Inertia effects on the migration of a drop in simple shear flow

Role of Scaling Up Particle Size in Principal Stress Rotation under Simple Shear

Advancing the state of the art of cyclic direct simple shear Testing: Histories, current status, challenges and future trends

The material point method (MPM) has shown significant potential for simulating problems involving large deformations. However, many implicit MPM formulations based on the traditional Updated Lagrangian (UL) scheme still face challenges in terms of computational stability. In this study, we propose a novel Lagrangian equilibrium formulation for an implicit MPM that is tailored to large-deformation problems. (1) The previously converged state is utilized to simplify stiffness matrix computations, thereby improving the stability of the algorithm. (2) The framework supports a variety of high-order interpolation functions, which effectively mitigate numerical artifacts such as cell-crossing errors. (3) The B-bar technique is further incorporated to suppress spurious stress oscillations in the incompressible limit. The proposed method is validated through two classical benchmark tests, the simple shear of a single element and the cantilever beam problem, by comparing the simulation results with analytical solutions and alternative numerical approaches. Finally, its capability is demonstrated in slope stability and strip footing analyses, confirming the superior accuracy, stability, and robustness of the method for large-deformation elastoplastic problems.

The direct simple shear (DSS) test carried out under constant volume (CV) conditions forms one of the primary laboratory techniques to characterise soils and tailings. The use of CV conditions to simulate undrained shearing is supported by historical evidence on the testing of a saturated clay and sands, with this evidence being incorporated into current guidelines and state of practice procedures. However, some recent comparisons of the results of undrained hollow cylinder simple shear (HCSS) and CV DSS tests on predominately silt gold tailings adopting state of practice test procedures (i.e. inundation of the sample after loose moist tamping) showed much less post-peak strength loss in the gold tailings than the undrained HCSS tests. The current study investigated this discrepancy further by carrying out DSS tests under high back pressures, undrained simple shear tests with flexible membrane and constant cell pressure and DSS tests after flushing with carbon dioxide and with use of a small back pressure. In all cases, the undrained tests or DSS tests with greater effort put towards saturation exhibited greater post-peak strength loss more consistent with the HCSS and the critical state line. The importance of these results on the estimation of tailings brittleness in engineering practice was outlined.

This work presents experimental results of cyclic simple shear tests at low effective stresses and in the small strain range, thus representative of the dominant stress path, stress and strain levels experienced by soil tested in flexible soil containers at 1-g stress conditions. The results constitute a useful database for the formulation and calibration of soil constitutive models in research works aimed at replicating soil behaviour in flexible soil containers. The measurements of soil response show clearly the importance of consideration of two types of hysteresis when replicating the mechanical response of soil at different strain levels representing the propagation of shear waves at different excitation levels. Applications of the obtained experimental results beyond earthquake geotechnical engineering, in offshore geotechnical engineering and in extraterrestrial environment, are briefly highlighted.

Double 4-bar shear: A novel apparatus and method for simple shear mechanical analysis of membranes.

Yielding is observed for a wide range of soft materials. For attractive colloidal gels, recent experiments and Brownian dynamics simulations have revealed intriguing features, including delayed yielding and degelation, characterized by distinct temporal evolutions of the strain and strain rate in creep tests. The objective of this work is to encapsulate such features in a compact continuum-level rheological model suitable for flow simulations. The model has three core components: (i) a degelation criterion that reflects a sharp sol-gel transition; (ii) a structural parameter that represents the degree of bonding in the gel, whose evolution is dictated by bond breakage under deformation and formation of new bonds; and (iii) a dynamically evolving elastic strain that represents the state of elastic stress and energy in the gel. Applied to simple shear flows under a constant stress (creep), startup of simple shear and pressure-driven Poiseuille flow in a circular tube, the model predicts three regimes with increasing stress: nonyielding, yielding, and degelation. The distinction between the latter two regimes is that yielding marks the emergence of flow, whereas degelation is the total loss of microstructures in a gel-to-sol transition. The transition between neighboring regimes exhibits hysteresis, and shear banding occurs at a uniquely selected stress when diffusion is allowed across the boundary between the bands. The model captures the key rheological features of attractive colloidal gels and shows qualitative and, in certain cases, quantitative agreement with experiments.

Comparison between constant-volume and fully undrained cyclic simple shear tests using the strain-based energy concept

Viscosupplementation is a widely used treatment for osteoarthritis, aiming to restore the viscoelastic properties of synovial fluid and improve joint function. While hyaluronic acid (HA), BDDE-crosslinked hyaluronic acid (BDDE-HA), and polynucleotide (PN) have been studied individually, the rheological properties of their mixtures remain insufficiently explored. This study investigates the viscoelastic characteristics of PN/HA and PN/BDDE-HA blends through rheological evaluations, including simple shear tests, oscillatory shear tests, and 3-interval thixotropy tests. Results indicate that BDDE-HA maintains high viscosity over a range of shear rates, whereas PN exhibits viscosity loss at high shear rates. PN/HA exhibits synergistic structural recovery properties, consistent with clinical findings suggesting improved efficacy compared to individual components. PN/BDDE-HA exhibits improved viscoelastic behavior but prolonged structural recovery. These findings highlight the importance of comprehensive rheological analysis in understanding viscosupplement formulations and their potential clinical implications. This study provides fundamental data to support future clinical research on PN/BDDE-HA as a novel viscosupplement.

