Abstract 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 limit 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.

Abstract 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.

Abstract 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.

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 multiscale roughness.

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.

Abstract 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.

Abstract 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.

Abstract 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, numerical framework, and simulation implementation, with examples spanning dynamic systems, geometric and material nonlinearities, and external interactions like magnetics, fluids and contact, 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. We seek to enhance the accessibility and applicability of DDG methods, fostering further advancements in the simulation and analysis of highly flexible structures across diverse scientific and engineering domains.

Abstract 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.

Abstract In the framework of solid mechanics, the task of deriving material parameters from experimental data has recently reemerged with the progress in full-field measurement capabilities and the renewed advances of machine learning. In this context, new methods such as the virtual fields method and physics-informed neural networks have been developed as alternatives to the already established least-squares and finite element-based approaches. Moreover, model discovery problems are emerging and can be addressed in a parameter estimation framework. These developments call for a new unified perspective, which is able to cover both traditional parameter estimation methods and novel approaches in which the state variables or the model structure itself are inferred as well. Adopting concepts discussed in the inverse problems community, we distinguish between all-at-once and reduced approaches. With this general framework, we are able to structure a large portion of the literature on parameter estimation in computational mechanics—and we can identify combinations that have not yet been addressed, two of which are proposed in this paper. We also discuss statistical approaches to quantify the uncertainty related to the estimated parameters, and we propose a novel two-step procedure for identification of complex material models based on both frequentist and Bayesian principles. Finally, we illustrate and compare several of the aforementioned methods with mechanical benchmarks based on synthetic and experimental data.