arXiv subjects

Mingchao Liu

Publications and source records attributed to Mingchao Liu.

At least 19 recordsLinked to original sources

arXiv2026

Tunable Pathway Selection in Coupled Multistable Snap-Through Systems

Multistable mechanical systems can store and release elastic energy through snap-through instabilities, but controlling transition pathways between stable states remains challenging when multiple routes are accessible. Here, we introduce a two-mass von Mises truss as a general model for studying pathway selection governed by coupled saddle-node bifurcations. The system consists of two coupled snap-through units with geometric imperfections, giving rise to four stable configurations: a fully inverted state, a fully natural state, and two intermediate mixed states. We show that the coupling stiffness reorganizes the quasi-static bifurcation structure and selects among three transition pathways under release: sequential snapping through one mixed state, direct cooperative snapping, or sequential snapping through the other mixed state. Using pseudo-arclength continuation, we track the relevant saddle-node bifurcations and identify the parameter regimes associated with each quasi-static pathway. We then demonstrate that dynamic bifurcation delay provides an additional rate-dependent mechanism for pathway selection. Even when the quasi-static bifurcation structure favours a unique sequential pathway, finite-rate loading delays snap-through beyond the corresponding static saddle-node points and can reorder the snapping sequence of the two units. A local reduction of the coupled dynamics near each saddle-node yields normal forms with coupling-dependent critical points and coefficients. The resulting theory identifies distinct rate-dependent delay laws in the inertia-dominated and overdamped regimes and predicts the critical rate at which the snapping order reverses. These results establish a general mechanics framework for tuning transition pathways in multistable systems through elastic coupling and loading-rate control.

cond-mat.soft↗

arXiv2026

Bifurcation reordering programs snap-through symmetry in folded elastic ribbons

Snap-through in slender elastic structures is often viewed as a sudden transition between stable configurations, yet the pathway taken during this transition can differ fundamentally. A structure may snap while preserving symmetry, or first lose symmetry and pass through an asymmetric state before reaching its final configuration. What selects between these pathways remains less well understood, especially when the geometry and loading are themselves symmetric. Here, we show that snap-through symmetry can be programmed by reordering competing bifurcations in folded elastic ribbons. We study an elastic ribbon with two localized folds placed symmetrically about the midpoint and show that varying the fold position changes the relative order of two instabilities: a symmetry-breaking pitchfork bifurcation and a saddle-node bifurcation on the symmetry-preserving branch. When the pitchfork bifurcation occurs first, the ribbon loses symmetry before snapping and follows an asymmetric pathway. Conversely, when the saddle-node bifurcation occurs first, the ribbon loses stability while remaining on the symmetric branch, resulting in a symmetry-preserving transition. Combining experiments, discrete differential geometry simulations and numerical continuation, we map this exchange in bifurcation ordering and construct a phase diagram that predicts the switch between asymmetric and symmetric snap-through regimes. A reduced-order double-mass von Mises truss model captures the same mechanism as a generic competition between symmetry-breaking and symmetry-preserving instabilities. These results establish bifurcation reordering as a geometric mechanism for programming snap-through pathways in slender elastic structures, offering a design principle for multistable systems, morphing structures and instability-based mechanical devices.

cond-mat.soft↗

arXiv2026

Dimple-Encoded Reprogrammable Origami

Programmable folding of elastic sheets typically relies on predefined flexible creases or active materials-enabled hinges, which lack intrinsic bistability and limit reprogrammability within a single structure. Here, we present a dimple-encoded origami platform that converts bistable dimple snapping into spatially addressable hinges with prescribed folding angles in a continuous sheet. This interaction-enabled mechanism enables the design of distributed hinge networks through the arrangement and selective inversion of dimples. We establish folding-angle design charts that can be directly used to select local dimple arrangements for target fold angle, forming a practical hinge library without altering the underlying unit geometry. Using this approach, a single dimpled sheet can be reprogrammed to realize multiple distinct configurations, such as triangle, square, and pentagon shapes. We further extend the method to flat-to-3D morphing of polyhedral origami and validate the results through experiments and finite element simulations. As demonstrations, we realize self-supporting cubic shells with enhanced impact resistance and partially deployable cube configurations that remain stable upon opening, highlighting their potential for protective enclosures and deployable architectural structures. The proposed strategy provides a fabrication-friendly route to reprogrammable shape-morphing and adaptive mechanical systems.

