Blood is a complex fluid, comprising viscous plasma, elastic red blood cells (RBCs), and other components. The deformation of RBCs leads to viscoelastic blood rheology and hemolysis (cell rupture). While these two phenomena have been studied extensively in isolation, there is a lack of comprehensive models that integrate both. This paper investigates the potential of viscoelastic rheological models for the prediction of hemolysis. Specifically, we present a unified formulation for viscoelastic stretch-tensor equations and strain-based hemolysis models, demonstrating their formal similarity. We propose a combined model that inherently accounts for both phenomena. Further, we introduce a new tensor-based indicator of hemolysis that can be computed from the viscoelastic model without the need for additional equations. The analysis is complemented by numerical simulations of blood flow in a multiply corrugated tube, where flow characteristics and hemolysis indicators are evaluated.
Three-dimensional auxetic mechanical metamaterials have attracted extensive attention in structural protection, flexible devices, and lightweight functional materials owing to their unconventional transverse deformation, energy-absorption capability, and programmable mechanical responses. However, most existing three-dimensional auxetic structures rely on strut bending, thin-wall deformation, or complex topological configurations, and the direct mapping between geometric parameters and macroscopic Poisson's ratio remains insufficiently established. Here, a three-dimensional rotational auxetic structure based on an octahedral framework is proposed, in which tunable transverse deformation is achieved through the coordinated rotation of spatial triangular units. An idealized hinged model is developed to establish geometrical relationships among the configuration angle, geometric configuration factor, and macroscopic projected dimensions, revealing the piecewise evolution of Poisson's ratio induced by transitions of the governing projected vertices. Theoretical results show that the geometric configuration factor effectively regulates the magnitude of the negative Poisson's ratio and the anisotropic characteristics of the structure. Finite element analysis and compression experiments further validate the transverse contraction behavior and stable auxetic response, with an average Poisson's ratio of approximately −1.75 predicted for k= 2.0 within the stable working range. The proposed structure provides a geometrically interpretable and additively manufacturable route for the design of three-dimensional rotational auxetic metamaterials.
The manuscript investigates the dispersive behavior of one-dimensional nonlocal continua within the frameworks of peridynamics and stress-driven nonlocal elasticity. The peridynamic model is first analyzed, showing that the choice of the kernel function significantly affects the dispersion relation and may lead to anomalous dispersion phenomena characterized by non-monotonic trends and negative group velocity. The classical stress-driven model with Helmholtz kernel is then considered, highlighting its limitations in reproducing such effects due to its purely monotonic response and strictly positive group velocity. A three-parameter local/nonlocal stress-gradient model is also introduced, allowing for a more flexible description of the dispersive behavior through the variation of the nonlocal parameter, gradient length parameter and mixture parameter. However, despite this increased flexibility, anomalous dispersion cannot be captured within this framework. Finally, a generalized stress-driven model is proposed, in which the spectral representation of the nonlocal constitutive operator is not prescribed a priori but is determined so as to reproduce the peridynamic dispersion relation. The resulting model is shown to reproduce the same dispersive behavior as the peridynamic one, including anomalous dispersion phenomena. The results highlight that the capability of describing complex dispersive effects is strongly governed by the spectral structure of the adopted nonlocal kernel. The main results are presented and discussed by varying the governing parameters of the models.
Martensitic transformation (MT) is a rapid displacive process characterized by lattice reconfiguration and transformation strain. While MT is commonly analyzed under quasi-static mechanical equilibrium assumptions, the abrupt lattice distortion inherent to the transformation acts as a dynamic mechanical source that emits transient stress waves. The role of these elastodynamic fields in regulating subsequent phase evolution in polycrystalline solids remains insufficiently understood. In this work, we develop a fully coupled phase-field-elastodynamic framework that integrates phase kinetics with explicit wave propagation resolved through a high-order orthogonal polynomial approximation. Within this formulation, transformation strains generate stress waves that propagate across grains and continuously reshape the local mechanical driving forces. The simulation results demonstrate that, compared with quasi-static conditions, inertia significantly alters the distribution of mechanical energy, thereby influencing nucleation behavior and variant growth dynamics. In polycrystalline systems, the phase-field-elastodynamic model reproduces key microstructural features, including spatially alternating variant arrangements, block partitioning within grains, and characteristic variant width and growth directions. The results obtained with inertia effects are in close agreement with theoretical predictions and experimental observations. These findings extend the conventional understanding of MT in polycrystalline materials.
