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Bacteria adapt the mechanical properties of their cell envelope, including cell wall stiffness, turgor, and cell wall tension and deformation, to grow and survive in harsh environments. However, it remains a technical challenge to simultaneously determine these mechanical properties at a single cell level. Here we combined theoretical modelling with an experimental approach to quantify the mechanical properties and turgor of Staphylococcus epidermidis. It was found that high osmolarity leads to a decrease in both cell wall stiffness and turgor. We also demonstrated that the turgor change is associated with a change in the viscosity of the bacterial cell. We predicted that the cell wall tension is much higher in deionized (DI) water and it decreases with an increase in osmolality. We also found that an external force increases the cell wall deformation to reinforce its adherence to a surface and this effect can be more significant in lower osmolarity. Overall, our work highlights how bacterial mechanics supports survival in harsh environments and uncovers the adaption of bacterial cell wall mechanical integrity and turgor to osmotic and mechanical challenges.

The growth of biological tissues, which is regulated by a variety of factors, can induce stresses that may, in turn, destabilize the tissues into diverse patterns. In most previous studies, however, tissue growth was usually assumed as a prescribed parameter independent of stresses, limiting our understanding of the mechanobiological morphogenesis of real tissues. In this paper, we propose a theoretical model to investigate the mechanobiological response of soft tissues undergoing stress-modulated growth. Linear stability analysis is first performed to elucidate the surface instability mechanism induced by stress-modulated volumetric growth. We further conduct finite element simulations to validate the theoretical prediction and, particularly, to capture the post-buckling pattern evolution. Our results show that the non-uniform stresses, which evolve with the tissue growth and morphogenesis, exert mechanical feedback on the growth itself, producing up-down asymmetric surface morphologies as observed in, for example, the gyrification of human brains and brain organoids. It is also revealed that large residual stresses are unnecessary to cause mechanobiological instability and subsequent asymmetric patterning, which has long been believed to be driven by sufficiently high stresses. The present work could help us to understand the morphological changes of biological tissues under physiological and pathological conditions.

Cells migrate by adapting their leading-edge behaviours to heterogeneous extracellular microenvironments (ECMs) during cancer invasions and immune responses. Yet it remains poorly understood how such complicated dynamic behaviours emerge from millisecond-scale assembling activities of protein molecules, which are hard to probe experimentally. To address this gap, we established a spatiotemporal “resistance-adaptive propulsion” theory based on the protein interactions between Arp2/3 complexes and polymerizing actin filaments, and a multiscale dynamic modelling system spanning from molecular proteins to the cell. Combining spatiotemporal simulations with experiments, we quantitatively find that cells can accurately self-adapt propulsive forces to overcome heterogeneous ECMs via a resistance-triggered positive feedback mechanism, dominated by polymerization-induced actin filament bending and the bending-regulated actin-Arp2/3 binding. However, for high resistance regions, resistance triggered a negative feedback, hindering branched filament assembly, which adapts cellular morphologies to circumnavigate the obstacles. Strikingly, the synergy of the two opposite feedbacks not only empowers cells with both powerful and flexible migratory capabilities to deal with complex ECMs, but also endows cells to use their intracellular proteins efficiently. In addition, we identify that the nature of cell migration velocity depending on ECM history stems from the inherent temporal hysteresis of cytoskeleton remodelling. We also quantitatively show that directional cell migration is dictated by the competition between the local stiffness of ECMs and the local polymerizing rate of actin network caused by chemotactic cues. Our results reveal that it is the polymerization force-regulated actin filament-Arp2/3 complex binding interaction that dominates self-adaptive cell migrations in complex ECMs, and we provide a predictive theory and a spatiotemporal multiscale modelling system at the protein level.

Droplet impact on solid surfaces is essential for natural and industrial processes. Particularly, controlling the instability after droplet impact, and avoiding the satellite drops generation, have aroused great interest for its significance in inkjet printing, pesticide spraying, and hydroelectric power collection. Herein, we found that breaking the symmetry of the droplet impact dynamics using patterned-wettability surfaces can suppress the Plateau–Rayleigh instability during the droplet rebounding and improve the energy collection efficiency. Systematic experimental investigation, together with mechanical modeling and numerical simulation, revealed that the asymmetric wettability patterns can regulate the internal liquid flow and reduce the vertical velocity gradient inside the droplet, thus suppressing the instability during droplet rebounding and eliminating the satellite drops. Accordingly, the droplet energy utilization was promoted, as demonstrated by the improved hydroelectric power generation efficiency by 36.5%. These findings deepen the understanding of the wettability-induced asymmetrical droplet dynamics during the liquid–solid interactions, and facilitate related applications such as hydroelectric power generation and materials transportation., Satellite drops formed on droplet impact hinder applications from inkjet printing to drop energy harvest. Here, authors reveal that patterned-wettability surfaces can break the symmetry of droplet impacts and suppress the Plateau–Rayleigh instability, preventing satellite drop generation and improving the hydropower harvest.