cond-mat.soft↗

arXiv2026

Inverse design of a magneto-elastica for shape-morphing

Slender magnetic elements provide a versatile platform for programmable shape-morphing under remote magnetic actuation. However, a general and physically interpretable framework for the inverse design of a 'magneto-elastica' under prescribed boundary conditions remains lacking. In this work, we develop an explicit analytical formulation for the inverse design of a magneto-elastica based on the integral form of the moment equilibrium equations. Compared with purely local differential formulations, this integral approach makes the global constraints imposed by boundary conditions and moment balance explicit, and enables a systematic characterization of the feasible design space. We identify the key dimensionless parameters that govern the competition between magnetic torques and elastic restoring moments and show that the applied boundary conditions are an essential ingredient. We obtain closed-form solutions for the beam tapering profiles required to generate desired actuated shapes in the cases of clamped--free and clamped--clamped configurations; in the latter case, this includes analytical expressions for the boundary reactions. The formulation recovers the classical inverse elastica in the absence of magnetic fields and reveals a linear scaling between curvature deviation and magnetic mismatch. A tessellation strategy based on stiffness tailoring is further proposed for the design of discretized morphing surfaces. The theoretical predictions are validated against discrete elastic rod simulations and experiments across representative geometries. This work establishes a consistent analytical framework for the inverse design of a magneto-elastica and provides new insight into magnetically-induced shape programming in slender structures.

cond-mat.soft↗

arXiv2026

From Folding Mechanics to Robotic Function: A Unified Modeling Framework for Compliant Origami

Origami inspired architectures offer a powerful route toward lightweight, reconfigurable, and programmable robotic systems. Yet, a unified mechanics framework capable of seamlessly bridging rigid folding, elastic deformation, and stability driven transitions in compliant origami remains lacking. Here, we introduce a geometry consistent modeling framework based on discrete differential geometry (DDG) that unifies panel elasticity and crease rotation within a single variational formulation. By embedding crease panel coupling directly into a mid edge geometric discretization, the framework naturally captures rigid folding limits, distributed bending, multistability, and nonlinear dynamic snap through within one mechanically consistent structure. This unified description enables programmable control of stability and deformation across rigid and compliant regimes, allowing origami structures to transition from static folding mechanisms to active robotic modules. An implicit dynamic formulation incorporating gravity, contact, friction, and magnetic actuation further supports strongly coupled multiphysics simulations. Through representative examples spanning single fold bifurcation, deployable Miura membranes, bistable Waterbomb modules, and Kresling based crawling robots, we demonstrate how geometry driven mechanics directly informs robotic functionality. This work establishes discrete differential geometry as a foundational design language for intelligent origami robotics, enabling predictive modeling, stability programming, and mechanics guided robotic actuation within a unified computational platform.

cs.RO↗

arXiv2025

Harnessing Eversion Buckling for Ideal Omnidirectional Energy Absorption

Thin shells can undergo large shape changes governed by the competition between bending and membrane energies. Here, we identify an instability mechanism in everted toroidal shells, referred to as eversion buckling. After eversion, the axisymmetric configuration may either remain stable or lose stability through symmetry breaking, depending on geometry. A scaling analysis reveals a dimensionless parameter that characterizes the ratio between membrane and bending energies. This parameter defines a critical threshold separating a bistable regime, where the axisymmetric everted state persists, from a monostable regime, where the shell collapses into a non-axisymmetric configuration. The transition is consistent with a pitchfork-type bifurcation, leading to collapse without a preferred in-plane direction. Finite element simulations and experiments validate the proposed scaling and the associated stability boundary across different shell geometries. In the bistable regime, individual everted shells exhibit rapid snap-through accompanied by large volumetric contraction and show limited sensitivity of the critical response to boundary constraints. Building on this mechanism, assemblies of such shells form granular systems with a stable stress plateau and high energy absorption efficiency. These results provide a mechanics-based framework for designing shell-based systems with robust and direction-insensitive energy absorption.