We develop a one-dimensional isothermal model of nonlinear viscoelasticity within Rational Extended Thermodynamics (RET) without postulating an additive decomposition of either the stress or the internal energy. The total stress is taken as an independent field and is associated with an additional balance law whose density, flux, and production are initially unspecified. Compatibility with the energy-dissipation principle determines the thermodynamically admissible structure of this balance law and leads to a theory governed by a single, generally non-separable internal-energy potential. The total stress is thereby represented as the sum of two potential-derived contributions associated, respectively, with deformation and the internal relaxation variable; in general, both depend on the full constitutive state. The relaxation variable is constitutively centered so that the same value represents equilibrium for every admissible deformation. The production law is then chosen so that the first relaxation approximation recovers the prescribed parabolic constitutive behavior. For the Newtonian class considered here, this yields a linear dissipative relation between the production and the nonequilibrium stress contribution associated with the relaxation variable. The resulting equilibrium reduction reproduces the formal step underlying the first Maxwellian iteration for gases, whereas the same constitutive strategy also accommodates non-Newtonian parabolic responses. Under suitable convexity assumptions, the resulting system is symmetric hyperbolic. Its linearization recovers the classical Zener solid, while the previous RET model with a separable energy potential is included as a special case. A simple coupled potential is used to illustrate the effects of the new constitutive freedom on nonlinear stress relaxation and wave dispersion, and the K-condition is verified on the equilibrium manifold.
The paper presents a consistent thermomechanical framework for strongly nonlocal continua, a type of generalized media in which a material’s response at a point depends on deformation and temperature gradients within its neighborhood. Such dependence is responsible for localization phenomena having an intrinsic size, and nonlocal modeling also serves as a practical regularization tool to prevent mesh dependence. Nonlocality is of the integral type, using a kernel function that gives the relative influence of neighboring points on a central point. The paper develops three sources of nonlocality: (1) nonlocal momentum balance equations; (2) nonlocal conservation laws (including the first and second laws of thermodynamics); and (3) a material’s nonlocal constitutive structure. Balance equations are derived using the principle of virtual power, permitting non-smooth force and displacement fields and non-smooth boundary surfaces with indistinct normal directions. The balance equations differ from those of classical local continua. Conservation laws also differ from those of local continua, with the mechanical power and heating at a point being averaged over its neighborhood. These laws are developed for processes that are sufficiently slow to minimize additional meso-scale kinetic energy due to internal turbulence. Stress, entropy, and dissipative forces are obtained as averaged derivatives of the free energy function with respect to strain, temperature, and internal variables. An example is presented of a stretched elastoplastic bar with a small defect, and nonlocality is shown to impart a characteristic size to the deformation pattern.
The Poynting and Swift-type responses are commonly used to describe axial deformation under torsion in soft tissues, although the mechanism governing the transition between these responses remains unclear. This work develops an analytical model to investigate the transition from Swift-type to Poynting-type response in torsion of soft tissues, incorporating the effect of fiber dispersion. The torsional response is represented by linear (L), quadratic (Q), and higher-order (H) nonlinear contributions associated with fiber anisotropy, matrix deformation, and nonlinear stiffening. A dimensionless transition parameter, Π=L/Q, is derived to identify the relative dominance of Swift-type and Poynting-type mechanisms, with the corresponding critical twist defined as τc=Π. The results indicate that fiber dispersion plays an important role in determining the critical transition point, as it alters the ratio of anisotropic to isotropic responses. The theoretical predictions show good agreement with experimental data reported for the rabbit papillary muscle under torsion.