Morphogenesis of active shells such as cells is a fundamental chemomechanical process that often exhibits three-dimensional (3D) large deformations and chemical pattern dynamics simultaneously. Here, we establish a chemomechanical active shell theory accounting for mechanical feedback and biochemical regulation to investigate the symmetry-breaking and 3D chiral morphodynamics emerging in the cell cortex. The active bending and stretching of the elastic shells are regulated by biochemical signals like actomyosin and RhoA, which, in turn, exert mechanical feedback on the biochemical events via deformation-dependent diffusion and inhibition. We show that active deformations can trigger chemomechanical bifurcations, yielding pulse spiral waves and global oscillations, which, with increasing mechanical feedback, give way to traveling or standing waves subsequently. Mechanical feedback is also found to contribute to stabilizing the polarity of emerging patterns, thus ensuring robust morphogenesis. Our results reproduce and unravel the experimentally observed solitary and multiple spiral patterns, which initiate asymmetric cleavage in Xenopus and starfish embryogenesis. This study underscores the crucial roles of mechanical feedback in cell development and also suggests a chemomechanical framework allowing for 3D large deformation and chemical signaling to explore complex morphogenesis in living shell-like structures.

Mechanical nociception is an evolutionarily conserved sensory process required for the survival of living organisms. Previous studies have revealed much about the neural circuits and key sensory molecules in mechanical nociception, but the cellular mechanisms adopted by nociceptors in force detection remain elusive. To address this issue, we study the mechanosensation of a fly larval nociceptor (class IV da neurons, c4da) using a customized mechanical device. We find that c4da are sensitive to mN-scale forces and make uniform responses to the forces applied at different dendritic regions. Moreover, c4da showed a greater sensitivity to more localized forces, consistent with them being able to sense the poking of sharp objects, such as wasp ovipositor. Further analysis reveals that high morphological complexity, mechanosensitivity to lateral tension and active signal propagation in the dendrites altogether facilitate the mechanosensitivity and sensory features of c4da. In particular, we discover that Piezo and Ppk1/Ppk26, two key mechanosensory molecules, make differential but additive contributions to the mechanosensation of c4da. In all, our results provide updates into understanding how c4da process mechanical signals at the cellular level and reveal the contributions of key molecules.

Phase transitions are common in inanimate systems and have been studied extensively in natural sciences. Less explored are the rich transitions that take place at the micro- and nano-scales in biological systems. In conventional phase transitions, large-scale properties of the media change discontinuously in response to continuous changes in external conditions. Such changes play a significant role in the dynamic behaviours of organisms. In this review, we focus on some transitions in both free-living and biofilms of bacteria. Particular attention is paid to the transitions in the flagellar motors and filaments of free-living bacteria, in cellular gene expression during the biofilm growth, in the biofilm morphology transitions during biofilm expansion, and in the cell motion pattern transitions during the biofilm formation. We analyse the dynamic characteristics and biophysical mechanisms of these phase transition phenomena and point out the parallels between these transitions and conventional phase transitions. We also discuss the applications of some theoretical and numerical methods, established for conventional phase transitions in inanimate systems, in bacterial biofilms.

Growing axons are one-dimensional active structures that are important for wiring the brain and repairing nerves. However, the biophysical mechanisms underlying the complex kinetics of growing axons remain elusive. Here, we develop a theoretical framework to recapitulate force-regulated states and their transitions in growing axons. We demonstrate a unique negative feedback mechanism that defines four distinct kinetic states in a growing axon, whose transitional boundaries depend on the interplay between cytoskeletal dynamics and axon-substrate adhesion. A phase diagram for axonal growth is formulated based on two dimensionless numbers.

