Abstract Underwater implosion of submerged structures has been studied for more than a century, yet recent high-profile failures have renewed awareness of the remaining risk in modern undersea systems. As pipelines, AUVs, and deep-sea submersibles operate at greater depths and under cyclic loading, exceeding a structure's critical external pressure can trigger a two-stage implosion process: rapid inward wall collapse, followed by abrupt wall arrest that emits damaging pressure pulses. Several notable implosion disasters in the last two decades have prompted increased interest in understanding and preventing catastrophic failure as well as protecting structures and surrounding environments. This review presents the current state-of-the-art of underwater implosion across experimental, numerical, and analytical domains. Emphasis is placed on how shell shape, geometry, and material govern both collapse dynamics and the emitted pressure pulse. Furthermore, UNDEX initiated implosion, sympathetic structures, and partially or fully confined environments are explored. Finally, damage mitigation techniques, including ring stiffeners, foam fillers, and buckle arrestors are discussed. This understanding of a century of work on mechanics, environments, and mitigation strategies provides a framework for treating implosion as a primary design consideration within the undersea engineering ecosystem rather than an unquantified risk.
Abstract This review examines the development of concepts and models describing the spontaneous spatial separation—segregation—of dense flowing granular mixtures. Although particle-scale interactions are largely understood and modern discrete element methods can resolve system dynamics in detail, a central challenge remains: prediction has advanced more rapidly than understanding. Simulation can reveal what happens; it does not, by itself, explain why. We argue that progress requires integrating four complementary approaches: particle-based simulations, continuum descriptions based on continuity, statistical methods extending kinetic theory to dissipative systems, and conceptual models that isolate dominant mechanisms. These are not competing paradigms but distinct lenses on a multi-scale phenomenon. Across them, common mathematical structures recur, including Newtonian dynamics at the particle level and flux--divergence formulations governing transport. A central thesis is that conceptual models remain indispensable. By distilling mechanisms such as kinetic sieving, squeeze expulsion, and force balance, they provide explanatory structure that complements both simulation and formal theory. Recent advances applying particle-level force models of segregation illustrate the value of combining these perspectives. At the same time, each framework encounters limitations. The central challenge is therefore to identify organizing principles that connect mechanisms across scales. Granular segregation serves as a testbed for a broader question: how understanding emerges in systems where the microscopic governing laws are known, yet collective behavior remains difficult to explain.
Abstract The prevalence of gastric diseases is rising worldwide, especially among young adults. Many conditions of the stomach seem to be closely related to its mechanical properties, geometry, and underlying microstructure. Due to the complex coupling between these aspects, effective diagnosis and treatment are often difficult. Predictive material models of the stomach (wall) and simulations based on these could significantly contribute to the overall disease understanding, treatment choice, and surgical planning. However, the development of such material models requires experimental data on the mechanical behavior and structure. For this purpose, this review discusses current experimental approaches for the characterization of the stomach. First, all relevant anatomical, physiological, and mechanical aspects are summarized. Based on its complex organ geometry and regionally varying wall architecture, all experimental studies are grouped in terms of sample scale, differentiating between organ- and tissue-level. Further, the review comprises both mechanical and structural investigations for each sample scale. In particular, each experimental approach is evaluated in terms of working principles and applicability to gastric tissue. Key findings from different studies derived from the same technique are compared and discussed in context with the gastric physiology. Finally, current research gaps are identified, and future directions of gastric research are envisioned with the aim of fully characterizing the mechanical behavior and hierarchical structure of this vital organ. This review offers practical guidance for researchers in defining future experimental designs and a concise summary of existing datasets for constitutive modeling of the stomach
The interaction between wake vortices from an upstream body and a downstream boundary layer is significant for both fundamental and practical aspects of fluid mechanics. An in-depth understanding of the underlying flow physics is crucial for numerous problems in aeronautics, architectonics, and energy related to the complex interferences between different bodies or apparatuses. The incoming wake vortices can generally be divided into streamwise, vertical, and spanwise vortices based on their axial directions relative to the coordinate system of downstream boundary layer. They interact with the downstream boundary layer in different ways. However, the spanwise wake vortex has more profound effects on the downstream boundary layer than the other two, because it simultaneously disturbs the whole span region of boundary layer. Therefore, the vortex dynamics of interaction between spanwise wake vortices and a downstream boundary layer is focused on in this review. The efforts of unveiling the flow physics related to this kind of interaction with different canonical configurations are reviewed as the geometrical complexity increases. The wake-triggered spanwise secondary vortices and the laminar-to-turbulent transition routine caused by their destabilization are highlighted in particular. The transition process characterized by the evolution of secondary vortices is distinct from that of a natural transition or a bypass transition induced by freestream turbulence and is commonly encountered in flows around complex geometries. Finally, areas that deserve more attention in future work are outlined and discussed.
