equivalently, the ratio of output to input work. The transmission efficiency changes with the capacity to store elastic energy within helically wrapped fibers or associated musculature. This modeling offers a conceptual basis for understanding the relationship between the morphology of hydrostatic skeletons and their mechanical performance.

Jumping, a fundamental survival behavior observed in organisms, serves as a vital mechanism for adapting to the surrounding environment and overcoming significant obstacles within a given terrain. Here, we present a light-controlled soft jumping actuator inspired by asphondylia, which employs a closed-loop structure and utilizes a liquid crystal elastomer (LCE). Photo-mechanical coupling highlights the significant influence of the light source on the actuator\'s jumping behavior. Manipulating the light intensity, the relative position of stimulus and light lock, and the concentration of disperse red 1 (DR1) allows precise control over both the maximum take-off velocity and jump height. Furthermore, tailoring the size of the LCE actuator offers a means of regulating jumping behavior. Upon exposure to 460 nm LED irradiation, our actuator achieves remarkable performance, with a maximum jumping height of 10 body length (BL) and take-off velocity of 62 BL/s. These actuators accumulate and rapidly release energy, enabling the effective transportation of microcargos across substantial distances. Our research yields valuable insights into the realm of soft robotics, underscoring the pivotal importance of photo-mechanical coupling in the field of soft robotics, thereby serving as a catalyst for inspiring continued exploration of agile and capable systems by prestoring elastic energy.

Although the stretch that generates ventilator-induced lung injury (VILI) occurs within the peripheral tissue that encloses the alveolar space, airway pressures and volumes monitor the gas within the interior core of the lung unit, not its cellular enclosure. Measured pressures (plateau pressure, positive end-expiratory pressure, and driving pressure) and tidal volumes paint a highly relevant but incomplete picture of forces that act on the lung tissues themselves. Convenient and clinically useful measures of the airspace, such as pressure and volume, neglect the partitioning of tidal elastic energy into the increments of tension and surface area that constitute actual stress and strain at the alveolar margins. More sharply focused determinants of VILI require estimates of absolute alveolar dimension and morphology and the lung\'s unstressed volume at rest. We present a highly simplified but informative mathematical model that translates the radial energy of pressure and volume of the airspace into its surface energy components. In doing so it elaborates conceptual relationships that highlight the forces tending to cause end-tidal hyperinflation of aerated units within the \'baby lung\' of acute respiratory distress syndrome (ARDS).

Computational chemistry calculations are broadly useful for guiding the atom-scale design of hard-soft material interfaces including how molecular interactions of single-component liquid crystals (LCs) at inorganic surfaces lead to preferred orientations of the LC far from the surface. The majority of LCs, however, are not single-component phases but comprise of mixtures, such as a mixture of mesogens, added to provide additional functions such as responsiveness to the presence of targeted organic compounds (for chemical sensing). In such LC mixtures, little is understood about the near-surface composition and organization of molecules and how that organization propagates into the far-field LC orientation. Here, we address this broad question by using a multiscale computational approach that combines density functional theory (DFT)-based calculations and classical molecular dynamics (MD) simulations to predict the interfacial composition and organization of a binary LC mixture of 4\'-cyano-4-biphenylcarbolxylic acid (CBCA) and 4\'-n-pentyl-4-biphenylcarbonitrile (5CB) supported on anatase (101) titania surfaces. DFT calculations determine the surface composition and atomic-scale organization of CBCA and 5CB at the titania surface, and classical MD simulations build upon the DFT description to describe the evolution of the near-surface order into the bulk LC. A surprising finding is that the 5CB and CBCA molecules adopt orthogonal orientations at the anatase surface and that, above a threshold concentration of CBCA, this mixture of orientations evolves away from the surface to define a uniform far-field homeotropic orientation. These results demonstrate that molecular-level knowledge achieved through a combination of computational techniques permits the design and understanding of functional LC mixtures at interfaces.

A weak notion of elastic energy for (not necessarily regular) rectifiable curves in any space dimension is proposed. Our [Formula: see text]-energy is defined through a relaxation process, where a suitable [Formula: see text]-rotation of inscribed polygons is adopted. The discrete [Formula: see text]-rotation we choose has a geometric flavour: a polygon is viewed as an approximation to a smooth curve, and hence its discrete curvature is spread out into a smooth density. For any exponent [Formula: see text] greater than 1, the [Formula: see text]-energy is finite if and only if the arc-length parametrization of the curve has a second-order summability with the same growth exponent. In that case, moreover, the energy agrees with the natural extension of the integral of the [Formula: see text]th power of the scalar curvature. Finally, a comparison with other definitions of discrete curvature is provided. This article is part of the theme issue \'Foundational issues, analysis and geometry in continuum mechanics\'.