A falling liquid drop, after impact on a rigid substrate, deforms and spreads, owing to the normal reaction force. Subsequently, if the substrate is non-wetting, the drop retracts and then jumps off. As we show here, not only is the impact itself associated with a distinct peak in the temporal evolution of the normal force, but also the jump-off, which was hitherto unknown. We characterize both peaks and elucidate how they relate to the different stages of the drop impact process. The time at which the second peak appears coincides with the formation of a Worthington jet, emerging through flow-focusing, and it is independent of the impact velocity. However, the magnitude of this peak is dictated by the drop's inertia and surface tension. We show that even low-velocity impacts can lead to a surprisingly high peak in the normal force, namely when a more pronounced singular Worthington jet occurs due to the collapse of an air cavity in the drop., Comment: Please find the supplemental movies here: https://youtube.com/playlist?list=PLf5C5HCrvhLGmlYTF1Gg2WviZ-Bkmy2qr

Self-assembled films (SAFs) have been proposed to be a promising candidate for molecularly thin lubricants. However, the frictional performance of SAFs is sensitively dependent on their molecular structures that are susceptible to external environments. Taking erucamide, a fatty amide widely used as a macroscale slip additive, as an example, we demonstrate that SAFs can be readily formed on various substrates, including silicon oxide, sapphire, copper, and graphite. Through high-resolution topography and friction measurements, two types of erucamide SAFs are identified. The first type is atomically flat and exhibits clear atomic stick–slip friction behavior and ultra-low frictional dissipation; while the second type has a stripe-like nanoscale pattern and shows much higher (8 times higher) frictional dissipation. The sharp contrast between these two types of SAFs is attributed to their distinct molecular structures originating from different interactions between erucamide molecules and substrates. We further demonstrate that, by proper surface functionalization, we can actively and reliably control the molecular structures of SAFs through guided self-assembling, achieving rational friction tuning with patterning capability.

Collective cell migration is extensively observed in embryo development and cancer invasion. During these processes, the interactions between cells with distinct identities and fates are of importance for boundary formation and host defense against cancer. In this paper, we explore the collective dynamics of a two-dimensional cell mixing monolayer consisting of non-tumorigenic mammary epithelial cells and breast cancer cells. We show that the epithelial–cancerous cell mixing system displays unique sorting behaviors. The epithelial cells aggregate to form scattered clusters, which perform random motion with simultaneous translation and rotation, strikingly distinct from the classical persistent random walk of individual migratory cells. The motility of cancer cells is markedly promoted by the epithelial clusters, exhibiting remarkable contact enhancement of locomotion. A discrete model based on the Johnson–Kendall–Roberts contact mechanics is proposed to identify the influence of intercellular interactions, active migration forces and cell–substrate friction forces on the collective cell dynamics. These findings could advance our understanding of many biological processes, such as cancer metastasis and tissue morphogenesis. The epithelial–cancerous cell mixing system displays unique collective dynamics. The epithelial cells aggregate to form scattered clusters, which perform random motion with simultaneous translation and rotation, strikingly distinct from the classical persistent random walk of individual migratory cells. The interactions between the two cell types drive the evolution of collective migration dynamics and give rise to a behavior akin to the contact enhancement of locomotion. This study revealed the distinctive dynamic features and the underlying regulatory mechanisms arising from epithelial–cancerous interactions.

Pore bulk modulus in continuum apparent permeability models was generally treated as an independent parameter or deduced from the Betti-Maxwell reciprocal theorem neglecting the sorption effect, which is not appropriate for the unconventional reservoirs with strong gas sorption. In this work, pore bulk modulus was firstly derived from the Betti-Maxwell theorem with the consideration of the gas sorption strain and was incorporated into the solid–fluid coupling apparent permeability model. Numerical simulation was then conducted under the uniaxial strain condition and the stress confined condition to investigate the gas transport characteristics. The results showed that when taking into account for the sorption effect in the Betti-Maxwell theorem, the pore bulk modulus dramatically decreased with the falling pore pressure during the gas transport process under two loading conditions. Moreover, gas transport ability under the stress confined condition was greatly degraded while it was hardly changed under the uniaxial strain condition. Both the pore bulk modulus and the stress distribution in the reservoirs were found responsible for the variation of gas flow capacity. Finally, the effects of the parameters associated with the pore bulk modulus were examined to further discuss the impact of involving the sorption effect in the Betti-Maxwell theorem.

