Isotropic Loading Research Articles

A three-dimensional quasicontinuum approach for predicting biomechanical properties of malaria-infected red blood cell membrane

• A multiscale model for malaria-infected RBC biomechanical properties is proposed. • Vital elastic properties and mechanical responses are predicted for the first time. • Elastic properties except Poisson's ratio rise significantly as parasite matures. • Mechanical responses rise exponentially resulting in semi-log stress–strain curves. • Elastic properties increase as temperature rises in trophozoite infection stage. This paper presents the first attempt to comprehensively estimate the elastic properties and mechanical responses of malaria-infected red blood cell (iRBC) membrane when subjected to uniaxial, shear and isotropic area-dilation loading conditions. With the three-dimensional (3D) quasicontinuum approach, we predicted the biomechanical properties of the iRBC membrane for all infection stages. Effect of temperature on the membrane elastic properties during the trophozoite stage was also examined. It is found that a multifold increase in the elastic properties of the iRBC membrane occurs as infection progresses. The axial, shear and area stiffnesses of the iRBC membrane increase exponentially, resulting in semi-logarithmic stress–strain relationship curves. In addition, the rigidity of the iRBC membrane in the trophozoite stage increases as temperature rise. It is concluded that Plasmodium falciparum parasites significantly affect the biomechanical properties of the RBC membrane due to the structural remodeling of the iRBC membrane microstructure.

Reduced-order analysis of buffet flow of space launchers

A reduced-order analysis based on optimized dynamic mode decomposition (DMD) is performed on the turbulent wake of a generic axisymmetric space launcher configuration computed via a zonal large-eddy simulation at the free stream Mach number $Ma_{\infty }=0.8$ and the Reynolds number based on the main body diameter $Re_{D}=6\times 10^{5}$ to investigate the buffet phenomenon. The transonic wake is characterized by an unsteady recirculation region occurring around the nozzle due to the separation of the turbulent boundary layer at the main body shoulder and subsequent dynamic interaction of the unstable free-shear layer with the nozzle surface. This results in strongly periodic and antisymmetric wall pressure fluctuations, for which three distinct frequency ranges are identified using conventional spectral analysis, i.e. $Sr_{D}\approx 0.1$, $Sr_{D}\approx 0.2$ and $Sr_{D}\approx 0.35$. For the spatially integrated side (buffet) loads on the nozzle, the second range is found to be energetically most dominant. To clarify the origin of the detected wake dynamics, the underlying spatio-temporal coherent modes are extracted using DMD. Subsequent analysis of the reduced-order modelled flow field based on the identified DMD modes reveals that at $Sr_{D}\approx 0.1$ a longitudinal cross-pumping motion of the separation bubble takes place, caused by a harmonic antisymmetric oscillation of the main recirculation vortex in the streamwise direction. At $Sr_{D}\approx 0.2$, a cross-flapping motion of the shear layer is determined, triggered by antisymmetric vortex shedding which is in phase with the cross-pumping motion such that it occurs at twice the frequency value. The last range of $Sr_{D}\approx 0.35$ is attributed to a swinging motion of the shear layer caused by a higher harmonic of the vortex shedding mode. Conclusively, the controversial aspect of the true three-dimensional shape of the antisymmetric mode at $Sr_{D}\approx 0.2$ that dominates the buffet phenomenon is scrutinized. Inclined elongated closed-loop vortices are identified that are shed in alternating sequence from azimuthally opposite positions in a longitudinal plane of symmetry that changes its momentary orientation irregularly, maintaining an axisymmetric time-averaged field and spatially isotropic buffet loads.

Sand – rubber mixtures submitted to isotropic loading: a minimal model

The volume of scrap tyres, an undesired urban waste, is increasing rapidly in every country. Mixing sand and rubber particles as a lightweight backfill is one of the possible alternatives to avoid stockpiling them in the environment. This paper presents a minimal model aiming to capture the evolution of the void ratio of sand-rubber mixtures undergoing an isotropic compression loading. It is based on the idea that, submitted to a pressure, the rubber chips deform and partially fill the porous space of the system, leading to a decrease of the void ratio with increasing pressure. Our simple approach is capable of reproducing experimental data for two types of sand (a rounded one and a sub-angular one) and up to mixtures composed of 50% of rubber.

