arXiv subjects

Mingchao Liu

Publications and source records attributed to Mingchao Liu.

At least 37 records · Page 2Linked to original sources

arXiv2024

Transient amplification of broken symmetry in elastic snap-through

A snap-through bifurcation occurs when a bistable structure loses one of its stable states and moves rapidly to the remaining state. For example, a buckled arch with symmetrically clamped ends can snap between an inverted and a natural state as the ends are released. A standard linear stability analysis suggests that the arch becomes unstable to asymmetric perturbations. Surprisingly, our experiments show that this is not always the case: symmetric transitions are also observed. Using experiments, numerics, and a toy model, we show that the symmetry of the transition depends on the rate at which the ends are released with sufficiently fast loading leading to symmetric snap-through. Our toy model reveals that this behavior is caused by a region of the system's state space in which any initial asymmetry is amplified. The system may not enter this region when loaded fast (hence remaining symmetric) but will traverse it for some interval of time when loaded slowly, causing a transient amplification of asymmetry. Our toy model suggests that this behavior is not unique to snapping arches, but rather can be observed in dynamical systems where both a saddle-node and a pitchfork bifurcation occur in close proximity.

cond-mat.soft↗

arXiv2024

Can near-to-mid infrared spectral energy distribution quantitatively trace protoplanetary disk evolution?

Infrared (IR) spectral energy distribution (SED) is the major tracer of protoplanetary disks. It was recently proposed to use the near-to-mid IR (or K-24) SED slope $α$ defined between 2-24$μ$m as a potential quantitative tracer of disk age. We critically examine the viability of this idea and confront it with additional statistics of IR luminosities and SED shapes. We point out that, because the statistical properties of most of the complicated physical factors involved in disk evolution are still poorly understood in a quantitative sense, the only viable way is to assume them to be random so that an idealized `average disk' can be defined, which allows the $α$ histogram to trace its age. We confirm that the statistics of the zeroth order (luminosity), first order (slope $α$) and second order characteristics (concavity) of the observed K-24 SEDs indeed carry useful information upon the evolutionary processes of the `average disk'. We also stress that intrinsic diversities in K-24 SED shapes and luminosities are always large at the level of individual stars so that the application of the evolutionary path of the `average disk' to individual stars must be done with care. The data of most curves in plots are provided on GitHub.

astro-ph.SR↗

arXiv2024

Observation of strain-rate softening behavior in jammed granular media

The strain-rate sensitivity of confined granular materials has been widely explored, with most findings exhibiting rate-strengthening behaviors. This study, however, reveals a distinct rate-softening behavior across a certain strain rate range based on triaxial tests on particle clusters of various materials with different surface properties, particle sizes, shapes, and stiffness. This softening effect is especially pronounced in the case of common rice particles. By examining the behavior of rice particles under different confining pressure and surface conditions, and directly measuring the frictional coefficient across various loading rates, we find that the reduction in surface frictional coefficient with the increasing strain rate predominantly contributes to this rate-softening behavior. This conclusion is validated by results from Finite Element Method (FEM) simulations. Additionally, we identify confining pressure as a critical factor regulating the normal stress between particles, and thereby enhancing frictional behavior. Rheometer tests reveal that the shear modulus exhibits a similar rate-softening trend. This study of rate-softening behavior in granular materials enhances our understanding of the mechanisms during their deformation under confining pressure. It also suggests that local inter-particle tribology significantly impacts overall granular behavior.

cond-mat.soft↗

arXiv2024

Simplified discrete model for axisymmetric dielectric elastomer membranes with robotic applications

Soft robots utilizing inflatable dielectric membranes can realize intricate functionalities through the application of non-mechanical fields. However, given the current limitations in simulations, including low computational efficiency and difficulty in dealing with complex external interactions, the design and control of such soft robots often require trial and error. Thus, a novel one-dimensional (1D) discrete differential geometry (DDG)-based numerical model is developed for analyzing the highly nonlinear mechanics in axisymmetric inflatable dielectric membranes. The model captures the intricate dynamics of these membranes under both inflationary pressure and electrical stimulation. Comprehensive validations using hyperelastic benchmarks demonstrate the model's accuracy and reliability. Additionally, the focus on the electro-mechanical coupling elucidates critical insights into the membrane's behavior under varying internal pressures and electrical loads. The research further translates these findings into innovative soft robotic applications, including a spherical soft actuator, a soft circular fluid pump, and a soft toroidal gripper, where the snap-through of electroelastic membrane plays a crucial role. Our analyses reveal that the functional ranges of soft robots are amplified by the snap-through of an electroelastic membrane upon electrical stimuli. This study underscores the potential of DDG-based simulations to advance the understanding of the nonlinear mechanics of electroelastic membranes and guide the design of electroelastic actuators in soft robotics applications.

