Abstract Mode veering, a phenomenon where the frequencies of dispersion bands converge and then diverge while exchanging band characteristics, is critical for designing dynamic systems and predicting structural behavior. Although extensively observed in chiral metamaterial systems, the underlying mechanism governing this phenomenon remains inadequately understood, hindering the development of effective active control strategies. This study presents an actively tunable metamaterial chain consisting of compression–torsion coupling oscillators with dual independent control mechanisms: dynamically adjustable interoscillator coupling stiffness and modifiable rotational inertia. Through precise parameter modulation, continuous and reversible regulation of energy redistribution and polarization switching between the torsional flat band and the longitudinal dispersion band is achieved, enabling on-demand induction of mode veering. Further investigation of this process reveals that this phenomenon originates from an inherent conflict between band reversal and oscillatory incompatibility—a paradox resolved through shifts in the torsional natural frequency of the oscillator. Crucially, the interplay between this frequency shift and band trajectories is identified as the fundamental mechanism governing mode veering. Moreover, this study found that the nonlinear compression–torsion coupling effects can suppress the energy localization induced by the torsional flat band. These works establish a new paradigm for active elastic wave manipulation with promising applications in adaptive vibration isolation and programable metamaterial design.
Abstract Dynamic excitation enables rapid state switching of bistable beams under small forcing amplitudes, yet a controllable switching strategy relies on accurate prediction of beam dynamics. The Galerkin method offers a reliable and efficient approach, but the choice of trial functions varies across studies, leaving the optimal selection for both efficiency and accuracy unresolved. This article investigates the three most commonly used modal sets for a bistable curved beam: straight-beam buckling modes, straight-beam vibration modes, and curved-beam vibration modes. Substituting these trial functions into the governing equation with increasing truncation orders, we numerically compute and compare the dynamic response patterns. One-mode and two-mode truncations yield similar patterns across the three sets but fail to fully capture the primary resonance and main harmonic regions. The three-mode truncation, however, reveals significant discrepancies in the subharmonic interwell region between the buckling modes and the two vibration modes. These discrepancies arise from the axial force effects included in the buckling problem but neglected in the vibration problems, a mechanism substantiated by an axial-to-bending energy ratio analysis. This indicates faster convergence of the buckling modes, which is confirmed by the five-mode results, where all predictions converge and agree qualitatively with the three-mode buckling predictions. Finite element simulations and a parametric study further validate these findings. The study demonstrates that the buckling modes exhibit superior convergence and that a five-mode truncation is generally required to capture the full dynamics, providing a clear and reasoned basis for selecting trial functions and truncation order for bistable curved beams.
Abstract Thrombus fragmentation remains a major challenge in mechanical thrombectomy because it increases the risk of distal embolization. Thrombi are multiscale composites of fibrin networks and blood cells, and their failure depends on finite hyperelastic deformation, anisotropy, composition-dependent properties, and microscopic fiber rearrangement. Because fibrin fibers may reorient under large stretch, the local fiber architecture should be treated as an evolving structural variable rather than a fixed material descriptor. Here, we develop a finite-deformation anisotropic phase-field fracture model that couples composition-dependent constitutive parameters, fiber-induced anisotropy, stretch-driven fiber reorientation, and damage degradation. The preferred fiber direction evolves toward the local maximum principal stretch direction, linking fibrin-network adaptation to anisotropic energy storage and crack-driving forces. After validation against uniaxial fracture experiments, the model is used to study spontaneous crack initiation, branching, and propagation under mixed-mode loading relevant to aspiration thrombectomy. The results show that fiber dispersion and reorientation strongly regulate fragmentation. Increasing the dispersion parameter from 0.12 to 0.25 weakens anisotropy, reduces the critical tensile reaction force by 26.9%, and increases failure displacement by 30%, indicating a transition from tension-shear coupled failure to tensile-dominated rupture. Greater dispersion also suppresses crack branching and promotes localized failure paths. Composition-dependent simulations show that higher fibrin content increases fracture toughness, whereas increased hydration reduces total fracture energy despite increasing initial stiffness. These findings clarify how evolving microstructural anisotropy and biochemical composition govern thrombus fragmentation risk and may guide thrombectomy strategy optimization.