Nanoporous materials with a general isotropic plastic matrix: Exact limit state under isotropic loadings

In this paper, hydrostatic strength properties of nanoporous materials are investigated by addressing the limit state of a hollow sphere undergoing isotropic loading conditions. Void-size effects are modelled by treating the cavity boundary as a coherent-imperfect homogeneous interface. The hollow sphere is assumed to be comprised of a rigid-ideal-plastic material obeying to a general isotropic yield criterion. The latter is defined by considering a simplified form of the yield function proposed by Bigoni and Piccolroaz in [Int J Solids Struct; 41: 2855–2878], resulting able to account for a broad class of pressure-sensitive materials whose plastic response is also affected by the stress Lode angle. The corresponding support function is consistently derived and discussed. The exact solution of the limit-state problem is fully determined, providing a closed-form description of stress, strain-rate and velocity fields, as well as the macroscopic hydrostatic strength of nanoporous media. Proposed approach allows to consistently generalise available analytical solutions for porous and nanoporous materials, by accounting for a general plastic response of the solid matrix and for void-size effects. Finally, present exact solution, as well as the identification of the support function for the adopted general strength criterion, open towards novel kinematic limit-analysis approaches for describing macroscale strength properties of nanoporous materials under arbitrary triaxial loadings.

A unified mechanical and retention model for saturated and unsaturated soil behaviour

The coupled mechanical and water retention elasto-plastic constitutive model of Wheeler, Sharma and Buisson (the Glasgow coupled model, GCM) predicts unique unsaturated isotropic normal compression and unsaturated critical state planar surfaces for specific volume and degree of saturation when soil states are at the intersection of mechanical (M) and wetting retention (WR) yield surfaces. Experimental results from tests performed by Sivakumar on unsaturated samples of compacted speswhite kaolin confirm the existence and form of these unique surfaces. The GCM provides consistent representation of transitions between saturated and unsaturated conditions, including the influence of retention hysteresis and the effect of plastic volumetric strains on retention behaviour, and it gives unique expressions to predict saturation and de-saturation conditions (air-exclusion and air-entry points, respectively). Mechanical behaviour is modelled consistently across these transitions, including appropriate variation of mechanical yield stress under both saturated and unsaturated conditions. The expressions defining the unsaturated isotropic normal compression planar surfaces for specific volume and degree of saturation are central to the development of a relatively straightforward methodology for determining values of all GCM parameters (soil constants and initial state) from a limited number of laboratory tests. This methodology is demonstrated by application to the experimental data of Sivakumar. Comparison of model simulations with experimental results for the full set of Sivakumar’s isotropic loading stages demonstrates that the model is able to predict accurately the variation of both specific volume and degree of saturation during isotropic stress paths under saturated and unsaturated conditions.

Small-strain stiffness of sand subjected to stress anisotropy

Stiffness of soils at small strains expressed through the small-strain shear modulus is critical for the evaluation of deformations of geo-structures subjected to a variety of stress states. While most of the previous studies of small-strain shear modulus of sands have focused on the isotropic stress state, there exist innumerable situations in geotechnical engineering in which the soil is under an anisotropic stress state. In this study, the influence of stress anisotropy on the small-strain shear modulus (Gmax) of sands is evaluated using the results of a comprehensive set of bender element tests conducted on saturated sand samples under isotropic and anisotropic loading conditions. It is shown that the small-strain shear moduli of sands under anisotropic loading conditions are greater in magnitude than those subjected to isotropic stress states at a given mean effective stress. It is also shown that the influence of stress anisotropy on the small-strain shear modulus of sands is more pronounced for sands with irregular in shape grains and wider grain size distribution in comparison to uniform sands of relatively rounded and spherical grains. Based on the experimental results, a new Gmax model is developed which incorporates the contribution of grain size characteristics and particle shape in the prediction of the small-strain shear modulus of sands subjected to stress anisotropy.

An elastoplastic damage model for fractured porous media

An elastoplastic damage model is developed for fractured porous media. The elastic–plastic response of stress–strain is captured by a bounding surface plasticity within the critical state framework, while the damage evolution due to hydro-mechanical effects is addressed using a continuum damage model that is distinguished from the existing models by accounting for the plastic hardening parameter, stress ratio, confining pressure and strain rate. The coupling between the elastic–plastic response and damage is established by accounting for the effects of plastic volumetric strain and the damage parameter on the hardening of the bounding surface. The model is applied to different rocks subjected to isotropic and deviatoric loading in drained and undrained conditions. A good agreement is obtained between the numerical and experimental results demonstrating the ability of the model to capture the essential features of deformation in fractured porous media.