cond-mat.soft↗

arXiv2024

Discrete differential geometry-based model for nonlinear analysis of axisymmetric shells

In this paper, we propose a novel one-dimensional (1D) discrete differential geometry (DDG)-based numerical method for geometrically nonlinear mechanics analysis (e.g., buckling and snapping) of axisymmetric shell structures. Our numerical model leverages differential geometry principles to accurately capture the complex nonlinear deformation patterns exhibited by axisymmetric shells. By discretizing the axisymmetric shell into interconnected 1D elements along the meridional direction, the in-plane stretching and out-of-bending potentials are formulated based on the geometric principles of 1D nodes and edges under the Kirchhoff-Love hypothesis, and elastic force vector and associated Hession matrix required by equations of motion are later derived based on symbolic calculation. Through extensive validation with available theoretical solutions and finite element method (FEM) simulations in literature, our model demonstrates high accuracy in predicting the nonlinear behavior of axisymmetric shells. Importantly, compared to the classical theoretical model and three-dimensional (3D) FEM simulation, our model is highly computationally efficient, making it suitable for large-scale real-time simulations of nonlinear problems of shell structures such as instability and snap-through phenomena. Moreover, our framework can easily incorporate complex loading conditions, e.g., boundary nonlinear contact and multi-physics actuation, which play an essential role in the use of engineering applications, such as soft robots and flexible devices. This study demonstrates that the simplicity and effectiveness of the 1D discrete differential geometry-based approach render it a powerful tool for engineers and researchers interested in nonlinear mechanics analysis of axisymmetric shells, with potential applications in various engineering fields.

cond-mat.soft↗

arXiv2023

Exploiting dynamic bifurcation in elastic ribbons for mode skipping and selection

In this paper, we systematically study the dynamic snap-through behavior of a pre-deformed elastic ribbon by combining theoretical analysis, discrete numerical simulations, and experiments. By rotating one of its clamped ends with controlled angular speed, we observe two snap-through transition paths among the multiple stable configurations of a ribbon in three-dimensional (3D) space, which is different from the classical snap-through of a two-dimensional (2D) bistable beam. Our theoretical model for the static bifurcation analysis is derived based on the Kirchhoff equations, and dynamical numerical simulations are conducted using the Discrete Elastic Rods (DER) algorithm. The planar beam model is also employed for the asymptotic analysis of dynamic snap-through behaviors. The results show that, since the snap-through processes of both planar beams and 3D ribbons are governed by the saddle-node bifurcation, the same scaling law for the delay applies. We further demonstrate that, in elastic ribbons, by controlling the rotating velocity at the end, distinct snap-through pathways can be realized by selectively skipping specific modes, moreover, particular final modes can be strategically achieved. Through a parametric study using numerical simulations, we construct general phase diagrams for both mode skipping and selection of snapping ribbons. The work serves as a benchmark for future investigations on dynamic snap-through of thin elastic structures and provides guidelines for the novel design of intelligent mechanical systems.

cond-mat.soft↗

arXiv2023

Inverse design and additive manufacturing of shape-morphing structures based on functionally graded composites

Shape-morphing structures possess the ability to change their shapes from one state to another, and therefore, offer great potential for a broad range of applications. A typical paradigm of morphing is transforming from an initial two-dimensional (2D) flat configuration into a three-dimensional (3D) target structure. One popular fabrication method for these structures involves programming cuts in specific locations of a thin sheet material (i.e.~kirigami), forming a desired 3D shape upon application of external mechanical load. In this paper, a novel inverse design strategy is proposed by modifying the bending stiffness via introducing distributed modulus in functionally graded composites (FGCs). The longitudinal modulus of each cross-sectional slice can be controlled through the rule of mixtures, hence matching the required modulus distribution along the elastic strip. Following the proposed framework, a diverse range of structures is obtained with different Gaussian curvatures in both numerical simulations and experiments. A very good agreement is achieved between the measured shapes of morphed structures and the targets. In addition, the compressive rigidity and specific energy absorption during compression of FGC-based hemi-ellipsoidal morphing structures with various aspect ratios were also examined numerically and validated against experiments. By conducting systematical numerical simulations, we also demonstrate the multifunctionality of the modulus-graded shape-morphing composites. This new inverse design framework provides an opportunity to create shape-morphing structures by utilising modulus-graded composite materials, which can be employed in a variety of applications involving multi-physical environments. Furthermore, this framework underscores the versatility of the approach, enabling precise control over material properties at a local level.

