Isotropic Tension Research Articles

A novel hydro-elastoplastic constitutive model incorporating hydrostatic damage for predicting high-pressure performance of concrete under blast loading

The evolution of damage and failure modes of concrete under blast or impact loads are the outcomes of stress wave propagation. The stress state at a point within the concrete changes instantaneously with time and space. Establishing a constitutive model that can cover the nonlinear behavior of materials under complex loading paths and histories is an extremely challenging task. The main difficulty lies in the construction of the damage model, which has not yet been fully resolved in commonly used concrete models. This paper, based on the mechanisms of damage and failure of concrete under hydrostatic pressure, constructs a state equation that includes the description of crushing and compaction damage due to the collapse and closure of pores, as well as their interactive model, negative pressure degradation caused by hydrostatic pressure, and nonlinear volumetric behavior under loading/unloading/reloading. By introducing independent shear and tensile deviatoric damage scaling functions and a damage scaling function under isotropic tension, the coupling relationship between deviatoric and volumetric damage is considered. Corresponding strength models and element erosion criteria are developed based on the new state equation and damage models. Then, single-element numerical experiments of unconstrained uniaxial compression and tension, triaxial compression under different confining pressures, monotonic and cyclic hydrostatic compression, and isotropic tension were conducted to verify the predictive accuracy of the proposed model under single loading paths. Finally, numerical experiments of contact explosion on plain concrete thick and thin targets were carried out using the proposed model, revealing the propagation laws and failure processes of the loading compression wave, unloading tensile wave, and reflected tensile wave within the concrete target. The predicted final failure modes are consistent with the experimental results.

Dynamic tensile fracture of iron: Molecular dynamics simulations and micromechanical model based on dislocation plasticity

Molecular dynamics (MD) shows a difference in the mechanisms of fracture of iron under uniaxial and isotropic tension. Uniaxial tension leads to the formation of a complex dislocation structure in the bulk of material, which reduces the pore formation threshold and spall strength. Increase in temperature up to about 900 K suppresses increase in dislocation density during uniaxial tension, which leads to increase in the spall strength to the level close to the case of hydrostatic (isotropic) tension. This temperature-induced increase in dynamic tensile strength is rather unusual. Preliminary compression of material mimicking the shock compression prior to tension creates a defect structure, which reduces the spall strength during the following tension. The MD results of isotropic tension are used to model the material fracture dynamics on continuum level. The Bayesian approach to model calibration is used to identify the parameters of the fracture model. The parameterized fracture model describes well the MD results in the considered temperature range 300–1100 K. The fracture model with additional accounting of void initiation on initial defects of material is used to describe the experimental observations of the spall strength of iron over a wide range of strain rates. The simulation results for undeformed iron are in good agreement with the experimental values of the spall strength at strain rates greater than 4 × 105 s-1 and give overestimated values at lower strain rates. The results of calculations for precompressed iron describe well the spall strength over the entire range of strain rates indicating that accounting for the defect structure created by the shock compression prior to tension is critical for moderate strain rates.

Molecular dynamics investigation of loading orientation effect on dynamic behaviors of void in aluminum

The micro-damage mechanisms in ductile metals play a very important role in the spallation process. Nonequilibrium molecular dynamics (NEMD) is used to examine the effect of loading orientation on void evolution in single crystal (SC) and nanocrystalline (NC) aluminum under isotropic tensions. Besides void nucleation, growth, and coalescence, a brand-new phenomenon, void collapse, is also discovered in the late growth stage, and the collapse behavior is confirmed by the atomic trajectory tracing approach (ATTA). The loading orientation has a significant impact on the maximum void number, maximum void surface area, and void collapse velocity in the SC model but not in the NC model; while the void volume and its fraction that can capture the void collapse behavior are unaffected by the loading direction in the SC and NC models. In the SC model, the loading orientations [−110][001][110] and [100][010][001] make void collapse hardest and simplest. Meanwhile, with the help of the slicing method, it is discovered that the damage mechanism in the NC model is dominated by intracrystalline, intercrystalline, and transcrystalline fractures, with the second being the directional fracture along the grain boundary, whereas it belongs to the intracrystalline fracture in the SC model. In addition, the material experiences the hardening and softening phases during the nucleation stage, which are distinguished by the maximal tensile stress.