Elastic moduli and strain-dependent lateral strain to axial strain ratio in semi-dilute polyacrylamide hydrogels.

Tubular titanium components have been widely used in advanced equipment in aerospace, marine, energy, and healthcare fields over the past decades. For commercial pure titanium (CP-Ti) tubes with hexagonal close-packed (HCP) crystal structure, the limited slip systems and the strong texture caused by multi-pass thermal–mechanical processing make the material always exhibit a strong anisotropy in damage evolution, which easily leads to early failure of components during forming processes. The accurate characterization and modeling of anisotropic damage evolution is a non-trivial issue for excavating the forming potential of materials. In this study, firstly, by taking the large-diameter thin-walled CP-Ti tube as a case material, the uniaxial tension tests along the 0°, 45°, and 90° directions, as well as the simple shear and plane strain tension tests, were designed and conducted to obtain the anisotropic plasticity and fracture behaviors. Then, by integrating a direction-dependent damage rate multiplier and the Hill'48 yield function into the Lode-parameter dependent Lemaitre (Lode-Lemaitre) damage model, the modified Lode-Lemaitre model was established, numerically implemented, and calibrated for the description of the anisotropic damage evolution of the CP-Ti tube. Finally, the prediction ability of the modified Lode-Lemaitre model was evaluated, and the damage evolution of the CP-Ti tube under various loading conditions was analyzed. The comparisons of the experimental and simulation results show that the prediction error of fracture displacement was reduced from 43.2% to 5.48%, and the wall thickness distribution of the Y-shaped tube was accurately predicted. These results prove that the modified Lode-Lemaitre model can accurately describe the anisotropic damage evolution of the CP-Ti tube.

Traumatic brain injury is a significant healthcare burden, mild traumatic brain injuries such as concussions comprising most of these, despite rampant underdiagnosis. While evidence shows repeat concussions are a risk factor for aggressive neurodegeneration, the mechanism by which concussions damage the brain is not well understood, with the clinical hypothesis of shear delamination at the grey/white matter interface being challenging to validate using current scanning technology. Thirty-five fresh ovine brains were dissected, generating ~ 950 samples for testing. Samples of grey and white matter were subjected to unconfined compression and tension, simple shear, tensile and shear fracture, and stress relaxation, load rate variation, and volumetric analysis in compression and tension. Samples at the grey/white interface were subjected to tensile and shear fracture. Grey and white matter differ between cortex/corona radiata and deep brain/corpus callosum, with additional corona radiata variance in shear. The stress relaxation magnitude of grey matter is not strain rate dependent long term; however, white matter relaxation is. Grey and white matter show asymmetric compressibility, with more volume change in tension than in compression. Fracture is not limited to grey/white interface in tension or shear, also occurring in bulk grey and white matter. Fracture initiation stress is similar between grey and white in both modes, and is lower at the interface, with the ductility variance between tissues reflected in fracture energy. Regional variance in constitutive behaviour was uncovered, in addition to novel viscoelastic, volumetric, and fracture behaviour, which has significant implications for in vitro/in silico brain models.

We investigate the angular dynamics of a single spheroidal particle with large particle-to-fluid density ratio in simple shear flows, focusing on the influence of the fluid-inertial torque induced by slip velocity. A linear stability analysis is performed to examine how the fluid-inertial torque, viscous shear torque and particle inertia affect the various stable rotation modes, including logrolling, tumbling and aligning modes. As particle inertia increases, bistable or tristable rotation modes emerge depending on initial conditions. For prolate spheroids, three distinct stable-mode regimes are identified, i.e. logrolling, tumbling and tumbling–logrolling (TL). The presence of these modes depends on particle shape and inertia. For oblate spheroids, when the Stokes number is small, we observe monostable modes (logrolling, tumbling and aligning) and bistable modes (TL, aligning–logrolling) varying with different factors. As Stokes number increases, the tristable mode (aligning–tumbling–logrolling) of oblate spheroids appears. These results of the stability analysis further highlight the intricate and significant effect of fluid-inertial torque compared with the results in the absence of fluid-inertial torque. When we apply fluid-inertial torque to the point-particle model, we reproduce the stable rotation modes observed in particle-resolved simulations, which validates the present stability analysis.

The upper triangular decomposition provides an alternative method to multiplicatively decompose the deformation gradient tensor into a product of a rotation tensor and an upper triangular distortion tensor. The six components of the distortion tensor can be directly related to pure stretch and simple shear deformations, which are physically measurable. In this study, four new constitutive models for hyperelastic materials are developed by using strain energy density functions in terms of the distortion tensor. An untangled cross-linked network model and a tube-like constraint model are employed along with four different inverse Langevin function approximations to construct four micromechanically motivated strain energy density functions, each of which involves the first and second invariants and contains three material parameters. The Cauchy stress components, derived directly as partial derivatives of the strain energy density function with respect to the distortion tensor components, have simpler expressions than those based on the invariants of the right Cauchy–Green deformation tensor. Four fundamental deformation modes—uniaxial tension/compression, pure shear, equi-biaxial tension, and simple shear—together with the general biaxial stretch case are analyzed by directly applying the newly proposed constitutive models. The four new analytical models are validated by comparing the predicted stress-deformation curves with those obtained experimentally for brain tissue and rubber under various loading conditions. The numerical results reveal that the four models can effectively capture the mechanical behavior of hyperelastic materials, thereby providing a new approach based on the upper triangular decomposition and offering physically interpretable constitutive equations.