Investigation of energy mechanisms at the collective cell scale is a challenge for understanding various biological processes, such as embryonic development and tumor metastasis. Here we investigate the energetics of self-sustained mesoscale turbulence in confluent two-dimensional (2D) cell monolayers. We find that the kinetic energy and enstrophy of collective cell flows in both epithelial and non-epithelial cell monolayers collapse to a family of probability density functions, which follow the q-Gaussian distribution rather than the Maxwell–Boltzmann distribution. The enstrophy scales linearly with the kinetic energy as the monolayer matures. The energy spectra exhibit a power-decaying law at large wavenumbers, with a scaling exponent markedly different from that in the classical 2D Kolmogorov–Kraichnan turbulence. These energetic features are demonstrated to be common for all cell types on various substrates with a wide range of stiffness. This study provides unique clues to understand active natures of cell population and tissues. Understanding the mechanisms underlying collective motion in cells is central to understanding tissue development as well as the emergence of several pathologies. Here, the authors study the mesoscale turbulence of confluent cell monolayers through a combined experimental and numerical approach, finding that energetic statistics are independent of cell types and substrate stiffness.

Human brain experiences vibration of certain frequency during various physical activities such as vehicle transportation and machine operation or accidents, which may cause traumatic brain injury or other brain diseases. However, little is known about what happened to brain after vibration stimuli. Here, with a custom-built electromagnetic actuator, vibration was induced in the brain while cerebral blood flow (CBF) and brain stiffness were measured at 20, 30, 40 Hz for 52 healthy volunteers. With increasing frequency, multiple regions of the brain showed increasingly reduced CBF, while the size of such regions also expanded. The vibration-induced CBF reduction regions largely fell inside the brain’s default mode network (DMN), with about 58 or 46 % overlap at 30 or 40 Hz, respectively. By establishing a biomechanical co-variance network based on tissue stiffness, analysis of small-world properties and modularity showed an increased disruption of the network with increased frequency. These findings demonstrate frequency-dependent features of vibration modulation to brain. Furthermore, the overlap between CBF reduction regions and DMN, and the vibration-induced decrease of biomechanical network connections suggest a interweaved relationship between blood flow, tissue stiffness, and cognitive functions. These may provide critical insights into the mechanical stimulus to brain and vibration-induced brain pathologies.

The growth and development of biological tissues and organs strongly depend on the requirements of their multiple functions. Plant veins yield efficient nutrient transport and withstand various external loads.Victoria cruziana, a tropical species of the Nymphaeaceae family of water lilies, has evolved a network of three-dimensional and rugged veins, which yields a superior load-bearing capacity. However, it remains elusive how biological and mechanical factors affect their unique vein layout. In this paper, we propose a multi-functional and large-scale topology optimization method to investigate the morphomechanics ofVictoria cruzianaveins, which optimizes both the structural stiffness and nutrient transport efficiency. Our results suggest that increasing the branching order of radial veins improves the efficiency of nutrient delivery, and the gradient variation of circumferential vein sizes significantly contributes to the stiffness of the leaf. In the present method, we also consider the optimization of the wall thickness and the maximum layout distance of circumferential veins. Furthermore, biomimetic leaves are fabricated by using the three-dimensional printing technique to verify our theoretical findings. This work not only gains insights into the morphomechanics ofVictoria cruzianaveins, but also helps the design of, for example, rib-reinforced shells, slabs and dome skeletons.

Turgor pressure and envelope elasticity of bacterial cells are two mechanical parameters that play a dominant role in cellular deformation, division, and motility. However, a clear understanding of these two properties is lacking because of their strongly interconnected mechanisms. This study established a nanoindentation method to precisely measure the turgor pressure and envelope elasticity of live bacteria. The indentation force-depth curves of Klebsiella pneumoniae bacteria were recorded with atomic force microscopy. Through combination of dimensional analysis and numerical simulations, an explicit expression was derived to decouple the two properties of individual bacteria from the nanoindentation curves. We show that the Young's modulus of bacterial envelope is sensitive to the external osmotic environment, and the turgor pressure is significantly dependent on the external osmotic stress. This method can not only quantify the turgor pressure and envelope elasticity of bacteria, but also help resolve the mechanical behaviors of bacteria in different environments.

Progression of cancers involves complicated and coupled interactions among mechanical, physical, chemical, and biological factors. Given the broad implications of tumor morphogenesis in clinics, we review the state-of-the-art morphomechanics of solid tumors, with an aim to highlight mechanistic factors that might potentially collude with oncology to drive cancer progression. Particular attention is given to theoretical modeling of morphological and structural evolutions, anisotropic growth, angiogenesis, invasion and metastasis of tumors. Continuum and discrete mechanobiological models for predicting the mechanical properties and constitutive relations of cancerous tissues and cells are summarized and recapitulated. These recent advances not only generate new insights into biomechanical and biophysical mechanisms underlying tumor development, but also provide inspirations for clinical diagnosis and treatments of cancer.