physics.app-ph↗

arXiv2022

Snap-induced morphing: From a single bistable shell to the origin of shape bifurcation in interacting shells

The bistability of embedded elements provides a natural route through which to introduce reprogrammability to elastic meta-materials. One example of this is the soft morphable sheet, in which bistable elements that can be snapped up or down, are embedded within a soft sheet. The state of the sheet can then be programmed by snapping particular elements up or down, resulting in different global shapes. However, attempts to leverage this programmability have been limited by the tendency for the deformations induced by multiple elastic elements to cause large global shape bifurcations. We study the root cause of this bifurcation in the soft morphable sheet by developing a detailed understanding of the behaviour of a single bistable element attached to a flat 'skirt' region. We study the geometrical limitations on the bistability of this single element, and show that the structure of its deformation can be understood using a boundary layer analysis. Moreover, by studying the compressive strains that a single bistable element induces in the surrounding skirt we show that the shape bifurcation in the soft morphable sheet can be delayed by an appropriate design of the lattice on which bistable elements are placed.

cond-mat.soft↗

arXiv2022

Disk dissipation, giant planet formation and star-formation-rate fluctuations in the past three-million-year history of Gould's Belt

Although episodic star formation (SF) had been suggested for nearby SF regions, a panoramic view to the latest episodic SF history in the solar neighborhood is still missing. By uniformly constraining the slope $α$ of infrared spectral energy distributions (SEDs) of young stellar objects (YSOs) in the 13 largest Gould's Belt (GB) protoclusters surveyed by Spitzer Space Telescope, we have constructed a cluster-averaged histogram of $α$ representing YSO evolution lifetime as a function of the $α$ value. Complementary to the traditional SED classification scheme (0, I, F, II, III) that is based on different $α$ values, a staging scheme (A,B,C,D,E) of SED evolution is advised on the basis of the $α$ statistical features that can be better matched to the physical stages of disk dissipation and giant planet formation. This has also allowed us to unravel the fluctuations of star formation rate (SFR) in the past three-million-year (3 Myr) history of these GB protoclusters. Diverse evolutionary patterns such as single peak, double peaks and on-going acceleration of SFR are revealed. The SFR fluctuations are between $20\%\sim60\%$ ($\sim40\%$ on average) and no dependence on the average SFR or the number of SFR episodes is found. However, spatially close protoclusters tend to share similar SFR fluctuation trends, indicating that the driving force of the fluctuations should be at size scales beyond the typical cluster sizes of several parsec.

astro-ph.SR↗

arXiv2022

Shape-morphing structures based on perforated kirigami

Shape-morphing structures, which are able to change their shapes from one state to another, are important in a wide range of engineering applications. A popular scenario is morphing from an initial two-dimensional (2D) shape that is flat to a three-dimensional (3D) target shape. One of the exciting manufacturing paradigms is transforming flat 2D sheets with prescribed cuts (i.e. kirigami) into 3D structures. By employing the formalism of the 'tapered elastica' equation, we develop an inverse design framework to predict the shape of the 2D cut pattern that would generate a desired axisymmetric 3D shape. Our previous work has shown that tessellated 3D structures can be achieved by designing both the width and thickness of the cut 2D sheet to have particular tapered designs. However, the fabrication of a sample with variable thickness is quite challenging. Here we propose a new strategy -- perforating the cut sheet with tapered width but uniform thickness to introduce a distribution of porosity. We refer to this strategy as perforated kirigami and show how the porosity function can be calculated from our theoretical model. The porosity distribution can easily be realized by laser cutting and modifies the bending stiffness of the sheet to yield a desired elastic deformation upon buckling. To verify our theoretical approach, we conduct finite element simulations and physical experiments. We also examine the loading-bearing capacity of morphed structures via indentation tests in both FEM simulations and experiments. As an example, the relationship between the measured geometric rigidity of morphed half-ellipsoids and their aspect ratio is investigated in details.