math-ph↗

arXiv2025

Inverse Discrete Elastic Rod

Inverse design of slender elastic structures underlies a wide range of applications in computer graphics, flexible electronics, biomedical devices, and soft robotics. Traditional optimization-based approaches, however, are often orders of magnitude slower than forward dynamic simulations and typically impose restrictive boundary conditions. In this work, we present an inverse discrete elastic rods (inverse-DER) method that enables efficient and accurate inverse design under general loading and boundary conditions. By reformulating the inverse problem as a static equilibrium in the reference configuration, our method attains computational efficiency comparable to forward simulations while preserving high fidelity. This framework allows rapid determination of undeformed geometries for elastic fabrication structures that naturally deform into desired target shapes upon actuation or loading. We validate the approach through both physical prototypes and forward simulations, demonstrating its accuracy, robustness, and potential for real-world design applications.

cs.GR↗

arXiv2025

Discrete Differential Geometry for Simulating Nonlinear Behaviors of Flexible Systems: A Survey

Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry (DDG) has emerged as a geometry first, structure preserving paradigm for modeling such behaviors. Unlike finite element or mass spring methods, DDG discretizes geometry rather than governing equations, allowing curvature, twist, and strain to be defined directly on meshes. This approach yields robust large deformation dynamics, accurate handling of contact, and differentiability essential for inverse design and learning based control. This review consolidates the rapidly expanding landscape of DDG models across 1D and 2D systems, including discrete elastic rods, ribbons, plates, and shells, as well as multiphysics extensions to contact, magnetic actuation, and fluid structure interaction. We synthesize applications spanning mechanics of nonlinear instabilities, biological morphogenesis, functional structures and devices, and robotics from manipulation to soft machines. Compared with established approaches, DDG offers a unique balance of geometric fidelity, computational efficiency, and algorithmic differentiability, bridging continuum rigor with real time, contact rich performance. We conclude by outlining opportunities for multiphysics coupling, hybrid physics data pipelines, and scalable GPU accelerated solvers, and by emphasizing DDG role in enabling digital twins, sim to real transfer, and intelligent design of next generation flexible systems.

cond-mat.soft↗

arXiv2025

Inverse Elastica: A Theoretical Framework for Inverse Design of Morphing Slender Structures

Inverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the forward equations to identify optimal designs. Such methods, however, are computationally intensive and often susceptible to local minima issues. In contrast, solving the inverse problem theoretically, which can bypass the need for optimizations, is highly efficient yet remains challenging, particularly for cases involving arbitrary boundary conditions (BCs). Here, we develop a systematic theoretical framework, termed inverse elastica, for the direct determination of the undeformed configuration from a target deformed shape along with prescribed BCs. Building upon the classical elastica, inverse elastica is derived by supplementing the geometric equations of undeformed configurations. The framework shows three key features: reduced nonlinearity, solution multiplicity, and inverse loading. These principles are demonstrated through two representative models: an analytical solution for a two-dimensional arc and a numerical continuation study of the inverse loading of a three-dimensional helical spring. Furthermore, we develop a theory-assisted optimization strategy for cases in which the constrains of the undeformed configurations cannot be directly formulated as BCs. Using this strategy, we achieve rational inverse design of complex spatial curves and curve-discretized surfaces with varying Gaussian curvatures. Our theoretical predictions are validated through both discrete elastic rod simulations and experiments.

cond-mat.soft↗

arXiv2025

Midveins regulate the shape formation of drying leaves

Dried leaves in nature often exhibit curled and crumpled morphologies, typically attributed to internal strain gradients that produce dome-like shapes. However, the origin of these strain gradients remains poorly understood. Although leaf veins--particularly the midvein--have been suggested to influence shape formation, their mechanical role has not been systematically investigated. Here, we demonstrate that mechanical constraints imposed by the midvein play a crucial role in generating the diverse morphologies that emerge during leaf drying. Combining numerical simulations and theoretical analysis, we show that a uniformly shrinking leaf lamina constrained by a non-shrinking midvein gives rise to two distinct types of configurations: curling-dominated and folding-dominated morphologies. In the curling-dominated regime, both S-curled and C-curled shapes emerge, with C-curled configurations more commonly observed due to their lower elastic energy. In contrast, the folding-dominated regime features folding accompanied by edge waviness. Theoretical modeling reveals a linear relationship between midvein curvature and mismatch strain, consistent with simulation results. Moreover, we find that the morphological outcome is governed by the ratio of bending stiffnesses between the lamina and the midvein. We construct a comprehensive phase diagram for the transitions between different configurations. These findings provide a mechanical framework for understanding shape formation in drying leaves, offering new insights into natural morphing processes and informing the design of bio-inspired morphable structures.