Abstract The multifield coupled mechanical behavior at the contact interface of thermoelectric devices is a key scientific issue restricting their service performance and structural reliability, so relevant theoretical investigations possess important engineering and academic significance. This article addresses the thermo-electro-mechanical coupled contact problem between a rigid periodic wavy surface and functionally graded thermoelectric materials. A singular integral equation with a cotangent kernel is established, in which the kernel function involves an infinite series summation and material gradient parameters, enabling simultaneous characterization of the spatially inhomogeneous distributions of electrical conductivity, shear modulus, and thermal expansion coefficient. The Chebyshev collocation method is adopted to achieve highly accurate numerical solutions, with emphasis on the regulation mechanisms of surface morphology, material gradients, electric current load, and energy flux load on contact stress. Results show that surface period, gradient parameters, and energy flux load can significantly modify the contact stress level and the distribution profile. Proper gradient matching and energy flux input can effectively alleviate contact stress and realize active control of the contact state. The multifield coupled contact model constructed in this work provides direct theoretical support and numerical references for stress optimization and structural design of contact interfaces in thermoelectric devices.
Functionally graded beams (FGBs) offer transformative potential for lightweight, high-performance designs; however, their widespread adoption is constrained by the difficulty of verifying manufactured material properties. This article addresses the fundamental challenge of nondestructively characterizing the spatially varying stiffness in FGBs-an ill-posed inverse problem that conventional small-deflection methods fail to resolve due to insufficient sensitivity. We introduce a novel paradigm that deliberately exploits geometric nonlinearity as an information amplifier. By driving a cantilever FGB into the large-deflection regime, we break the kinematic symmetry inherent in linear approaches, dramatically enhancing the observability of internal stiffness gradients. The methodology is established through a rigorous digital twin framework, integrating a derived analytical model for large-deflection kinematics with high-fidelity nonlinear finite element simulations. This validated forward solver enables a comprehensive feasibility study using synthetic data. The inverse problem is solved via a two-stage computational strategy: a deterministic optimization scheme successfully reconstructs complex stiffness profiles under ideal conditions, while a probabilistic Bayesian inference framework rigorously quantifies the identification uncertainty in the presence of realistic measurement noise. Results demonstrate the method's capability to characterize diverse grading patterns, including symmetric distributions, and confirm the property of scale invariance-effectively decoupling the relative stiffness gradient from the absolute material modulus. This study conclusively establishes that combining large deformation mechanics with statistical uncertainty quantification provides a robust, physics-informed tool for the quality control and assurance of advanced graded structures.
We present a nonlinear spectral invariant-based framework for modeling the electromechanical behavior of viscoelastic stiff fiber-reinforced electro-active composites. Within a couple-stress theory, we derive general constitutive equations for the total stress and total couple-stress that capture the coupling between mechanical and electrical fields. To model materials in which resistance to fiber bending is dominant, the constitutive equations are specialized by restricting their dependence on the gradient of the fiber direction to the directional derivative along the fiber axis. The resulting constitutive models are expressed in terms of spectral invariants, each of which admits a clearer physical interpretation than classical invariants. This feature makes the models particularly suitable for experimental identification using systematic curve-fitting procedures for the free-energy function. The number of complete, irreducible, and minimal spectral invariants is significantly smaller than that of the classical complete-irreducible invariants reported in the literature, leading to a substantial reduction in modeling complexity. The applicability of the specialized model is illustrated through boundary-value problems involving fiber bending and inflation, highlighting its relevance for experimental and applied settings. The proposed framework provides a rigorous basis for the modeling and simulation of viscoelastic electro-active materials with stiff fiber microstructure.
Supported lipid bilayers (SLBs) adhered to solid substrates provide an important model system for studying membrane mechanics and for developing biomimetic membrane platforms. In this work, we examine the mechanical response of SLBs supported on cylindrical substrates, with particular emphasis on the role of membrane-substrate contact angle. Classical membrane-substrate interaction models restricted to normal-incidence contact are extended through a linearized representation of the membrane unit normal at the interaction boundary, enabling orientation-dependent boundary conditions while preserving analytical tractability. Closed-form analytical solutions are derived for membrane shape and curvature within the prescription of small incremental deformations superposed on a finite initial configuration. The results demonstrate that decreasing the contact angle strengthens adhesion, increases curvature, and enhances membrane deformation, whereas larger contact angles yield weakly adhered, near-planar membrane configurations. These trends establish contact angle as an effective geometric control parameter governing membrane-substrate interactions on cylindrical supports. The proposed analytical framework advances existing membrane-substrate theories and provides a mechanics-based foundation for interpreting and tuning supported lipid bilayer behavior in applications involving biosensing interfaces and lipid-based drug delivery systems.