Elastic strain energy that is stored and released from long, distal tendons such as the Achilles during locomotion allows for muscle power amplification as well as for reduction of the locomotor energy cost: as distal tendons perform mechanical work during recoil, plantar flexor muscle fibres can work over smaller length ranges, at slower shortening speeds, and at lower activation levels. Scant evidence exists that long distal tendons evolved in humans (or were retained from our more distant Hominoidea ancestors) primarily to allow high muscle-tendon power outputs, and indeed we remain relatively powerless compared to many other species. Instead, the majority of evidence suggests that such tendons evolved to reduce total locomotor energy cost. However, numerous additional, often unrecognised, advantages of long tendons may speculatively be of greater evolutionary advantage, including the reduced limb inertia afforded by shorter and lighter muscles (reducing proximal muscle force requirement), reduced energy dissipation during the foot-ground collisions, capacity to store and reuse the muscle work done to dampen the vibrations triggered by foot-ground collisions, reduced muscle heat production (and thus core temperature), and attenuation of work-induced muscle damage. Cumulatively, these effects should reduce both neuromotor fatigue and sense of locomotor effort, allowing humans to choose to move at faster speeds for longer. As these benefits are greater at faster locomotor speeds, they are consistent with the hypothesis that running gaits used by our ancestors may have exerted substantial evolutionary pressure on Achilles tendon length. The long Achilles tendon may therefore be a singular adaptation that provided numerous physiological, biomechanical, and psychological benefits and thus influenced behaviour across multiple tasks, both including and additional to locomotion. While energy cost may be a variable of interest in locomotor studies, future research should consider the broader range of factors influencing our movement capacity, including our decision to move over given distances at specific speeds, in order to understand more fully the effects of Achilles tendon function as well as changes in this function in response to physical activity, inactivity, disuse and disease, on movement performance.

Over the last couple of decades, numerous piezoelectric footwear energy harvesters (PFEHs) have been reported in the literature. This paper reviews the principles, methods, and applications of PFEH technologies. First, the popular piezoelectric materials used and their properties for PEEHs are summarized. Then, the force interaction with the ground and dynamic energy distribution on the footprint as well as accelerations are analyzed and summarized to provide the baseline, constraints, potential, and limitations for PFEH design. Furthermore, the energy flow from human walking to the usable energy by the PFEHs and the methods to improve the energy conversion efficiency are presented. The energy flow is divided into four processing steps: (i) how to capture mechanical energy into a deformed footwear, (ii) how to transfer the elastic energy from a deformed shoes into piezoelectric material, (iii) how to convert elastic deformation energy of piezoelectric materials to electrical energy in the piezoelectric structure, and (iv) how to deliver the generated electric energy in piezoelectric structure to external resistive loads or electrical circuits. Moreover, the major PFEH structures and working mechanisms on how the PFEHs capture mechanical energy and convert to electrical energy from human walking are summarized. Those piezoelectric structures for capturing mechanical energy from human walking are also reviewed and classified into four categories: flat plate, curved, cantilever, and flextensional structures. The fundamentals of piezoelectric energy harvesters, the configurations and mechanisms of the PFEHs, as well as the generated power, etc., are discussed and compared. The advantages and disadvantages of typical PFEHs are addressed. The power outputs of PFEHs vary in ranging from nanowatts to tens of milliwatts. Finally, applications and future perspectives are summarized and discussed.

Energy storage of passive muscles plays an important part in frequent activities of honey bee abdomens due to the muscle distribution and open circulatory system. However, the elastic energy and mechanical properties of structure in passive muscles remain unclear. In this article, stress relaxation tests on passive muscles from the terga of the honey bee abdomens were performed under different concentrations of blebbistatin and motion parameters. In stress relaxation, the load drop with the rapid and slow stages depending on stretching velocity and stretching length reflects the features of myosin-titin series structure and cross-bridge-actin cyclic connections in muscles. Then a model with 2 parallel modules based on the 2 feature structures in muscles was thus developed. The model described the stress relaxation and stretching of passive muscles from honey bee abdomen well for a good fitting in stress relaxation and verification in loading process. In addition, the stiffness change of cross-bridge under different concentrations of blebbistatin is obtained from the model. We derived the elastic deformation of cross-bridge and the partial derivatives of energy expressions on motion parameters from this model, which accorded the experimental results. This model reveals the mechanism of passive muscles from honey bee abdomens suggesting that the temporary energy storage of cross-bridge in terga muscles under abdomen bending provides potential energy for springback during the periodic abdomen bending of honey bee or other arthropod insects. The finding also provides an experimental and theoretical basis for the novel microstructure and material design of bionic muscle.