Cerebral aneurysms are dilations of brain blood vessels that can cause a life-threatening stroke upon rupture. Embolization is a widely used treatment in which embolic agents (e.g., coils, particles) are delivered through a mechanical catheter to occlude the aneurysm. However, conventional catheter-based embolization faces delivery challenges in narrow and tortuous vasculature. Recently, magnetically actuated soft robots have emerged as a promising strategy for robotic embolization due to their ability to access hard-to-reach vascular regions. In particular, tangentially magnetized magnetic fiberbots (MFBs) can elongate to navigate through confined vessels and subsequently aggregate under a reversed magnetic field to enable aneurysm occlusion. Unlike conventional helical robots with single-direction magnetization, the mechanics governing this elongation–aggregation shape morphing under frictional confinement remain poorly understood, making the magnetic control of stably retained aggregation difficult. To elucidate the dual-mode shape morphing of MFBs, we establish a magneto-mechanical framework by coupling Kirchhoff rod elasticity with distributed magnetic torques and frictional rod–wall contact. Then, we develop a reduced analytical theory for the elongation response under a magnetic field aligned with the initial net magnetic moment. Under a reversed magnetic field, the coupled effects of magnetic actuation and frictional confinement give rise to aggregation or reversed elongation, while subsequent unloading determines whether aggregation is recoverable or retained. To resolve these geometrically nonlinear deformations, we adopt the discrete elastic rod (DER) method for numerical simulations and perform a parametric analysis to quantify how helix geometry and frictional confinement affect the critical magnetic fields governing retained aggregation. Both the analytical theory and the numerical simulations are validated by experiments, demonstrating their accuracy and effectiveness. These findings offer theoretical guidance for accurate magnetic control of MFBs in stable robotic embolization.
Controlling thermal conductivity is essential for manipulating heat flux, a task that often requires metamaterials with highly anisotropic and spatially non-uniform properties. This study investigates the thermal behaviour of spinodal metamaterials generated via the Cahn–Hilliard equation. Their smooth and bi-continuous topology enables seamless tuning of structural anisotropy, making them promising candidates for directional heat transport. However, while their mechanical behaviour has been extensively investigated, their thermal conductive behaviour remains largely unexplored. To address this gap, a finite-element-based computational homogenization framework to evaluate their effective thermal conductivities is presented. A parametric analysis maps thermal conductivity as a function of the design parameters, providing a basis for inverse design. The core contribution of this work is the derivation of a thermomechanical cross-property relation for spinodal metamaterials with a 50–50 composition, providing a direct link between effective thermal conductivity and Young’s modulus. This enables the prediction of thermal properties using more accessible mechanical data. The mechanical and thermal homogenization approaches, along with the derived cross-property relations, are experimentally validated on manufactured samples. Young’s moduli are obtained through compression tests, while thermal conductivities are measured via a steady-state dual-Peltier setup. Overall, this work provides a validated tool for the characterization and inverse design of spinodal thermal metamaterials with extension to additional compositions representing a straightforward generalization of the approach. This tool can be used for efficient thermo-structural optimization by eliminating the need for demanding thermal experiments, allowing designs to be solely based on mechanical analyses, or vice-versa if necessary.
This study presents a workflow to extract the frequency (ω) dependent storage modulus G′(ω) and loss modulus G″(ω) – which are commonly used viscoelastic functions to describe small amplitude oscillatory shear (SAOS) flow of complex fluids – from the frame-invariant upper-convected Maxwell (UCM) model using the semi-inverse approach. The SAOS flow is set up between two parallel circular plates, and this resembles a conventional rheometric apparatus normally utilized to experimentally obtain the dynamic moduli. The differential equations governing the shear stress and normal stress as functions of shear rate are derived using the semi-inverse approach, and then solved analytically. Explicit expressions for G′(ω) and G″(ω) are derived from the analytical solution: these exactly match those derived using the phenomenological spring-dashpot Maxwell element. The equations are also solved numerically; here G′(ω) and G″(ω) are extracted from the spectral phase lag between shear stress and shear rate which is obtained using a Fast Fourier Transform. The numerically derived values for G′,G″ show excellent consistency with the UCM derived analytical solutions, thus validating the numerical procedure. These results provide a continuum mechanics derivation for the spring-dashpot framework: a result that keeps with intuitive expectation. A framework to extract dynamic moduli for a generalized multi-mode UCM is also provided. The utility of the workflow is demonstrated by successfully describing in-house experimental SAOS data for a variety of viscoelastic materials ranging from polymer solutions to composite hydrogels.