This article studies an inverse problem in plane elasticity concerning the preservation of the cross-sectional area of a hole under remote loading. The problem is motivated primarily by the need to stabilize internal fluid environments in flexible structures and microfluidic systems, for which deformation-induced area change may lead to an internal pressure increment and consequently alter the mechanical response of the surrounding structure. Restricting attention to plane deformation, we consider a cylindrical fluid inclusion of arbitrary shape and seek combinations of far-field loading and inclusion geometry such that the cross-sectional area of the inclusion remains unchanged. Under this condition, the pressure increment inside a compressible liquid inclusion vanishes, and the problem can be equivalently treated as that of an area-invariant, traction-free hole in an infinite elastic plane. By exploiting the complex variable method for plane elasticity, we derive for an arbitrary constant far-field loading the explicit condition imposed on the configuration of the hole for the corresponding area-invariance requirement. It is shown that in terms of combinations of symmetric hole shapes and pure shear loadings, the area invariance is achieved only when the symmetry axis of the hole is aligned with one of the principal directions of the shear loading, except for the cases of special symmetric hole shapes (e.g., circular, hypocycloidal, regularly polygonal) in which the area invariance can be always ensured for arbitrary orientations under pure shear loading. For biaxial tensile/compressive loadings, several representative numerical examples are presented to illustrate the evolution of the desired hole shapes relative to the ratio of the biaxial loading.
The unique deformation and energy absorption mechanisms of sandwich plates under trouser tearing conditions are not yet well understood. In this article, trouser tearing fracture characteristics of the metal foam sandwich plate under tensile loading are investigated by theoretical analysis and numerical simulations. An analytical model for trouser tearing fracture characteristics of the metal foam sandwich plate is established, considering foam compression, plastic bending deformation, unbending deformation, and tearing of the cracks. The finite element simulation of trouser tearing fracture characteristics of the metal foam sandwich plate is conducted to verify the theoretical model, showing good consistency between the numerical and analytical results. The effects of the trouser leg width, foam thickness, bending radius, and foam strength on trouser tearing fracture characteristics of the metal foam sandwich plate are discussed. The tearing load and energy absorption increase with the increase of trouser leg width, foam thickness, and foam strength. The tearing load and energy absorption decrease with the increase of the bending radius. It is found that these factors have a crucial influence on the trouser tearing fracture characteristics of the metal foam sandwich plate. The present theoretical model can effectively predict the trouser tearing fracture characteristics of the metal foam sandwich plate.
In this article, a central result in the theory of linearized elasticity, namely, the reciprocity theorem, is outlined for a continuous solid body, performing the exegesis of the original formulation by Enrico Betti (1823-1892), comparing the proofs he provided with those permitted by modern approaches in continuum mechanics. For linear elastic structures under small displacements, rotations, and strains, legitimating the superposition of the structural responses under multiple loading systems, in the absence of volume forces Betti's theorem allows one to deduce relations involving only loading and displacements over the boundary surface, without requiring the knowledge of the body's elastic stiffness nor making reference explicitly to the distribution of strains and stresses (as it occurs for the conventional formulation of the virtual work). We discuss the auxiliary use of this theorem made by Betti in his works on continuum mechanics, inspired by the potential theory, in particular involving Green's identities. The outlined theoretical strategies, resting on the rigorous deduction of analytical expressions, can nowadays represent a reference for scholars prevalently devoted to repetitive numerical simulations, and an indispensable tool to investigate truly innovative material models.
Up to a few years ago, fracture mechanics has focused on the role of singular stress field at the crack front or on a crack with scalar cohesive stress imagined existing near the front, while the influence of non-singular crack-parallel stresses has been ignored. However, recent studies show that different levels of such stresses can significantly alter fracture behaviors in many materials, often doubling the apparent fracture energy or reducing it nearly to zero. These findings challenge conventional linear elastic fracture mechanics (LEFM) and highlight the need to investigate the effect of non-singular stress states. In this study, we employ molecular dynamics models to examine crack-parallel stress effects at the atomistic level. We identify two distinct mechanisms of the crack-parallel effect on the atomic scale that explain the observed non-monotonic work-to-fracture response under increasing crack-parallel compression. Under moderate parallel compression, the displacements of surface atoms required by the creation of surface energy and the atomic-level densification increase the energy density and therefore enhance the material's fracture energy. At higher levels of compression, the generation of local defects destabilizes the fracture process zone, thus reducing the material's fracture energy. By probing these mechanisms at the nanoscale, our study provides a computational foundation for fracture models that connect to the newly observed macroscale behaviors and inform the design of crack-tolerant quasi-brittle materials.