Collective cell dynamics plays significant roles in various physiological or pathological processes including embryo development, wound healing, and cancer invasion. It involves the self-organization of cytoskeleton and biochemical signaling transduction, as well as complex cell-cell interactions and cell-environment interactions. Therefore, collective cell dynamics is a hot topic in the interdisciplinary fields of biology, mechanics, physics and chemistry, attracting increasing efforts, both experimentally and theoretically, toward understanding the underlying biomechanical principles. In this review, we focus on the collective cell dynamics in cell monolayer systems and introduce the research progresses in recent years. A cell monolayer refers to a single layer of cells in which cells connect to their neighbors via cell-cell adhesions and adhere to the subjacent substrate via focal adhesions. We first introduce collective cell migration modes in cell monolayer systems under various boundary constraints. In confluent cell monolayers of large size, cells always self-organize into dynamic swirling motion patterns, as observed in various cell lines. Such motion patterns stem from active cell motility and cell-cell interactions, and can be theoretically accounted for by both continuum mechanical theory such as active gel theory and discrete models such as active vertex model. Boundary constraints affect collective cell migration modes significantly. For example, for cell monolayers in confined spaces, the persistent rotation mode, the collectively directed motion mode, and the shear flow mode have been observed. While for freely expanding cell monolayers, deformation waves emerge spontaneously and propagate toward the interior region of the cell monolayer. As a confluent cell monolayer matures, the cell density increases while cell motions gradually slow down, indicating a jamming-like behavior. Such jamming-like behavior of collective cell migration has been suggested similar to the jamming behavior of particle systems. We next introduce the statistics of cell shape and cell orientation, and discuss the relation between collective cell migration, cell fate and topological defects formed by cell orientation. Specifically, reported experiments indicated that in two-dimensional cell monolayers +1/2 topological defects trigger cell accumulation or cell extrusion while −1/2 topological defects lead to cell escape, accompanied with distinct tissue flow patterns. This topological defect-dictated cell fate has been observed in both eukaryotic cell monolayers and bacterial suspensions, revealing its potential universality. We further introduce collective cell shape oscillations and the underlying biomechanical mechanisms. Cell shape oscillation has been observed in both isolated cell systems and collective cell systems, stemming from the negative feedback between myosin activity and cell deformation. Compared with isolated cell oscillations, collective cells exhibit coordinated oscillatory morphodynamics, including aligned oscillatory patterns, polarized oscillation directions, and synchronized oscillatory amplitudes, which may help signaling transmission and synchronization among cells over large scales. In addition, collective cell dynamics on curved substrates and the role of substrate curvature is briefly introduced. This topic is in its infancy and plenty of questions remain to be explored. Finally, we introduce the cellular vertex model, an extensively used mechanical model in the study of epithelial mechanics and collective cell dynamics. In the cellular vertex model, cells are represented by interconnected polygons and vertices refer to tri-cellular junctions. The history, development, theoretical foundation, and applications of the cellular vertex model are briefly introduced.

This paper reports (1) an application of the modified hyperbolic sine law to P92 for the minimum creep strain rate over a wider range of stress level, and 2) the calibration of the creep ca...

As a species of insects living on water, water striders jump from the water surface to avoid predation and then steadily land without piercing the surface. This spectacular property has attracted extensive interests since it provides bio-inspirations for designing functional microrobots moving on water. In this work, we investigate the landing dynamics of water striders by using artificial striders with different masses and leg lengths. It is found that once a water strider has landed, it oscillates on the water surface and the amplitude decays gradually, triggering a sequence of surface waves. Through scaling analysis, we relate the depth of the dimple that the strider leg displaces to its landing velocity, as well as its leg length and body mass. The subsequent time evolution of the interface where the strider lands is modeled as a damped oscillator, and its energy is exhausted by the surface waves. Moreover, we discuss the maximum depth of the dimple excited by the landing and find that the dynamic process can store more energy than the statically deforming process. Finally, we put forward a criterion of piercing the water surface from the energy point of view. These findings should be of great importance for understanding the locomotion of insects on water and for designing robust water-walking bionic robots.