The peripheral tissues consist of skin and subcutaneous tissue. Their multilayered biomechanical properties serve as key health indicators and are crucial for clinical applications. Flexible electronics offer a promising approach for continuous in vivo monitoring of peripheral tissue biomechanics. However, these methods depend on complex dispersion analysis or extensive experimental data fitting, which limits their practicality. This study develops an analytical model based on an eccentric rotating mass (ERM) motor for direct and simultaneous measurement of the elastic moduli and thickness of the top skin layer of bilayer tissue. The analytical model used to evaluate tissue compliance involves three dimensionless parameters: the modulus ratio between the top and bottom layers, the normalized thickness of the top skin layer, and one parameter related to ERM. Both simulations and experiments confirm the model's accuracy, showing average errors of only 10% in the inverse characterization of bilayer moduli and thickness for representative bilayer tissue phantoms, paving the way for the development of flexible devices for in vivo tissue health monitoring.
This short opinion piece identifies declining priorities in academia and funding agencies in preserving and passing on a few key fundamental principles of engineering science. The article focuses on structural stability in mechanics and rotating machinery in dynamics as examples of where such principles are critical to model and design robust, safe and efficient industrial systems. The note concludes with some suggestions to help alleviate this problem.
Physical modeling of biological matter has conventionally treated them as engineering or physical materials that subscribe to laws of equilibrium physics and are considered “passive” or ”nonliving”. However, biological systems are “active” or “alive” with their own energy source, capable of circumventing equilibrium considerations. In fact, active biological matter including self-propelled particles, filaments, and membranes, is the hallmark of living matter and drives life?s most dynamic processes. Unlike passive soft materials that exhibit only equilibrium thermal fluctuations at the microscopic scales, active systems consume energy to generate unique mechanical behavior. Examples of such behavior include persistent dynamics, stress generation, and large deformations that violate fluctuation?dissipation relations from equilibrium statistical mechanics, placing active matter far from equilibrium. This tutorial introduces a unified approach that combines continuum theory with non-equilibrium statistical mechanics to study soft active biological matter. The discussion is organized by dimensionality: we begin with zero-dimensional active Brownian particles, proceed to one-dimensional active filaments modeled as elastic rods, and conclude with two-dimensional active membranes described using linear curvature elasticity. For each class of active matter, we review equilibrium and non-equilibrium models, illustrate key concepts through simple examples, and provide a concise survey of the literature. Our aim is to emphasize physical interpretation and practical modeling tools, equipping readers with a coherent framework for understanding the existing body of work and pursuing research in non-equilibrium statistical mechanics of living systems.
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.
In recent years, Artificial intelligence (AI) has become ubiquitous, empowering various fields, especially integrating artificial intelligence and traditional science (AI for Science: Artificial intelligence for science), which has attracted widespread attention. In AI for Science, using artificial intelligence algorithms to solve partial differential equations (AI for PDEs: Artificial intelligence for partial differential equations) has become a focal point in computational mechanics. The core of AI for PDEs is the fusion of data and partial differential equations (PDEs), which can solve almost any PDEs. Therefore, this article provides a comprehensive review of the research on AI for PDEs, summarizing the existing algorithms and theories. The article discusses the applications of AI for PDEs in computational mechanics, including solid mechanics, fluid mechanics, and biomechanics. The existing AI for PDEs algorithms include those based on Physics-Informed Neural Networks (PINNs), Deep Energy Methods (DEM), Operator Learning, and Physics-Informed Neural Operator (PINO). AI for PDEs represents a new method of scientific simulation that provides approximate solutions to specific problems using large amounts of data, then fine-tuning according to specific physical laws, avoiding the need to compute from scratch like traditional algorithms. Thus, AI for PDEs is the prototype for future foundation models in computational mechanics, capable of significantly accelerating traditional numerical algorithms.