Phase field theory for fracture at large strains including surface stresses

Phase field theory for fracture is developed at large strains with an emphasis on a correct introduction of surface stresses at nanoscale. This is achieved by multiplying the cohesion and gradient energies by the local ratio of the crack surface areas in the deformed and undeformed configurations and with the gradient energy in terms of the gradient of the order parameter in the reference configuration. This results in an expression for the surface stresses which is consistent with the sharp surface approach. Namely, the structural part of the Cauchy surface stress represents an isotropic biaxial tension, with the magnitude of a force per unit length equal to the surface energy. The surface stresses are a result of the geometric nonlinearities, even when strains are infinitesimal. They make multiple contributions to the Ginzburg-Landau equation for damage evolution, both in the deformed and undeformed configurations. Important connections between material parameters are obtained using an analytical solution for two separating surfaces, as well as an analysis of the stress-strain curves for homogeneous tension for different degradation and interpolation functions. A complete system of equations is presented in the deformed and undeformed configurations. All the nanoscale phase field parameters are obtained utilizing the existing first principle simulations for the uniaxial tension of Si crystal in the [100] and [111] directions.

Effects of fluid–cell–vessel interactions on the membrane tensions of circulating tumor cells in capillary blood flows

The membrane tensions of suspended nucleated cells moving in blood flows in capillary networks are quite different from those of spreading cells, a fact that is crucial to many pathological processes, such as the metastasis of cancers via circulating tumor cells (CTCs). However, a few studies have examined membrane tensions in suspended cells, especially when interacting with other cells of different stiffnesses in low-Reynolds number flows at the cellular level. Taking CTCs as an example, we use the immersed boundary method to analyze the relationship between membrane tensions and their motional behaviors under the influence of fluid–cell–vessel interactions. The effects of vessel diameter and hematocrit on the shear tension and average isotropic tension are also analyzed. The results suggest that the confinement of the vessel wall determines membrane tensions on CTCs until the ratio of the vessel diameter to cell size becomes slightly larger than unity, at which point cell–cell interactions become the crucial factor. The increase in interactions between red blood cells and CTCs with the increase in the hematocrit in larger vessels promotes membrane tensions not only through the migration of CTCs to the vessel wall but also through a reduction in the translational motion and rotation of CTCs. The present study provides support rooted in biofluid mechanics for mechanobiological research on the metastasis and apoptosis of CTCs in microvessels.

Stiffening of under-constrained spring networks under isotropic strain.

Disordered spring networks are a useful paradigm to examine macroscopic mechanical properties of amorphous materials. Here, we study the elastic behavior of under-constrained spring networks, i.e. networks with more degrees of freedom than springs. While such networks are usually floppy, they can be rigidified by applying external strain. Recently, an analytical formalism has been developed to predict the scaling behavior of the elastic network properties close to this rigidity transition. Here we numerically show that these predictions apply to many different classes of spring networks, including phantom triangular, Delaunay, Voronoi, and honeycomb networks. The analytical predictions further imply that the shear modulus G scales linearly with isotropic stress T close to the rigidity transition. However, this seems to be at odds with recent numerical studies suggesting an exponent between G and T that is smaller than one for some network classes. Using increased numerical precision and shear stabilization, we demonstrate here that close to the transition a linear scaling, G ∼ T, holds independent of the network class. Finally, we show that our results are not or only weakly affected by finite-size effects, depending on the network class.

Surface-tension-induced budding drives alveologenesis in human mammary gland organoids.

Organ development involves complex shape transformations driven by active mechanical stresses that sculpt the growing tissue 1,2. Epithelial gland morphogenesis is a prominent example where cylindrical branches transform into spherical alveoli during growth3-5. Here we show that this shape transformation is induced by a local change from anisotropic to isotropic tension within the epithelial cell layer of developing human mammary gland organoids. By combining laser ablation with optical force inference and theoretical analysis, we demonstrate that circumferential tension increases at the expense of axial tension through a reorientation of cells that correlates with the onset of persistent collective rotation around the branch axis. This enables the tissue to locally control the onset of a generalized Rayleigh-Plateau instability, leading to spherical tissue buds6. The interplay between cell motion, cell orientation and tissue tension is a generic principle that may turn out to drive shape transformations in other cell tissues.