cond-mat.soft↗

arXiv2021

OpenBox: A Generalized Black-box Optimization Service

Black-box optimization (BBO) has a broad range of applications, including automatic machine learning, engineering, physics, and experimental design. However, it remains a challenge for users to apply BBO methods to their problems at hand with existing software packages, in terms of applicability, performance, and efficiency. In this paper, we build OpenBox, an open-source and general-purpose BBO service with improved usability. The modular design behind OpenBox also facilitates flexible abstraction and optimization of basic BBO components that are common in other existing systems. OpenBox is distributed, fault-tolerant, and scalable. To improve efficiency, OpenBox further utilizes "algorithm agnostic" parallelization and transfer learning. Our experimental results demonstrate the effectiveness and efficiency of OpenBox compared to existing systems.

cs.LG↗

arXiv2020

Delayed bifurcation in elastic snap-through instabilities

We study elastic snap-through induced by a control parameter that evolves dynamically. In particular, we study an elastic arch subject to an end-shortening that evolves linearly with time, i.e. at a constant rate. For large end-shortening the arch is bistable but, below a critical end-shortening, the arch becomes monostable. We study when and how the arch transitions between states and show that the end-shortening at which the fast 'snap' happens depends on the rate at which the end-shortening is reduced. This lag in snap-through is a consequence of delayed bifurcation and occurs even in the perfectly elastic case when viscous (and viscoelastic) effects are negligible. We present the results of numerical simulations to determine the magnitude of this lag as the loading rate and the importance of external viscous damping vary. We also present an asymptotic analysis of the geometrically-nonlinear problem that reduces the salient dynamics to that of an ordinary differential equation; the form of this reduced equation is generic for snap-through instabilities in which the relevant control parameter is ramped linearly in time. Moreover, this asymptotic reduction allows us to derive analytical results for the observed lag in snap-through that are in good agreement with the numerical results of our simulations. Finally, we discuss scaling laws for the lag that should be expected in other examples of delayed bifurcation in elastic instabilities.

cond-mat.soft↗

arXiv2020

Fingering patterns in hierarchical porous media

Porous media with hierarchical structures are commonly encountered in both natural and synthetic materials, e.g., fractured rock formations, porous electrodes and fibrous materials, which generally consist of two or more distinguishable levels of pore structure with different characteristic lengths. The multiphase flow behaviours in hierarchical porous media have remained elusive. In this study, we investigate the influences of hierarchical structures in porous media on the dynamics of immiscible fingering during fluid-fluid displacement. By conducting a series of numerical simulations, we found that the immiscible fingering can be suppressed due to the existence of secondary porous structures. To characterise the fingering dynamics in hierarchical porous media, a phase diagram is constructed by introducing a scaling parameter, i.e., the ratio of time scales considering the combined effect of characteristic pore sizes and wettability. The findings present in this work provide a basis for further research on the application of hierarchical porous media for controlling immiscible fingerings.

cond-mat.soft↗

arXiv2019

Two-dimensional modeling of the self-limiting oxidation in silicon and tungsten nanowires

Self-limiting oxidation of nanowires has been previously described as a reaction- or diffusion-controlled process. In this letter, the concept of finite reactive region is introduced into a diffusion-controlled model, based upon which a two-dimensional cylindrical kinetics model is developed for the oxidation of silicon nanowires and is extended for tungsten. In the model, diffusivity is affected by the expansive oxidation reaction induced stress. The dependency of the oxidation upon curvature and temperature is modeled. Good agreement between the model predictions and available experimental data is obtained. The developed model serves to quantify the oxidation in two-dimensional nanostructures and is expected to facilitate their fabrication via thermal oxidation techniques. https://doi.org/10.1016/j.taml.2016.08.002