Archard's Wear Law and its variants have remained fundamental to wear prediction for over 70 years, despite frequent criticism regarding their simplicity and the variability of the wear coefficient. Numerous recent sliding wear experiments were evaluated to determine whether these models still hold and to what degree and to identify areas for improvement. A total of 75 papers with detailed wear data were chosen for in-depth review, and 39 of them were selected for a regression analysis. Modified Archard models, incorporating variable exponents for load, sliding distance, and material hardness, were optimized for each independent study. A Gaussian mixture model was then used to cluster the optimized exponents into two groups: one centered around the original Archard model, and the other reflecting alternative optimized exponents. The review found that 81% of the papers referencing a wear model employed a variant of the Archard model. Models using material hardness as the primary factor influencing wear volume struggled to make physically sound or accurate predictions. Although the Archard-type model maintains its relevance in relating wear volume to applied load and sliding speed, its dependence on a constant wear coefficient and material hardness falls short in describing wear phenomena comprehensively. Further improvement of the model using mechanics is necessary to enhance the accuracy of wear predictions.
Flying-wing aircraft with high-aspect ratios have received extensive attention due to their outstanding aerodynamic efficiency and stealth capabilities. This type of aircraft, however, may suffer from rigid-elastic coupling flutters, such as a body-freedom flutter, owing to the interaction among flight dynamics, structural dynamics, and aerodynamics. This paper surveys the advances in modeling and analysis methods, control strategies, and experimental validations related to those flutters and their active suppressions. The paper begins with the modeling approaches in different frames of reference for a rigid-elastic coupling aero-servo-elastic system to emphasize their roles and merits in describing rigid-elastic interactions. Then, it discusses the mechanism of a rigid-elastic coupling flutter, accounting for the coupling of flight dynamics and aeroelastic vibrations. Afterward, the paper presents a comparison among the control performances of typical active flutter suppression strategies to evaluate the capacity of enhancing aircraft stability and increasing flutter speed. The paper also reviews the wind-tunnel tests and flight tests to verify the active flutter suppression techniques. Unlike other tests, the flight tests of the aeroelastic flight demonstrator (AFD) made by the authors indicate that the active controller could successfully remove the rigid-elastic coupling flutter and greatly increase the flutter speed till the occurrence of a bending-torsion flutter of higher order. Finally, the paper outlines future studies on flying-wing aircraft and active flutter suppression techniques.
Acoustic metamaterials (AMs), including phononic crystals, have revolutionized wave manipulation through artificially engineered microstructures that show unprecedented control over elastic and sound waves. These materials exhibit unique properties such as bandgap formation, wave localization, and anomalous wavefront control, which are unattainable in natural materials. This review presents a comprehensive survey with analysis of AMs for the fundamental mechanism of wave attenuation, such as Bragg scattering and local resonance, and highlights advanced techniques for bandgap widening, multi-band resonance, and inertial amplification. The role of defects in achieving wave localization and waveguiding is discussed, alongside innovative concepts like gradient refractive index (GRIN) AMs and metasurfaces for precise wavefront manipulation. The integration of topological phases into AMs has led to the development of topological acoustic metamaterials (TAMs), supporting robust wave propagation and energy localization at interfaces. Recent advances in actively controllable AMs are also reviewed, leveraging multi-field coupling materials and mechanically reconfigurable structures to achieve real-time tunability. Despite significant progress, challenges remain in the fabrication, scalability, and practical implementation of AMs, particularly in complex engineering environments. The review concludes with an outlook on future research directions, emphasizing the need for novel fabrication technologies, optimization strategies, and the integration of artificial intelligence for future advancement of the field.
Medical diagnostics continues to be one of the most difficult challenges in healthcare, with diagnostic errors constituting the most common, costly, and harmful category of medical errors. They contribute to millions of adverse outcomes globally each year. The principal difficulty lies in the extraordinary complexity of the human body, a multiscale, adaptive, nonlinear dynamical system whose hidden states defy simplifications and contradict intuitive thinking. Current practice, largely dependent on heuristic guidelines, physician judgment, and black box machine learning, remains fundamentally limited, perpetuating diagnostic failures and preventing true personalization. This paper argues that nonlinear mechanics and dynamics are not just refinements but essential to understanding physiology. Nonlinear phenomena such as instabilities, bifurcations, chaos, fractals, adaptive feedback, and multiscale interactions occur across all the systems in the body including cardiovascular, respiratory, metabolic, neural, immune, and musculoskeletal subsystems, and are central to both health and disease. Ignoring these phenomena costs us mechanistic understanding and puts accurate diagnostics out of reach. At the same time, mechanistic models, data-driven Artificial Intelligence, and physician expertise each have unique strengths but are inadequate when applied in isolation. We propose their synthesis through physics-informed machine learning, hybrid frameworks, and the emerging paradigm of digital twins. Such systems combine mechanistic insights, data-driven computations, and experiential clinical wisdom to deliver interpretable and personalized diagnostics. Importantly, embedding nonlinear mechanics in real-time, patient-specific, hybrid models provides an exciting path toward reducing errors, improving outcomes, and transitioning from reactive, guideline-driven practice to truly pro-active, precision medicine.