130 Skin ageing: an explorative study based on mechanical properties investigated by Atomic Force Microscopy

Skin constitutes a barrier against external injuries and contributes to the maintenance of homeostasis. Dermis with collagen and elastin fibres has a role of support with the extracellular matrix (ECM). During ageing numerous mechanisms induce skin degradation by loss of elasticity, skin thickness and collagen network disorganization. Atomic Force Microscopy (AFM) has been described as a reliable tool to study mechanical properties of various samples. The purpose here is to develop an AFM-based method to quantify nanoscale changes in the biomechanical properties of the different skin layers. Firstly, the global skin explant mechanical properties were measured by AFM Stiffness Tomography (ST), secondly the impact of skin ageing at cellular level was explored (structure and tension between cells, tension between cell and matrix). Three groups from 10 different ages donors were studied (below 30 years old (yo), from 30 to 50 yo and above 50 yo). At the tissue level, a controlled AFM indentation with a spherical tip was applied on fresh tissue sample. Skin explant was maintained by a special device designed to induce an isotropic tension. Mechanical properties were extracted gradually by ST along the skin depth. A global skin elastic modulus evaluation was provided according to the different ages. Then, cryosectionned skin samples were characterized with a sharper AFM tip. The elastic modulus of cell-cell junctions was measured in epidermis and ECM mechanical properties were assessed in the dermis (papillary and reticular). Data showed a general increase of dermis and epidermis elastic modulus across ageing. At the cellular level, epidermic elastic modulus heterogeneity has been showed with an increase of the basal layer skin stiffness. We also observed a bell-curve distribution of the elastic modulus for the papillary dermis and an increase of the reticular dermis rigidity.

Shape bistability in 2D chromonic droplets

An extensive experimental study of the shapes of two-dimensional bipolar droplets of the chromonic nematic phase of disodium cromoglycate (DSCG) sandwiched between glass plates, by Kim et al was published in (2013 J. Phys.: Condens. Matter 25 404202). The paper includes a mathematical model of this system. We have extended this study by further theoretical modelling. Our results are in good, quantitative agreement with the experimental data. The model has produced what promises to be a more accurate estimate for the isotropic surface tension at the nematic/isotropic solution interface—and predicts a regime of shape bistability (which has not yet been observed) for larger droplets, where tactoids (pointed, zeppelin-shaped droplets) and smooth-edged discoids can coexist in equilibrium. The general method presented in this paper is also applied to the tactoids formed by F-actin filaments in solution, for which an estimate is given for the value of the isotropic surface tension at the nematic/isotropic interface.

Computational interfacial rheology

Fluid–fluid interfaces, laden with polymers, particles or other surface-active moieties, often show a rheologically complex response to deformations, in particular when strong lateral interactions are present between these moieties. The response of the interface can then no longer be described by an isotropic surface tension alone. These “structured” soft-matter interfaces are found in many industrial applications, ranging from foods, cosmetics and pharmaceuticals, to oil recovery. Also many biomedical applications involve such interfaces, including those involving lung surfactants and biofilms. In order to understand, design and optimize processes in which structured interfaces are present, flow predictions of how such multiphase systems deform are of the utmost importance, which is the goal of “computational interfacial rheology”, the main topic of this review. We start by rigorously establishing the stress boundary condition used in the computation of multi-phase flows, and show how this changes when the interface is rheologically complex. Then, constitutive models for the extra stress in interfaces, ranging from 2D generalized Newtonian to hyperelastic and viscoelastic, are reviewed extensively, including common pitfalls when applying these models. This is followed by an overview of different approaches to measure interfacial rheological properties, and a discussion of advanced numerical implementations for deforming interfaces. We conclude with an outlook for this relatively young and exciting field.