A thorough understanding of esophageal biomechanics is essential for predicting tissue failure and preventing iatrogenic tearing during surgical procedures, such as esophageal atresia repair. This knowledge is also crucial for the engineering design of mechanically compatible tissue replacements. Melatonin, known for its regenerative properties, could improve the mechanical integrity of esophageal tissue and minimize post-surgical complications, including anastomotic leakage. This study characterizes the passive hyperelastic and damage behavior of the neonatal lamb esophagus and evaluates the effect of melatonin treatment.In-vitro monotonic uniaxial tensile tests were performed on esophageal samples from newborn lambs, which were divided into control (n=4) and melatonin-treated (n=4) groups. The samples were separated into internal (mucosa/submucosa), external (muscularis), or integrated (intact wall) layers, and tested in both longitudinal and circumferential directions. A hyperelastic-damage constitutive model was calibrated to the experimental data to quantify the anisotropic and softening response of the tissues.The esophageal tissue exhibited significant anisotropy, with greater stiffness in the longitudinal direction. No statistically significant differences were observed between the control and melatonin-treated groups, in the Cauchy stress versus stretch response or in an analysis of characteristic curve descriptors computed in nominal stress (q>0.05). However, the small sample sizes left the study underpowered to detect the moderate-to-large effect sizes (Hedges’ g = 0.5-0.9) observed in several comparisons, which therefore warrant confirmation in adequately powered cohorts. The proposed constitutive model accurately captured the non-linear hyperelastic and damage behavior, including the softening up to rupture, across all tissue layers (R2>0.86).This study provides experimentally calibrated material parameters for an anisotropic hyperelastic-damage model of the neonatal lamb esophagus, extending prior hyperelastic descriptions to include softening behavior. Although a 30-day low-dose melatonin treatment did not produce robust alterations in passive mechanical properties, the established constitutive framework provides valuable baseline data to inform computational simulations of surgical procedures and optimize tissue-engineered esophageal grafts.
Understanding how wall shear rate (WSR) influences platelet activation is essential for predicting thrombotic events and for designing hemocompatible medical devices. In our previous work, platelet activation under low shear conditions was evaluated by repeatedly reinjecting blood samples into a microfluidic chip to control the exposure time. However, such a reinjection approach is not practical for real-world applications. In this study, the reinjection protocol was replaced with a pulsatile circulation pump, and the effects of microchannel geometry and stenosis bend on shear-induced platelet activation were systematically investigated. Transient computational fluid dynamics (CFD) simulations were performed to quantify the distributions of wall shear stress (WSS), WSR, velocity magnitude, and bend-induced vortical flow under pulsatile inlet conditions. Three microchannel designs were simulated, of which two were fabricated for experimental validation: a straight channel, a serpentine channel with circular bend, and a serpentine channel with rectangular bend. The simulations showed that the rectangular-bend design generated steeper wall-shear gradients and higher local WSS, with the peak of the area-averaged wall shear stress reaching 45 Pa, compared with the other configurations. Based on the CFD results, microfluidic chips with circular and rectangular serpentine geometries were fabricated for experimental validation using whole blood. The experiments confirmed that platelet activation occurred after the first circulation in the rectangular-bend channel, whereas activation appeared after the second circulation in the circular-bend channel. Moreover, repeated circulation led to a larger platelet adhesion area in both designs, with significantly higher activation observed in the rectangular-bend channel. This behavior is attributed to a sharp bend combined with pulsatile flow, which promotes von Willebrand factor unfolding and subsequent GPIb-mediated platelet activation. Overall, this integrated CFD–experimental platform demonstrates that microchannel geometry plays a critical role in shear-driven platelet responses and provides a practical and reproducible approach for investigating thrombosis mechanisms and guiding the design of next-generation blood-contacting medical devices.
Kerf patterns enable creating spatially flexible structures and tunable functional properties through geometric patterning that forms networks of slender beams. This study introduces a framework for quantifying tortuosity in chiral fractal kerf cells based on Archimedean spirals to investigate how geometric architecture governs their mechanical deformation, stress wave propagation, and thermal transport behavior within linear responses. Square and hexagonal kerf cells with increasing fractal order were analyzed to quantify geometrical and several physical tortuosity. Geometrical tortuosity, which we define as the shortest meander path length of kerf cells, increases linearly with fractal order due to the proportional increase in the number of folded beam segments and individual beam lengths with fractal order. By analyzing the interplay of microstructural patterns and physical mechanisms governing the deformation, wave propagation, and thermal transport behaviors, we unravel unique relationships between geometrical and physical tortuosity of kerf cells. We demonstrate that tortuosity provides a useful conceptual and quantitative tool for predicting the multifunctional performance of different kerf architectures.
