Abstract Myriad random phenomena in nature possess fractal and Hurst characteristics. Random processes/fields, such as those with Cauchy or Dagum correlations, enable modeling such stochastic structures in time and space. In the first place, this paper provides a compact review of these models, including their spectral properties, for wide ranges of the fractal dimension and Hurst parameter. The Cauchy and Dagum models can be used to determine stochastic responses of dynamical systems and/or spatial problems in 1d, 2d, or 3d in the presence of fractal and Hurst characteristics. The paper surveys various examples ranging from vibration problems, rods and beams with random properties under random loadings, waves and wavefronts, fracture, homogenization of random media, and statistical turbulence, to stochastically evolving spontaneous violations of the entropy inequality in granular flows. The latter case shows the route to examine whether a mechanical system gives rise to stochastics with such intriguing features. Common features brought out in this survey show what can and how can be achieved with Cauchy and Dagum-type models and related constructs in mechanics.

Abstract Many animals in nature travel in groups either for protection, survival, or endurance. Among these, certain species do so under the burden of aero/hydrodynamic loads, which incites questions as to the significance of the multibody fluid-mediated interactions that are inherent to collective flying/swimming. Prime examples of such creatures are fish, which are commonly seen traveling in highly organized groups of large numbers. Indeed, over the years, there have been numerous attempts to examine hydrodynamic interactions among self-propelled fish-like swimmers. Though many have studied this phenomenon, their motivations have varied from understanding animal behavior to extracting universal fluid dynamical principles and transplanting them into engineering applications. The approaches utilized to carry out these investigations include theoretical and computational analyses, field observations, and experiments using various abstractions of biological fish. Here, we compile representative investigations focused on the collective hydrodynamics of fish-like swimmers. The selected body of works are reviewed in the context of their methodologies and findings, so as to draw parallels, contrast differences, and highlight open questions. Overall, the results of the surveyed studies provide foundational insights into the conditions (such as the relative positioning and synchronization between the members, as well as their swimming kinematics and speed) under which hydrodynamic interactions can lead to efficiency gains and/or group cohesion in two- and three-dimensional scenarios. They also shed some light on the mechanisms responsible for such energetic and stability enhancements in the context of wake-body, wake-wake, and body-body interactions.

Abstract In fluid dynamics, predicting and characterizing bifurcations, from the onset of unsteadiness to the transition to turbulence, is of critical importance for both academic and industrial applications. Different tools from dynamical systems theory can be used for this purpose. In this review, we present a concise theoretical and numerical framework focusing on practical aspects of the computation and stability analyses of steady and time-periodic solutions, with emphasis on high-dimensional systems such as those arising from the spatial discretization of the Navier–Stokes equations. Using a matrix-free approach based on Krylov methods, we extend the capabilities of the open-source high-performance spectral element-based time-stepper Nek5000. The numerical methods discussed are implemented in nekStab, an open-source and user-friendly add-on toolbox dedicated to the study of stability properties of flows in complex three-dimensional geometries. The performance and accuracy of the methods are illustrated and examined using standard benchmarks from the fluid mechanics literature. Thanks to its flexibility and domain-agnostic nature, the methodology presented in this work can be applied to develop similar toolboxes for other solvers, most importantly outside the field of fluid mechanics.

Abstract The development of next-generation batteries, utilizing electrodes with high capacities and power densities requires a comprehensive understanding and precise control of material interfaces and architectures. Electro-chemo-mechanics plays an integral role in the morphological evolution and stability of such complex interfaces. Volume changes in electrode materials and the chemical interactions of electrode/electrolyte interfaces result in nonuniform stress fields and structurally different interphases, fundamentally affecting the underlying transport and reaction kinetics. The origin of this mechanistic coupling and its implications on degradation is uniquely dependent on the interface characteristics. In this review, the distinct nature of chemo–mechanical coupling and failure mechanisms at solid–liquid interfaces and solid–solid interfaces is analyzed. For lithium metal electrodes, the critical role of surface/microstructural heterogeneities on the solid electrolyte interphase (SEI) stability and dendrite growth in liquid electrolytes, and on the onset of contact loss and filament penetration with solid electrolytes is summarized. With respect to composite electrodes, key differences in the microstructure-coupled electro-chemo-mechanical attributes of intercalation- and conversion-based chemistries are delineated. Moving from liquid to solid electrolytes in such cathodes, we highlight the significant impact of solid–solid point contacts on transport/mechanical response, electrochemical performance, and failure modes such as particle cracking and delamination. Finally, we present our perspective on future research directions and opportunities to address the underlying electro-chemo-mechanical challenges for enabling next-generation lithium metal batteries.

Abstract It has been 5 years since this review of elastic-plastic contact mechanics was published. The area still remains very active, and many advancements have been made since then. This discussion summarizes these advances and points out what might be considered the most significant ones. In some cases, experimental measurements have confirmed previous theoretical predictions. In most cases, the models of contact mechanics have increased in complexity in order to improve predictions for real applications. As a fundamental area, contact mechanics will undoubtedly remain active as its implementation is often required for new applications of technology to succeed.