Effect of temperature on the evolution dynamics of voids in dynamic fracture of single crystal iron: a molecular dynamics study

ABSTRACT We employ molecular dynamics simulations to investigate the role of temperature on the evolution dynamics of the voids in single crystal iron. We simulate isotropic tension in single crystal iron at a constant strain rate with temperature in the range of 300–1200 K. We find that the number of voids is highest at 1200 K in comparison to that at 300 K indicating high nucleation events at high temperatures. The growth rate of the voids is highest at 300 K in comparison to that at 1200 K, indicating rapid growth of the voids at 300 K. The overall void volume fraction is highest at 300 K. The nucleation and growth of the voids at 1200 K occur earlier in time in comparison to that at 300 K indicating the earlier damage of the material at 1200 K. The individual void volume fraction evolves with many discrete jumps due to the coalescence of the voids. The dislocation density is highest at 300 K in comparison to that at 1200 K.

Early OA Stage Like Response Occurs after Dynamic Stretching of Human Synovial Fibroblasts.

As events triggering early osteoarthritis onset can be related to mechanical stress and proinflammatory signaling, we investigated the effect of different mechanical strain protocols on the expression of proinflammatory genes, as well as extracellular matrix remodelling in human synovial fibroblasts. Three distinct models of tensile stretching were applied: static isotropic tensile strain at 0 Hz, 16% tension for 48 h; short-term high-frequency cyclic tension at 1 Hz, 10% tension for 4 h; and dynamic tensile stretching for 48 h, consisting of two blocks of moderate stretching at 0.2 Hz, 2%, advanced stretching at 0.5 Hz, 15%, or a combination of both. General signs of inflammation were present after static isotropic tension, whereas short-term high-frequency cyclic tension showed increased levels of IL-6 paired with diminished levels of IL-1β. Reduced inflammatory effects of TNF-α, IL-6, and IL-1β were observed when exposed to advanced stretching. Long-term tensile strain induced extracellular matrix remodelling at the gene and protein levels. While hyaluronan acid synthesis was increased with static tensile strain, dynamic tensile stretching had a reducing effect. Our study revealed that proinflammatory markers were activated by mechanical strain as seen in static isotropic tension and short-term high-frequency tensile strain, whereas long-term exposure induced extracellular matrix remodelling processes.

Isotropic myosin-generated tissue tension is required for the dynamic orientation of the mitotic spindle.

The ability of cells to divide along their longest axis has been proposed to play an important role in maintaining epithelial tissue homeostasis in many systems. Because the division plane is largely set by the position of the anaphase spindle, it is important to understand how spindles become oriented. While several molecules have been identified that play key roles in spindle orientation across systems, most notably Mud/NuMA and cortical dynein, the precise mechanism by which spindles detect and align with the long cell axis remain poorly understood. Here, in exploring the dynamics of spindle orientation in mechanically distinct regions of the fly notum, we find that the ability of cells to properly reorient their divisions depends on local tissue tension. Thus, spindles reorient to align with the long cell axis in regions where isotropic tension is elevated, but fail to do so in elongated cells within the crowded midline, where tension is low, or in regions that have been mechanically isolated from the rest of the tissue via laser ablation. Importantly, these differences in spindle behavior outside and inside the midline can be recapitulated by corresponding changes in tension induced by perturbations that alter nonmuscle myosin II activity. These data lead us to propose that isotropic tension within an epithelium provides cells with a mechanically stable substrate upon which localized cortical motor complexes can act on astral microtubules to orient the spindle.

Nonlinear isotropic elastic reduced and full Cosserat media: waves and instabilities

We consider two types of the nonlinear elastic Cosserat media: a full one, in which the strain energy depends both on the Cosserat deformation tensor and wryness tensor, and the reduced one, in which the strain energy depends only on the Cosserat deformation tensor, thus excluding its dependence on the gradient of micro-rotation. For these media, we obtain the equations for small deviations for an arbitrary nonlinear equilibrium and any type of elastic energy, which can be expanded into the Taylor series near this equilibrium. Then we consider an isotropic material under isotropic tension or compression and show that the equations for small deviations coincide with the equations of motion for the corresponding linear elastic continuum. For a wide class of materials with convex energy, strong compression leads to the instability of the medium caused by shear perturbations, and strong tension—to the instability with respect to shear–rotational perturbations. The last mechanism of instability is absent in the classical elastic continuum. For the reduced medium in the stable domain, shear–rotational wave has a forbidden band of frequencies, demonstrates strong dispersion near this zone, and there is a resonant frequency corresponding to the independent rotational oscillations. Characteristic frequencies depend on the stress state. Thus, it is a single negative acoustic metamaterial with a tunable band gap, depending on the nonlinear stress state, with respect to the shear waves. In the forbidden zone, localization phenomena near heterogeneities are present.