Kirigami, as a scientific concept that emerges with but distinguishes from origami, provides a paradigm for engineering the mechanical properties of a surface through geometric analysis. The cutting geometry pattern that enables panel rotations around shared nodes—by itself or in conjunction with folding geometry that allows panel rotations around shared edges—yields predictable mechanical responses ranging from two-dimensional (2D) to three-dimensional (3D) deformations and from shape-fitting to metamaterial functionalities. This contribution reviews the deterministic relationships between geometry of a kirigami surface and its mechanical responses under given external loading. We highlight rigid and nonrigid 2D deformations determined by the convexity, compatibility, or symmetry of the cutting patterns (e.g., tessellations characterized by wallpaper groups); 3D deformations controlled by cutting distance versus surface thickness, slit shapes, or the combined effect of cuts and folds; and mechanical metamaterial functionalities arising from unique lattice connections and panel orientations, including topological polarization transformation, static nonreciprocity, and Poisson's ratio functional variation. We address various methodologies for linking geometry and mechanics in kirigami surfaces, including theoretical analyses, surrogate modeling, finite element simulations, and experimental evaluations. We also discuss strategies for fabricating kirigami surfaces, such as 3D printing, molding, assembling, cutting, and folding. Finally, we project a vision for the field of kirigami engineering by emphasizing the mechanisms that transform subtle geometric characteristics of kirigami surfaces into their unique mechanical properties.
Mechanical instabilities, phenomena in which solids and structures lose stability under external stimuli, were traditionally regarded as failure mechanisms but have recently been harnessed to design various functional structures and systems. Over the past century, significant progress has been made in both understanding the fundamental mechanisms behind mechanical instabilities and leveraging them for innovative functional applications. In this review, we classify mechanical instabilities into five categories based on their underlying failure mechanisms: buckling instability, snap-buckling instability, surface instability, buckling-driven delamination, and dynamic instability. First, a brief historical overview of research in this field is presented. Then, for each category of mechanical instabilities, we systematically introduce the underlying mechanisms and associated functional applications, with a particular focus on three fundamental aspects: the conditions under which instability is triggered, the evolution of the system after the onset of instability, and the strategies for exploiting these instabilities in functional design. Finally, we discuss several promising directions for future research. We expect that this review can help readers have a deeper understanding of mechanical instabilities and thereby inspire their broader application in advanced materials and structural systems.
The relationship between continuum concepts and the microscopic behavior of materials has long intrigued researchers in both the mechanics and physics communities. While continuum mechanics typically assumes a well-defined reference (undeformed) configuration, materials at the atomic scale are never truly static. Even solid materials experience continuous random deformations–known as thermal fluctuations–driven by ambient thermal energy. When these fluctuations become comparable to at least one characteristic length scale of a nanostructure, they can significantly impact its mechanical and physical properties. Examples of such nanostructures include crystalline membranes (commonly referred to as two-dimensional materials), which appear in various morphologies such as nanotubes, nanoribbons, and form the foundational elements of nanoscale metamaterials, kirigami/origami structures, nanocomposites, among others. Flexible nanostructures also play crucial roles in biological systems, including biological membranes, microtubules, actin filaments, and DNA. In this paper, we aim to provide an overview of the fundamental concepts underlying entropy-driven mechanics in flexible nanostructures, focusing on biological and crystalline membranes–two classes of systems where thermal fluctuations are particularly significant. We will review the current state of continuum mechanics modeling of fluctuating surfaces, highlighting key technical challenges, open questions, and future research directions. Although this article is extensive, it is not meant to serve as a comprehensive literature review. Instead, its goal is to introduce a broad audience from mechanics, materials science and cell mechanics to the core ideas of entropy-driven mechanics and to lay the groundwork for incorporating statistical mechanics into continuum modeling of flexible nanostructures.