A general third-gradient one-dimensional beam formulation is introduced through energy postulation. This novel formulation incorporates the effects of nonrigid (or deformable) boundary constraints by using the spring analogy. The Euler-Lagrange equations for equilibria and expressions for boundary conditions are derived. For certain specific cases, analytic solutions are found by reducing the problem to that of finding a single descriptor that accounts for the rotation of the cross section. Based upon the obtained analytical solutions, parametric studies are conducted by varying the stiffness coefficients and boundary spring coefficients. It is found that the deformable boundaries, represented by the boundary springs, modulate the highly nonlinear response of these curvature gradient beams. Both numerical and analytic solutions are compared, revealing exotic shapes when various external actions, such as couples, double couples, and boundary terms, are activated. Finally, an example of a microstructure, whose homogenized limit is representative of curvature-gradient beams, is presented. It is shown that the conceived continuum model describes the behavior of such a microstructure subjected to a concentrated boundary couple with high accuracy. This study, therefore, represents a significant advancement in the general formulation for higher-gradient energy.
We consider the general nonlinear theory of Cosserat elastic shells with a single deformable director and apply the methods of variational calculus to obtain the relevant Legendre-Hadamard inequalities. These are pointwise necessary conditions for stable equilibrium states, which are obtained from the property that the second variation of the total potential energy is non-negative. Thus, we establish a stability criterion that must be satisfied by any stable solution of the equilibrium equations for shells.
The morphological and stress response of a thin elastic plate to the presence of two positive disclinations is investigated within the framework of von K & aacute;rm & aacute;n plate theory. Bifurcation plots are used to establish that the system undergoes a pitchfork bifurcation at a critical stretching-to-bending ratio (which increases with increasing defect separation) where the plate transitions from a flat to a buckled deformed configuration. With the stretching-to-bending rigidity (denoted by Gamma) becoming increasingly large, a ridge appears along the line connecting the two disclinations. Along the ridge, a monopolar concentration in bending strain and a quadrupolar concentration in stress develop as Gamma ->infinity. The former is indicative of fold formation along the ridge. The appearance of the quadrupolar stress concentration is expected in order for the fold-like feature to satisfy the transverse force equilibrium condition.
Visualizing and quantifying internal stresses in solids is fundamental to mechanical analysis and design. Photoelasticity, a classic experimental technique for this task, faces two major challenges that hinder its application: the time-consuming manufacture of photoelastic analogs and the inability to readily distinguish tension from compression. Here, we overcome these two challenges by introducing a new technique, tension-compression aware photoelasticity, that is particularly well-suited for 3D-printed specimens. We begin by systematically investigating the residual stress in 3D-printed photoelastic specimens as a function of print orientation. Rather than avoiding residual stresses, as done in conventional photoelastic testing, we leverage them to distinguish tensile and compressive stresses induced by external loads. We demonstrate, using two examples, that our technique quantifies tensile and compressive stresses in structures with good accuracy. Our new technique significantly improves photoelastic testing by accelerating the manufacturing of the photoelastic analogs using 3D printing and endowing photoelasticity with tension-compression awareness.
Transient friction in granular shear layers at shallow effective normal stress is governed by the evolution of the load-bearing contact network and granular fabric; yet, rate and state friction (RSF) parameters in this regime remain poorly constrained. We quantify RSF behavior in a ring-shear rheometer at normal stresses of 10-20 kPa using three idealized materials selected to isolate grain-shape and grain-size effects: a fine angular silica powder and small and large spherical glass-bead packs. Velocity-stepping and slide-hold-slide tests constrain steady-state rate dependence, direct and evolution effects, characteristic evolution distance, and frictional healing, while systematic variations in layer thickness test geometric control of state evolution. Under high humidity, both glass-bead systems exhibit resolvable RSF transients and velocity-weakening behavior, with micron-scale characteristic slip distances that increase modestly with grain size. In contrast, the angular silica powder is nearly velocity-neutral and yields a substantially larger effective characteristic distance despite its finer grains, indicating that state evolution depends on localization style and fabric/contact-network evolution rather than grain size alone. The characteristic distance is also insensitive to imposed shear-layer thickness over a threefold range. For the silica powder, velocity-step transients and hold-phase stress relaxation are well captured by Ruina slip-law evolution, whereas the magnitude of log-time healing is better described by the Dieterich aging law. Together, these results provide a reproducible benchmark for low-stress transient friction and clarify how particle morphology, grain size, humidity, and layer geometry shape RSF behavior in near-surface shear zones.