ABSTRACTBackgroundStability of the spine and intervertebral disc (IVD) integrity is enabled by the highly organized fibrocartilaginous annulus fibrosus (AF). The shear properties of the AF are important in maintaining IVD integrity. AF shear mechanics in degenerative disc (DD) remain underexplored, especially in comparing minimally degenerative (non‐DD) and symptomatic DD individuals. This study measured tissue mechanical properties (AF simple shear modulus and dynamic shear properties) and examined structure (with optical coherence tomography (OCT)) in surgical DD and non‐DD control individuals.MethodsWhole AF tissue samples were collected from non‐DD donors (N = 13) and DD surgical individuals (N = 30). Two anterior outer AF (OAF) 5 mm cubes were sectioned from each sample and subjected to shear in two orientations, radial (coronal plane, G1) and circumferential (sagittal plane, G2). Tissues underwent static shear and dynamic shear protocols to a maximum of 10% shear strain. Following mechanical tests, average lamellar thickness was assessed using OCT.ResultsStatic shear moduli were significantly reduced for DD tissue compared to non‐DD in both the radial (G1) (non‐DD: 83.0 ± 41.3 kPa, DD: 24.1 ± 23.7 kPa) and the circumferential (G2) (non‐DD: 226.2 ± 81.9 kPa, DD: 54.0 ± 40.2 kPa) orientations (p < 0.05). Further dynamic mechanical alterations were detected in hysteresis, phase shift, and dynamic modulus. Shear moduli correlated negatively with lamellar thickness (G1: rs = −0.63, G2: rs = −0.71).ConclusionsThere were significant alterations in AF shear moduli and dynamic properties in DD individuals when compared to non‐DD controls. Structural correlations highlight the role of the highly organized AF lamellar structure on shear modulus values. These findings suggest that altered AF mechanics may contribute to DD pathology and associated low back pain, warranting further investigation into structural and functional AF changes in symptomatic individuals.

ABSTRACTMelt rupture of a bimodal molecular weight distribution polyethylene is studied under simple shear via flow visualization techniques for the first time. We demonstrated that this catastrophic failure is not exclusive to extensional flows. It was found that melt rupture is a time‐dependent phenomenon occurring after steady‐state plateau in slip velocity and stress. The rupture happens at the three‐phase (polymer‐air‐plate) common line and propagates through the specimen. The common line recedes slightly and stops slipping just before the onset of rupture. The presence of polytetrafluoroethylene lubrication (low surface energy coating) changes the nature of the slip mechanism toward adhesive failure and accelerates melt rupture in terms of time‐to‐rupture‐onset (at the same nominal shear rate). Surface roughness reduces the time to rupture onset but without affecting the nature of the slip. A time‐dependent phenomenon at the interface like fractionation or changes in conformation and entanglement density of the interfacial chains is likely the reason for the transition from slip to melt rupture. This conclusion holds substantial industrial relevance, especially since the prevailing approach to prevent rupture involves promoting slip and reducing stress. However, our research demonstrates that even after achieving a relatively high steady‐state slip velocity, rupture can occur.

Deep Neural Network Hybrid Simulations to Evaluate the Poynting Effect in 3D Ogden Hyperelastic Modeling of Brain White Matter.

Large deflections of miniature elastic structures incorporating large curvature of micro-particles: a new simple polynomial shear deformation theory

This study investigates the breakup of ferrofluid droplets in both planar extensional and simple shear flows under the influence of external magnetic fields. Using a three-dimensional model, we analyze the impact of the external field configuration on the minimum strain rate required to induce droplet breakup, covering a wide range of droplet-to-ambient liquid viscosity ratios. The methodology involves solving the incompressible Navier–Stokes equations augmented by capillary and magnetic terms, Maxwell's equations at the magnetostatic limit, and an evolution equation for the level set function used to capture the droplet interface. In planar extensional flows, we find that magnetic fields applied in the extension direction facilitate droplet breakup, while fields in the compression and neutral directions have the opposite effect. In simple shear flows, we find that magnetic fields applied in either the velocity or vorticity directions prevent droplet breakup. In contrast, we find that magnetic fields applied in the velocity gradient direction induce droplet breakup. Importantly, we show that magnetic fields in the velocity gradient direction can be used to break very viscous droplets, highlighting a strong contrast with the standard case of purely viscous droplets well established in the literature. As importantly, we report a unique tumbling-like dynamics for high viscosity droplets with S- and N-like shapes that periodically return to the initial spherical shape, further underscoring the complex coupling between viscous, capillary, and magnetic effects in magnetic multiphase systems.