cond-mat.soft↗

arXiv2025

A tutorial on simulating nonlinear behaviors of flexible structures with the discrete differential geometry (DDG) method

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.

cond-mat.soft↗

arXiv2025

Localization of deformation in the central hub of hub-and-spoke kirigami

A recent approach to the design of flexible electronic devices consists of cutting a two-dimensional sheet to form a central hub connected to several tapered `spokes', resembling the hub-and-spoke of a bicycle wheel. When radially compressed, the resulting cut sheet buckles out-of-plane forming a structure whose three-dimensional shape can be chosen by designing the tapering of the spokes. While the deformation of the spokes in this `hub-and-spoke' kirigami are approximately cylindrical (i.e.~zero Gaussian curvature and hence small elastic strain), this is not the case in the central hub. The central hub is deformed radially because of continuity with the spokes but, because of its own circular symmetry, it must develop Gaussian curvature, and hence strain. In this article we quantify this strain, focussing in particular on its magnitude and its location. We find that the strain is localized in a boundary layer near the edge of the hub region, whose size is controlled by the moment applied on it by the deformed spokes. We discuss the implications of our results for avoiding material failure in flexible-electronic devices.

cond-mat.soft↗

arXiv2025

Localized tension-induced giant folding in unstructured elastic sheets

Buckling in compression is the archetype of elastic instability: when compressed along its longest dimension, a thin structure such as a playing card will buckle out-of-plane accommodating the imposed compression without a significant change of length. However, recent studies have demonstrated that tension applied to sheets with microscopic structure leads to out-of-plane deformation in applications from `groovy metasheets' for multi-stable morphing to kirigami grippers. Here, we demonstrate that this counter-intuitive behavior -- a large transverse folding induced by a relatively small imposed longitudinal tension -- occurs also in unstructured sheets of isotropic material. The key to this behavior is that a localized uniaxial tension induces giant folding; we refer to this as `localized TUG folding' to reflect the importance of localized tension and its mode of actuation. We show that localized TUG folding occurs because of an efficient transfer of applied tensile load into compression -- a geometric consequence of a localized applied tension. We determine scaling results for the folding angle as a function of applied strain in agreement with both experiments and simulations. The generic nature of localized TUG folding suggests that it might be utilized in a broader range of materials and structures than previously realized.

cond-mat.soft↗

arXiv2025

Real-time simulation enabled navigation control of magnetic soft continuum robots in confined lumens

Magnetic soft continuum robots (MSCRs) have emerged as a promising technology for minimally invasive interventions, offering enhanced dexterity and remote-controlled navigation in confined lumens. Unlike conventional guidewires with pre-shaped tips, MSCRs feature a magnetic tip that actively bends under applied magnetic fields. Despite extensive studies in modeling and simulation, achieving real-time navigation control of MSCRs in confined lumens remains a significant challenge. The primary reasons are due to robot-lumen contact interactions and computational limitations in modeling MSCR nonlinear behavior under magnetic actuation. Existing approaches, such as Finite Element Method (FEM) simulations and energy-minimization techniques, suffer from high computational costs and oversimplified contact interactions, making them impractical for real-world applications. In this work, we develop a real-time simulation and navigation control framework that integrates hard-magnetic elastic rod theory, formulated within the Discrete Differential Geometry (DDG) framework, with an order-reduced contact handling strategy. Our approach captures large deformations and complex interactions while maintaining computational efficiency. Next, the navigation control problem is formulated as an inverse design task, where optimal magnetic fields are computed in real time by minimizing the constrained forces and enhancing navigation accuracy. We validate the proposed framework through comprehensive numerical simulations and experimental studies, demonstrating its robustness, efficiency, and accuracy. The results show that our method significantly reduces computational costs while maintaining high-fidelity modeling, making it feasible for real-time deployment in clinical settings.

cond-mat.soft↗

arXiv2025

Harnessing Discrete Differential Geometry: A Virtual Playground for the Bilayer Soft Robotics