Rigidity of the extracellular matrix markedly regulates many cellular processes. However, how cells detect and respond to matrix rigidity remains incompletely understood. Here, we propose a unified two-dimensional multiscale framework accounting for the chemomechanical feedback to explore the interrelated cellular mechanosensing, polarization, and migration, which constitute the dynamic cascade in cellular response to matrix stiffness but are often modeled separately in previous theories. By combining integrin dynamics and intracellular force transduction, we show that substrate stiffness can act as a switch to activate or deactivate cell polarization. Our theory quantitatively reproduces rich stiffness-dependent cellular dynamics, including spreading, polarity selection, migration pattern, durotaxis, and even negative durotaxis, reported in a wide spectrum of cell types, and reconciles some inconsistent experimental observations. We find that a specific bipolarized mode can determine the optimal substrate stiffness, which enables the fastest cell migration rather than the largest traction forces that cells apply on the substrate. We identify that such a mechanical adaptation stems from the force balance across the whole cell. These findings could yield universal insights into various stiffness-mediated cellular processes within the context of tissue morphogenesis, wound healing, and cancer invasion.

Active topological phase transitions widely occur in active matters and biological systems, such as developing embryos. Since the discovery of the intriguing bulk-boundary effects of topological insulators in Hermitian and non-Hermitian systems, various electric, optical, acoustic, and mechanical topological metamaterials with efficient energy transmission and robust defect-immunization have been designed. To date, however, it remains a challenge to precisely and fast manipulate the topological phase transitions in elastic topological insulators. In this paper, on the basis of theoretical analysis and numerical simulations, we propose an active strategy to achieve this aim through a combination of pneumatic actuation and liquid metals. The proposed method can precisely tune the connecting stiffness and vertex mass in the tight Su–Schrieffer–Heeger model. Thus, we realize the effective and fast control of topological phase transitions and elastic wave bandgap switching. We also uncover the active spinning bulk-boundary effects and higher-order topological states in the elastic topological insulators, demonstrating the high effectiveness and practicability of the proposed method. In addition, the differences between the 1D edge and 0D corner higher-order states are specified by information entropy theory. This work not only gains insights into the active manipulation of topological phase transitions but also inspires novel strategies to design active topological materials through untethered methods, e.g., magnetism or biological cells.

Hydrogels are widely used as substrates to investigate interactions between cells and their microenvironment as they mimic many attributes of the extracellular matrix. The stiffness of hydrogels is an important property that is known to regulate cell behavior. Beside stiffness, cells also respond to structural cues such as mesh size. However, since the mesh size of hydrogel is intrinsically coupled to its stiffness, its role in regulating cell behavior has never been independently investigated. Here, we report a hydrogel system whose mesh size and stiffness can be independently controlled. Cell behavior, including spreading, migration, and formation of focal adhesions is significantly altered on hydrogels with different mesh sizes but with the same stiffness. At the transcriptional level, hydrogel mesh size affects cellular mechanotransduction by regulating nuclear translocation of yes-associated protein. These findings demonstrate that the mesh size of a hydrogel plays an important role in cell-substrate interactions. STATEMENT OF SIGNIFICANCE: Hydrogels are ideal platforms with which to investigate interactions between cells and their microenvironment as they mimic many physical properties of the extracellular matrix. However, the mesh size of hydrogels is intrinsically coupled to their stiffness, making it challenging to investigate the contribution of mesh size to cell behavior. In this work, we use hydrogel-on-glass substrates with defined thicknesses whose stiffness and mesh size can be independently tuned. We use these substrates to isolate the effects of mesh size on cell behavior, including attachment, spreading, migration, focal adhesion formation and YAP localization in the nucleus. Our results show that mesh size has significant, yet often overlooked, effects, on cell behavior, and contribute to a further understanding of cell-substrate interactions.

When two bodies are in contact, various surface/subsurface damage problems may arise, which significantly shorten the service lives of functional components. These damage problems may further interact with one another and be influenced by such factors as friction and lubrication. Contact mechanics plays an important role in understanding the complex phenomena and analyzing the damage evolution. This paper aims to provide a comprehensive review of the recent progress in contact mechanics for tribological and contact damage–related problems. After a brief introduction of the contact mechanics, the applications of contact mechanics in various problems are systematically elaborated. Finally, the review concludes with future perspectives and major challenges to be addressed. Nanyang Technological University National Research Foundation (NRF) The authors acknowledge the financial support from the National Natural Science Foundation of China (12072272 and 11921002) and the SMRT-NTU Smart Urban Rail Corporate Laboratory with funding support from the National Research Foundation, Singapore, SMRT, Singapore, and Nanyang Technological University, Singapore.