THE EFFECT OF ANISOTROPIC SURFACE TENSION ON THE LAMELLAR EUTECTIC GROWTH IN DIRECTIONAL SOLIDIFICATION

For the case of small interlamellar spacing relative to the solute diffusion length, the steady spatially periodic lamellar eutectic growth with the anisotropic effect of surface tension in directional solidification is studied by the approach of the interfacial wave (IFW) theory. The anisotropic surface tension is expressed as the fourfold symmetric function. We obtained a family of the uniformly valid asymptotic solutions for the steady lamellar eutectic growth and determined the corresponding interfacial patterns affected by anisotropic surface tension. The analytical solution reveals the anisotropic effect of surface tension on the interface shape of lamellar eutectic growth near the triple point. The temperature distribution at the interface shows a noticeable nonuniformity and there is a thin boundary layer for temperature and concentration near the triple point. As the anisotropic surface tension increases, the interface temperature away from the triple-point increases, whereas near the triple point the interface temperature decreases. Compared with the lamellar eutectic growth with isotropic surface tension, the anisotropic surface tension changes the position of the triple point and accelerates the growth of the lamellar eutectic. The theoretical prediction shows quantitatively consistent with recent experimental data without making any artificial adjustments to parameters.

EFFECT OF ANISOTROPIC SURFACE TENSION ON THE MORPHOLOGICAL STABILITY OF DEEP CELLULAR CRYSTAL GROWTH IN DIRECTIONAL SOLIDIFICATION

This paper studies the effect of anisotropic surface tension on the morphological stability of deep cellular crystal in directional solidification by using the matched asymptotic expansion method and multiple variable expansion method. We find that the morphological stability of deep cellular crystal growth with anisotropic surface tension shows the same mechanism as that with isotropic surface tension. The deep cellular crystal growth contains two types of global instability mechanisms: the global oscillatory instability, whose neutral modes yield strong oscillatory dendritic structures, and the low-frequency instability, whose neutral modes yield weakly oscillatory cellular structures. Anisotropic surface tension has the significant effect on the two global instability mechanisms. As the anisotropic surface tension increases, the unstable domain of global oscillatory instability decreases, whereas the unstable domain of the global low-frequency instability increases.

A sharp interface model for deterministic simulation of dendrite growth

A high order level set model is developed for deterministic simulation of dendritic growth in unstable solidifying systems. The model captures motion of the front implicitly on a structured finite difference grid, enables calculation of its geometric properties and also applies boundary conditions on the immersed interface. Interfacial capillary effect is incorporated in the model through the Gibbs-Thomson condition. Canonical problems for evaluating grid convergence of the numerical method and validation tests for stability of a growing nucleus in the presence of isotropic surface tension are presented. The growth morphology of solidifying nuclei in undercooled metallic melts is quantitatively analyzed. Effects of crystal anisotropy and melt undercooling on the front geometry, propagation speed and formation of branched dendritic structures are examined. The complex morphological changes, such as remelting of secondary perturbations under specific conditions of undercooling, are also captured during the quantitative analysis.