Enhancing the reversibility and reducing the hysteresis of antiferroelectric (AFE)-to-ferroelectric (FE) transformations is essential for improving the functionality of energy-storage devices by using antiferroelectric ceramics. In this work, we show that, in PbZr1-xTixO3 (PZT), the AFE-FE transformation occurs as a rhombohedral-to-orthorhombic transition-a symmetry-breaking process that is not conventionally expected to be reversible. Through thermal and structural analysis, we find that this transformation can become reversible when a stable rhombohedral phase mediates the transition, satisfying geometric compatibility conditions. We theorize transformation pathways, derive lattice correspondence and compatibility criteria, and identify that the Ti0.005 composition closely satisfies the conditions of compatibility and exhibits the lowest thermal hysteresis and reduced bias field for AFE-FE switching. Micropillar compression experiments confirm mechanical reversibility is enhanced at this composition, validating the theoretical predictions. These results establish phase compatibility as a design principle for achieving reversible AFE-FE switching in functional oxides.
This work derives an O(h3) electroelastic plate theory for thin dielectric sheets from a three-dimensional variational formulation, incorporating material nonlinearity and Maxwell stresses. The theory captures wrinkling behavior in the presence of mechanical traction and externally applied electric fields. The resulting two-dimensional formulation is specialized to an isotropic, incompressible material obeying reflection symmetry about the sheet mid-surface, and field-dependent explicit expressions are obtained for the elasticity tensor, electroelastic coupling coefficient, and permittivity. The strong-form equations are then derived from the two-dimensional variational formulation by setting the first variation of the potential to vanish. These equations are employed to analyze the wrinkling response of a stretched rectangular sheet subjected to a uniform electric field about a biased reference state. Approximate analytical solutions are obtained via linearization of the plate equations for small slopes, to understand the influence of electric field intensity and applied stretch on the onset and amplitude of wrinkling. The results show that increasing voltage raises the critical loads and wrinkle amplitude while reducing wrinkle count, thereby establishing voltage as a tunable parameter to control wrinkling.
This work presents an analytical investigation of the free radial vibration of solid and hollow spherical bodies composed of heavy hard sphere-filled elastic metacomposites. Focusing on spherically symmetric vibration modes, the governing equations of motion are formulated in terms of the effective Lam & eacute; constants of the metacomposite medium while accounting for the dynamic interaction between the embedded heavy hard spheres as local resonators and the surrounding matrix. Closed-form solutions are derived using spherical Bessel functions and are extended to accommodate various boundary conditions. The resulting frequency equations are employed to study the influence of boundary conditions, geometric parameters, and the radius ratio of the sphere to the embedded hard spherical particles on the dimensionless natural frequencies. The analysis reveals that increasing the radius ratio systematically reduces the natural frequencies, while all natural frequencies are located in two separate ranges below and above the locally resonant bandgap, respectively. Furthermore, a pronounced clustering of natural frequencies is observed as the frequency approaches the lower bound of the bandgap, indicating a significant increase in the modal density. The proposed analytical framework provides explicit solutions without resorting to complex numerical procedures and offers new physical insights into the vibration behavior of metacomposite spherical structures, which are essentially different than the well-known free radial vibration of spherical elastic bodies and have not previously been reported in the literature.
McKibben actuators are soft pneumatic artificial muscles comprising a hyperelastic tube constrained by a nearly inextensible helical braid. This work develops an axisymmetric continuum formulation for a pressurized hyperelastic tube, incorporating braid inextensibility through a weak constraint applied at the outer surface. The formulation is implemented within an axisymmetric finite element framework and compared with a reduced-order analytical model based on an axially uniform deformation assumption. The results demonstrate that geometric end effects, neglected in reduced-order models, play a significant role in the nonlinear pressure-stretch response, particularly for actuators of finite length. The model achieves improved predictive accuracy over reduced-order approaches while remaining computationally efficient compared to detailed three-dimensional finite element models that explicitly resolve braid-tube contact. The finite element predictions agree well with experimental results from different sources and capture features not reproduced by the analytical model. Discrepancies often attributed to friction are shown to arise primarily from the omission of end effects.