cond-mat.mtrl-sci↗

arXiv2018

Pore-scale Modelling of Gravity-driven Drainage in Disordered Porous Media

Multiphase flow through a porous medium involves complex interactions between gravity, wettability and capillarity during drainage process. In contrast to these factors, the effect of pore distribution on liquid retention is less understood. In particular, the quantitative correlation between the fluid displacement and level of disorder has not yet been established. In this work, we employ direct numerical simulation by solving the Navier-Stokes equations and using volume of fluid method to track the liquid-liquid interface during drainage in disordered porous media. The disorder of pore configuration is characterized by an improved index to capture small microstructural perturbation, which is pivotal for fluid displacement in porous media. Then, we focus on the residual volume and morphological characteristics of saturated zones after drainage and compare the effect of disorder under different wettability (i.e., the contact angle) and gravity (characterized by a modified Bond number) conditions. Pore-scale simulations reveal that the highly-disordered porous medium is favourable to improve liquid retention and provide various morphologies of entrapped saturated zones. Furthermore, the disorder index has a positive correlation to the characteristic curve index (n) in van Genuchten equation, controlling the shape of the retention characteristic curves. It is expected that the findings will benefit to a broad range of industrial applications involving drainage processes in porous media, e.g., drying, carbon sequestration, and underground water remediation.

cond-mat.soft↗

arXiv2018

Modelling imbibition processes in heterogeneous porous media

Imbibition is a commonly encountered multiphase problem in various fields, and exact prediction of imbibition processes is a key issue for better understanding capillary flow in heterogeneous porous media. In this work, a numerical framework for describing imbibition processes in porous media with material heterogeneity is proposed to track the moving wetting front with the help of a partially saturated region at the front vicinity. A new interface treatment, named the interface integral method, is developed here, combined with which the proposed numerical model provides a complete framework for imbibition problems. After validation of the current model with existing experimental results of one-dimensional imbibition, simulations on a series of two-dimensional cases are analysed with the presences of multiple porous phases. The simulations presented here not only demonstrate the suitability of the numerical framework on complex domains but also present its feasibility and potential for further engineering applications involving imbibition in heterogeneous media.

cond-mat.soft↗

arXiv2018

Dynamics of Viscous Entrapped Saturated Zones in Partially Wetted Porous Media

As a typical multiphase fluid flow process, drainage in porous media is of fundamental interest in nature and industrial applications. During drainage processes in unsaturated soils and porous media in general, saturated clusters, in which a liquid phase fully occupies the pore space between solid grains, affect the relative permeability and effective stress of the system. In this study, we experimentally studied drainage processes in unsaturated granular media as a model porous system. The distribution of saturated clusters is analysed by an optical imaging method under different drainage conditions, in which pore-scale information from Voronoi and Delaunay tessellation was used to characterise the topology of saturated cluster distributions. By employing statistical analyses, the observed spatial and temporal information of multiphase flow and fluid entrapment in porous media are described. The results indicate that the distributions of both the crystallised cell size and pore size are positively correlated to the spatial and temporal distribution of saturated cluster sizes. The saturated cluster size is found to follow a lognormal distribution, in which the generalised Bond number correlates negatively to the scale parameter and positively to the shape parameter. These findings can be used to connect pore-scale behaviour with overall hydro-mechanical characteristics in partially saturated porous media, using both the degree of saturation and generalised Bond number.

cond-mat.soft↗

arXiv2017

Dynamic contact angle hysteresis in liquid bridges

This work presents a combined experimental and theoretical study of dynamic contact angle hysteresis using liquid bridges under cyclic compression and stretching between two identical plates. Under various loading rates, contact angle hysteresis for three different liquids was measured by examination of advancing and receding angles in liquid bridges, and the capillary forces were recorded. It is found that, for a given liquid, the hysteretic phenomenon of the contact angle is more pronounced at higher loading rates. By unifying the behaviour of the three liquids, power-law correlations were proposed to describe the relationship between the dynamic contact angle and the capillary number for advancing and receding cases. It is found that the exponents of obtained power-law correlations differ from those derived through earlier methods (e.g., capillary rise), due to the different kinematics of the triple-line. The various hysteretic loops of capillary force in liquid bridges under varied cyclic loading rates were also observed, which can be captured quantitatively by the prediction of our developed model incorporating the dynamic contact angle hysteresis. These results illustrate the importance of varying triple-line geometries during dynamic wetting and dewetting processes, and warrant an improved modelling approach for higher level phenomena involving these processes, e.g., multiphase flow in porous media and liquid transfer between surfaces with moving contact lines.

cond-mat.soft↗