Atomic-scale modeling of the void nucleation, growth, and coalescence in Al at high strain rates

Molecular dynamics (MD) simulations in single-crystal (SC) and nanocrystalline (NC) aluminum (Al) were performed using Large-scale Atomic/Molecular Massively Parallel Simulator software (LAMMPS) to investigate the nucleation, growth, and coalescence of voids at the micro-scale under isotropic and triaxial tension. The effects of temperature, strain rate, initial pressure, and grain size were examined. Compared with experimental results, the Hugoniot curve of Al was predicted to validate the accuracy of the selected potential function. Based on the relationship between the tensile stress and void volume fraction, the progressive micro-damage procedure was divided into four stages: atomic disorder, nucleation, growth, and coalescence of voids. These are characterized by the void volume fraction history and the cross-sectional internal and external snapshots of the void distribution. The strain rate had a more significant effect on the micro-fracture than temperature. In addition, an initial pressure of 1000 MPa impeded the time of initial void nucleation and growth. Intergranular, transgranular, and intragranular fractures occurred in NC Al but only intragranular fracture appeared in the SC Al. The void volume fraction of NC Al was independent of grain size (6 and 60 nm), which affected the void number inside the grains. Furthermore, the parameter identification of the nucleation and growth (NAG) model was achieved using an improved genetic optimal algorithm. Thus, the relationships between tensile stress, void volume fraction, and NAG parameters were explored.

Interaction of Giant Unilamellar Vesicles with the Surface Nanostructures on Dragonfly Wings.

The waxy epicuticle of dragonfly wings contains a unique nanostructured pattern that exhibits bactericidal properties. In light of emerging concerns of antibiotic resistance, these mechano-bactericidal surfaces represent a particularly novel solution by which bacterial colonization and the formation of biofilms on biomedical devices can be prevented. Pathogenic bacterial biofilms on medical implant surfaces cause a significant number of human deaths every year. The proposed mechanism of bactericidal activity is through mechanical cell rupture; however, this is not yet well understood and has not been well characterized. In this study, we used giant unilamellar vesicles (GUVs) as a simplified cell membrane model to investigate the nature of their interaction with the surface of the wings of two dragonfly species, Austrothemis nigrescens and Trithemis annulata, sourced from Victoria, Australia, and the Baix Ebre and Terra Alta regions of Catalonia, Spain. Confocal laser scanning microscopy and cryo-scanning electron microscopy techniques were used to visualize the interactions between the GUVs and the wing surfaces. When exposed to both natural and gold-coated wing surfaces, the GUVs were adsorbed on the surface, exhibiting significant deformation, in the process of membrane rupture. Differences between the tensile rupture limit of GUVs composed of 1,2-dioleoyl- sn-glycero-3-phosphocholine and the isotropic tension generated from the internal osmotic pressure were used to indirectly determine the membrane tensions, generated by the nanostructures present on the wing surfaces. These were estimated as being in excess of 6.8 mN m-1, the first experimental estimate of such mechano-bactericidal surfaces. This simple model provides a convenient bottom-up approach toward understanding and characterizing the bactericidal properties of nanostructured surfaces.

Interplay of phase boundary anisotropy and electro-auto-catalytic surface reactions on the lithium intercalation dynamics in LiXFePO4 plateletlike nanoparticles

Experiments on single crystal Li$_X$FePO$_4$ (LFP) nanoparticles indicate rich nonequilibrium phase behavior, such as suppression of phase separation at high lithiation rates, striped patterns of coherent phase boundaries, nucleation by binarysolid surface wetting and intercalation waves. These observations have been successfully predicted (prior to the experiments) by 1D depth-averaged phase-field models, which neglect any subsurface phase separation. In this paper, using an electro-chemo-mechanical phase-field model, we investigate the coherent non-equilibrium subsurface phase morphologies that develop in the $ab$- plane of platelet-like single-crystal platelet-like Li$_X$FePO$_4$ nanoparticles. Finite element simulations are performed for 2D plane-stress conditions in the $ab$- plane, and validated by 3D simulations, showing similar results. We show that the anisotropy of the interfacial tension tensor, coupled with electroautocatalytic surface intercalation reactions, plays a crucial role in determining the subsurface phase morphology. With isotropic interfacial tension, subsurface phase separation is observed, independent of the reaction kinetics, but for strong anisotropy, phase separation is controlled by surface reactions, as assumed in 1D models. Moreover, the driven intercalation reaction suppresses phase separation during lithiation, while enhancing it during delithiation, by electro-autocatalysis, in quantitative agreement with {\it in operando} imaging experiments in single-crystalline nanoparticles, given measured reaction rate constants.