Abstract The main motivation for “hierarchical biomechanics” is that the wide variability of mechanical properties encountered at the macroscopic scale may be traced back to just a few “universal” or invariant mechanical properties of elementary components at a sufficiently small scale (such as collagen, elastin, and water in case of soft tissues; complemented by hydroxyapatite in case of hard “mineralized” tissues such as bone), and to the nano-and microstructures which the latter build up. This challenging task requires a physically rigorous and mathematically sound basis, as provided by Finite Element and Fast Fourier Transform methods, as well as by continuum micromechanics resting on (semi-)analytical solutions for Eshelby-type matrix-inclusion problems. Corresponding numerical and analytical mathematical models have undergone diligent experimental validation, by means of data stemming from a variety of biophysical, biochemical, and biomechanical testing methods, such as light and electron microscopy, ultrasonic testing, and scanning acoustic microscopy, as well as physicochemical tests associated with dehydration, demineralization, decollagenization, ashing, and weighing in air and fluid. While elastic scale transition and homogenization methods have attained a high maturity level, the hierarchical nature of dissipative (i.e., viscous or strength) properties is still a vibrant field of research. This applies even more to hierarchical approaches elucidating the interface between biological cells and extracellular matrices (“mechanobiology”), to cells interacting in complex biofluids such as blood, and to the intricate and highly undiscovered mechanics unfolding within biological cells.

Abstract This work gives an overview of all types of constant torque mechanisms (CTMs) based on both function and structure. Based on their architecture, they can be divided into five distinct categories, which all have their specific behavior. It is also shown that these CTMs can be divided into two application types, namely, power assistance or torque stabilization. Constant force mechanisms (CFMs) are more prevalent in the literature; therefore, some discussion is proposed on how CFMs can be transformed into CTMs. It is also shown that some of these CTMs have a very high specific energy, which makes them potentially interesting for use as energy storage/power providers in novel fields like robotics.

Abstract This review article examines the last decade of studies investigating solid, molten, and liquid particle interactions with one another and with walls in heterogeneous multiphase flows. Such flows are experienced in state-of-the-art and future-concept gas turbine engines, where particles from the environment, including volcanic ash, runway debris, dust clouds, and sand, are transported by a fluid carrier phase and undergo high-speed collisions with high-temperature engine components. Sand or volcanic ash ingestion in gas turbine engines is known to lead to power-loss and/or complete engine failure. The particle-wall interactions that occur in high-temperature sections of an engine involve physics and intrinsic conditions that are sufficiently complex that they result in highly disparate and transient outcomes. These particles, which often times are made up of glassy constituents called calcium–magnesium–alumino–silicate (CMAS), are susceptible to phase change at combustor temperatures (1650°), and can deposit on surfaces, undergo elastic and plastic deformation, rebound, and undergo breakup. Considerable research has been put into developing empirical and physics-based models and numerical strategies to address phase interactions. This article provides a detailed account of the conceptual foundation of physics-based models employed to understand the behavior of particle-wall interaction, the evolution of numerical methods utilized for modeling these interactions, and challenges associated with improving models of particle-particle and particle-wall interactions needed to better characterize multiphase flows. It also includes description of a testbed for acquiring canonical data for model validation studies.

Abstract Various bio-inspired vibration isolators have been emerged in recent decades and applied successfully in the protection of sensitive components, improvement of operating comfort, enhancement of control accuracy, etc. They are generally developed by exploiting favorable nonlinearities in biological structures. The main contribution of this work is to provide a comprehensive review of recent studies on the bio-inspired isolators. The methodology of bio-inspired vibration isolation is proposed from the perspective of mechanics based on the elemental theory and design principles. The key isolation mechanisms are classified into three categories according to different dominant forces: stiffness adjustment mechanism, auxiliary mass mechanism, and damping mechanism, respectively. Some representative designs, performance analyses, and practical applications of each type of bio-inspired isolators are also provided. In bio-inspired isolators with variable stiffness, the inherent structural performances can be adjusted to deal with variation in external load. The auxiliary mass mechanism utilizes nonlinear inertial effects to achieve ultralow frequency vibration isolation. Unique damping mechanism of bio-inspired structures is often studied to protect devices and equipment from impact loads. Bio-inspired vibration methods can also be applied in active/semi-active control systems with advantages of low energy consumption and high robustness. Finally, the review ends with conclusions, which highlight resolved and unresolved issues and provide a brief outlook on future perspectives. This review aims to give a comprehensive understanding of bio-inspired isolation mechanism. It also provides guidance on designing new bio-inspired isolators for improving their vibration isolation performance.

Abstract This paper reviews recent progress in the development of silicon-based vapor chambers for heat spreading in electronic packages. Effective hotspot mitigation is an increasingly challenging issue in electronics thermal management, and the use of silicon vapor chambers creates opportunities for thermal-expansion matched, high performance heat spreaders that can be directly integrated with the semiconductor die. While silicon microheat pipes have been extensively studied as one-dimensional heat transport mechanisms for heat routing in semiconductor substrates, silicon vapor chambers require special consideration and different manufacturing approaches due to the different heat transport configurations involved. The following review therefore provides an overview on the evolution of silicon vapor chambers in terms of fabrication strategies and performance characterization. Particular focus is given to opportunities and challenges associated with using silicon as the vapor chamber envelope material rather than more traditional metal-based vapor chambers, such as the ability to optimize the wick geometry with greater fidelity and issues with manufacturing scalability.