Organic mixed ionic-electronic conductors (OMIECs) are a class of materials that can transport ionic and electronic charge carriers simultaneously. They have shown broad applications in soft robotics, electrochemical transistors, and bio-electronics. The structural response of OMIECs to the mixed conduction populates from molecular conformation to devices, presenting challenges in understanding their mechanical behavior and constitutive descriptions. Furthermore, OMIECs feature strong multiphysics interactions among mechanics, electrostatics, charge conduction, mass transport, and microstructural evolution. In this review, we summarize recent progress in mechanistic understanding of OMIECs and highlight dynamics and heterogeneity underlying each element of mechanics. We introduce strain activation and breathing, mechanical properties, and degradation of OMIECs upon electrochemical doping and dedoping. Drawing on the state-of-the-art experimental and simulation insights, we highlight the critical role of multiscale dynamics in governing the functionality of OMIECs. We discuss the current understanding and limitation of constitutive relations and present computational frameworks that integrate multiphysics. We synthesize mechanics-driven strategies—spanning strain modulation, material stretchability, and interfacial stability—from molecular design to macroscopic structural engineering. We conclude with our perspective on the outstanding questions and key challenges for continued research. This review aims to organize the fundamental mechanical principles of OMIECs, offering a multidisciplinary framework for researchers to identify, analyze, and address mechanical challenges in mixed conducting polymers and their applications.
Abstract Liquid metal interfacial flows occur in the fields of nuclear fusion and electromagnetic metallurgy. Due to the electrically conductive characteristics of the liquid metal, the presence of magnetic fields in these application scenarios has significant impacts on the interfacial flow behaviors. Then typical interfacial flows under the influence of magnetic fields, such as the free surface liquid metal flow, the liquid metal droplet impacting problems, and the bubble motion in liquid metal, are discussed in the present review. We comprehensively illustrate the flow characteristics of free surface liquid metal flow, the spreading of liquid metal droplets impacting onto solid or liquid surfaces, outcomes of collisions between metal droplets, and bubble dynamics in liquid metal, under the influence of magnetic fields along different directions. Meanwhile, we briefly review the current concepts of liquid metal free surface flow for the plasma facing comonents (PFCs) in fusion reactors and finally make a summary for the open questions related to the fundamental research and industrial applications of interfacial flow magnetohydrodynamics in the future.
Abstract With the increasing miniaturization of mechanical systems and the prevalence of rough surfaces in engineering applications, understanding and accurately characterizing the contact response at small scales has become crucial. This review article provides a comprehensive analysis of two significant aspects in the field of contact mechanics: the size-dependent response of single asperity due to strain gradients and surface effects, and the contact behavior of rough surfaces. The former forms the foundation for the latter analysis, as real surfaces are inherently rough and contact occurs at discrete asperities. At the microscale, strain gradients play a dominant role, as classical continuum mechanics fails to account for the intrinsic material length. Further downscaling to the nanoscale highlights the importance of surface effects due to the large surface-to-bulk ratio. The first section examines these distinct size-dependent effects and their implications for contact mechanics across different scales. The second section further focuses on the contact of rough surfaces, highlighting incremental contact models, contact behavior at large contact fraction where asperity interactions are significant, adhesive rough contact in soft materials, and experimental advances that improve the understanding and validation of these models. Together, these two topics underscore the need for refined theoretical and experimental approaches to accurately model and predict the contact behavior at small scales and with realistic multi-scale roughness.
Flexible elastic structures, such as beams, rods, ribbons, plates, and shells, exhibit complex nonlinear dynamical behaviors that are central to a wide range of engineering and scientific applications, including soft robotics, deployable structures, and biomedical devices. While various numerical methods have been developed to simulate these behaviors, many conventional approaches struggle to simultaneously capture geometric and material nonlinearities, as well as nonlinear external interactions, particularly in highly deformable and dynamically evolving systems. The Discrete Differential Geometry (DDG) method has emerged as a robust and efficient numerical framework that intrinsically preserves geometric properties, accommodates material nonlinearity, and accurately models interactions with external environments and fields. By directly discretizing geometric and mechanical quantities, DDG provides an accurate, stable, and efficient approach to modeling flexible structures, addressing key limitations of traditional numerical methods. This tutorial provides a systematic introduction to the DDG method for simulating nonlinear behaviors in flexible structures. It covers DDG theory, simulation frameworks, and MATLAB implementation, with examples spanning dynamic systems, geometric and material nonlinearities, and external interactions like magnetics and fluids, culminating in practical insights and future directions. By offering a comprehensive and practical guide, together with open-source MATLAB code, this tutorial aims to facilitate the broader adoption of DDG-based numerical tools among researchers and engineers in computational mechanics, applied mathematics, and structural design.