In crack scattering problems, analytical solutions have been derived only for circular or slit cracks. But real defects in solids often take the form of elliptical cracks, for which analytical elastodynamic solutions remain unavailable. For this reason, this study addresses this long-standing problem. We obtain a series-expansion solution for elastic wave scattering by a three-dimensional elliptical crack under incident plane waves with arbitrary propagation directions, polarizations and wavelengths and express crack opening displacements, stress intensity factors, scattering far fields and scattering cross sections in terms of expansion coefficients. The principal advantage of the proposed method over purely numerical approaches is that it allows the derivation of explicit, rigorous asymptotic solutions at both low and high frequencies. We have validated the solution by comparing the results with a variety of existing results in the corresponding cases. In the low-frequency limit the solution naturally reduces to static solutions, while in the high-frequency limit the solution coincides with Kirchhoff approximation for the problem of wave reflection by a traction-free half-plane. At intermediate frequencies, the solution converges as truncation number increases and shows good agreement with the results of boundary element method. Moreover, the closed-form expressions for low- and high-frequency asymptotic solutions can reveal prominent frequency-dependent characteristics of the cracks. Potential applications of the solutions include acoustic nondestructive testing of defects in solids, interpretation of seismic dispersion and attenuation in fractured reservoirs, and evaluation of dynamic effective properties of cracked materials. The solutions may also serve as a benchmark to check numerical methods for the same problem.
Characterizing the dynamic large-deformation behavior of ultra-soft materials is challenged by boundary constraints such as gripping and friction, as well as wave-propagation limits arising from low acoustic impedance. To overcome these limitations, a specialized dynamic testing platform integrating a high-speed servo motor, a fluid injection system, and displacement sensors was established to extend the Cylindrical Volume-Controlled Cavity Expansion (C-VCCE) method into the dynamic regime. By utilizing a pre-formed cylindrical cavity to guide uniform deformation, this gripping-free approach enables the precise testing of ultra-soft solids (with an elastic modulus on the order of 10 kPa) across low-to-intermediate strain rates (0.005 s⁻¹ to 15.0 s⁻¹) with excellent repeatability, thereby facilitating the derivation of a large deformation rate-dependent constitutive model. A Fluid-Structure Interaction (FSI) simulation model is established and utilized to uncover the dynamic expansion process. Results show that the simulation captures well the measured dynamic response, and is further employed to analyze the deformation uniformity at higher strain rates. Finally, a Deformation Uniformity Index is introduced to quantitatively define the valid operational envelope, establishing an upper strain rate limit of 60 s⁻¹ for the current testing configuration.
The Saint-Venant torsional stiffness underpins the torsional design of prismatic structural members, yet for most of the cross-sections met in practice – cold-formed, welded and built-up profiles – no closed-form solution exists, and design falls back on family-specific handbook formulas (Bredt for tubes, the thin-strip sum for open shapes) whose accuracy is not quantified. This paper proposes a primal–dual procedure that encloses the torsion constant Jt (the stiffness being GJt) within a two-sided certified interval: the classical Ritz lower bound is complemented by a constructive upper bound built on an equilibrated polynomial stress field, and the trial spaces are chosen so that every energy integral reduces to a rational moment over a rational triangle. For any polygon with rational vertex coordinates – that is, for any cross-section drawn on a CAD plane – both endpoints and the width of the interval are therefore exact rational numbers, free of floating-point round-off; on rational triangulations the same construction covers non-convex open profiles (C-, L-, T-sections) and multiply connected hollow sections. What the engineer gains is a guaranteed and exactly reproducible reference value: the interval brackets Jt where no closed form exists, its width measures the residual uncertainty, and it serves both to verify finite-element and boundary-element torsion solvers and to bound the error of the design formulas. The method encloses the unit square within a rational interval of width ∼10−4 around Jt=0.140577; it shows that the thin-strip formula overestimates the compact rectangle by +137% at aspect ratio b/t=1 and the reference channel by +0.6% to +1.3%, whereas Bredt’s formula underestimates rectangular tubes by −1.5% to −9.2% as the wall thickness grows — errors of opposite sign that the certified interval pins down exactly. As a by-product, an exact criterion singles out the equilateral triangle as the only triangle admitting an elementary Prandtl solution.