Soft robots have garnered significant attention due to their promising applications across various domains. A hallmark of these systems is their bilayer structure, where strain mismatch caused by differential expansion between layers induces complex deformations. Despite progress in theoretical modeling and numerical simulation, accurately capturing their dynamic behavior, especially during environmental interactions, remains challenging. This study presents a novel simulation environment based on the Discrete Elastic Rod (DER) model to address the challenge. By leveraging discrete differential geometry (DDG), the DER approach offers superior convergence compared to conventional methods like Finite Element Method (FEM), particularly in handling contact interactions -- an essential aspect of soft robot dynamics in real-world scenarios. Our simulation framework incorporates key features of bilayer structures, including stretching, bending, twisting, and inter-layer coupling. This enables the exploration of a wide range of dynamic behaviors for bilayer soft robots, such as gripping, crawling, jumping, and swimming. The insights gained from this work provide a robust foundation for the design and control of advanced bilayer soft robotic systems.

cs.RO↗

arXiv2024

IPS: In-Prompt Process Supervision for Short Video Content Moderation

Multimodal large language models (MLLMs) are effective at capturing the semantics of short video content; however, they often fail to attend to the policy-specific details required for reliable content moderation. To address this limitation, we introduce IPS, a novel framework that integrates In-prompt Process Supervision into MLLMs by introducing sequential reasoning over ancillary questions during fine-tuning. IPS consistently outperforms baseline MLLMs on public and proprietary benchmarks. Moreover, replacing human-annotated ancillary labels with MLLM-generated ones results in only marginal performance degradation, demonstrating robustness to noisy supervision and strong scalability with model-generated annotations. These findings establish IPS as a scalable and effective solution for complex multimodal classification in large-scale industrial settings.

cs.CL↗

arXiv2024

How do imperfections cause asymmetry in elastic snap-through?

A symmetrically-buckled arch whose boundaries are clamped at an angle has two stable equilibria: an inverted and a natural state. When the distance between the clamps is increased (i.e. the confinement is decreased) the system snaps from the inverted to the natural state. Depending on the rate at which the confinement is decreased ('unloading'), the symmetry of the system during snap-through may change: slow unloading results in snap-through occurring asymmetrically, while fast unloading results in a symmetric snap-through. It has recently been shown [Wang et al., Phys. Rev. Lett. 132, 267201 (2024)] that the transient asymmetry at slow unloading rates is the result of the amplification of small asymmetric precursor oscillations (shape perturbations) introduced dynamically to the system, even when the system itself is perfectly symmetric. In reality, however, imperfections, such as small asymmetries in the boundary conditions, are present too. Using numerical simulations and a simple toy model, we discuss the relative importance of intrinsic imperfections and initial asymmetric shape perturbations in determining the transient asymmetry observed. We show that, for small initial perturbations, the magnitude of the asymmetry grows in proportion to the size of the intrinsic imperfection but that, when initial shape perturbations are large, intrinsic imperfections are unimportant - the asymmetry of the system is dominated by the transient amplification of the initial asymmetric shape perturbations. We also show that the dominant origin of asymmetry changes the way that asymmetry grows dynamically. Our results may guide engineering and design of snapping beams used to control insect-sized jumping robots.

cond-mat.soft↗

arXiv2024

Inverse Design of Snap-Actuated Jumping Robots Powered by Mechanics-Aided Machine Learning

Exploring the design and control strategies of soft robots through simulation is highly attractive due to its cost-effectiveness. Although many existing models (e.g., finite element analysis) are effective for simulating soft robotic dynamics, there remains a need for a general and efficient numerical simulation approach in the soft robotics community. In this paper, we develop a discrete differential geometry-based numerical framework to achieve the model-based inverse design of a novel snap-actuated jumping robot. It is found that the dynamic process of a snapping beam can be either symmetric or asymmetric, such that the trajectory of the jumping robot can be tunable (e.g., horizontal or vertical). By employing this novel mechanism of the bistable beam as the robotic actuator, we next propose a physics-data hybrid inverse design strategy for the snap-jump robot with a broad spectrum of jumping capabilities. We first use the physical engine to study the influences of the robot's design parameters on the jumping capabilities, then generate extensive simulation data to formulate a data-driven inverse design solution. The inverse design solution can rapidly explore the combination of design parameters for achieving a target jump, which provides valuable guidance for the fabrication and control of the jumping robot. The proposed methodology paves the way for exploring the design and control insights of soft robots with the help of simulations.

cs.RO↗