Thermo-elastoplastic constitutive model for unsaturated soils

This study presents a simple approach to modelling the effect of temperature on the deformation and strength of unsaturated/saturated soils by using the average skeleton stress and degree of saturation. The concept of thermo-induced equivalent stress is introduced to consider the influence of temperature on the pre-consolidated stress. A skeleton stress–saturation framework is applied to enable the model to describe the thermo-elastoplastic behaviour of both unsaturated and saturated soils, as the skeleton stress can smoothly shift to Terzaghi’s effective stress if saturation changes from the unsaturated to the saturated condition. The new model only employs seven parameters, of which five parameters are the same as those used in the Cam-Clay model. The other two parameters can be easily determined by oedometer tests and simple thermo-mechanical tests. Numerical simulations of isotropic loading tests and triaxial shear tests under different conditions are conducted to illustrate the performance of the proposed model. By comparing with experimental temperature controlled oedometer tests and triaxial tests, it is confirmed that the proposed model is able to capture the thermo-mechanical behaviour of unsaturated/saturated normally and over-consolidated soils with a set of unified parameters.

The effect of fracture density and stress state on the static and dynamic bulk moduli of Westerly granite

AbstractElastic properties are key parameters during the deformation of rocks. They can be measured statically or dynamically, but the two measurements are often different. In this study, the static and dynamic bulk moduli (Kstatic and Kdynamic) were measured at varying effective stress for dry and fluid‐saturated Westerly granite with controlled fracture densities under isotropic and differential stress states. Isotropic fracturing of different densities was induced in samples by thermal treatment to 250, 450, 650, and 850°C. Results show that fluid saturation does not greatly affect static moduli but increases dynamic moduli. Under isotropic loading, high fracture density and/or low effective pressure results in a low Kstatic/Kdynamic ratio. For dry conditions Kstatic/Kdynamic approaches 1 at low fracture densities when the effective pressure is high, consistent with previous studies. Stress‐induced anisotropy exists under differential stress state that greatly affects Kstatic compared to Kdynamic. As a result, the Kstatic/Kdynamic ratio is higher than that for the isotropic stress state and approaches 1 with increasing axial loading. The effect of stress‐induced anisotropy increases with increasing fracture density. A key omission in previous studies comparing static and dynamic properties is that anisotropy has not been considered. The standard methods for measuring static elastic properties, such as Poisson's ratio, Young's and shear modulus, involve subjecting the sample to a differential stress state that promotes anisotropy. Our results show that stress‐induced anisotropy resulting from differential stress state is a major contributor to the difference between static and dynamic elasticity and is dominant with high fracture density.

Semi-analytical and semi-numerical method for plane strain consolidation of double-layer foundation considering stress paths

In this work, a simplified solution method is present for the elasto-plastic consolidation of a double-layer foundation under different stress paths. A double-yield surface model is introduced as the constitutive model framework for saturated clay and sand. Using a Gauss kernel function, a partial derivative coefficient sequences is obtained. Then, the model is applied to Biot’s consolidation equations and to establish incremental governing partial differential equations for the plane strain consolidation problem. By simplifying the continuity equation as a Poisson equation, the fundamental solutions are derived for double-layer foundation model. Based on it, a semi-analytical and semi-numerical method is presented which is implemented in our finite element program. Comparisons with different mesh show that the stability of the numerical method is good. Moreover, the consolidation of semi-infinite double-layer foundation models is analysed under two stress paths (conventional loading path under the condition of isotropic consolidation CTC and conventional loading path under the condition of anisotropic consolidation K0 + CTC). It is shown that the model can reflect the influence of stress path, loading distribution width and some other factors on the deformation of the soil skeleton and pore water pressure. This simplified solution appears to be more convenient than the traditional coupling stiffness matrix method.

MG-63 cells proliferation following various types of mechanical stimulation on cells by auxetic hybrid scaffolds.

BackgroundMechanical properties and cyto-compatibility of a composite scaffold which possessed negative (−) Poisson’s ratio (NPR) was investigated for effective load transfer from auxetic scaffold to cell.MethodsOrganic/inorganic composite scaffolds were prepared by mixing hydroxyapatite (HA) to poly(lactide-co-glycolide) (PLGA). To induce NPR in composite scaffold, 3-directional volumetric compression was applied during the scaffold fabrication at adequate temperature(60°C). The pore size of scaffold ranged between 355–400 μm.ResultsPoisson’s ratios of NPR scaffolds and control scaffolds were −0.07 and 0.16 at 10 % strain. For stable physical stimulating to loaded cells, ceramic/polymer composite scaffold was prepared by incorporating HA in PLGA to increase mechanical strength. Compressive strength of the HA/PLGA composite scaffold (15 wt. % HA to PLGA) was about 21.7 % higher than that of PLGA-only scaffold. The recovery rates of the NPR composite scaffold after applying compression in the dry and wet states were 90 % and 60 %, respectively. Also the composite scaffold was shown to have better hydrophilicity (61.9°) compared to the PLGA-only scaffolds (65.3°). Cell proliferation of osteoblast-like cell line (MG-63) in the composite scaffold was 20 % higher than in PLGA-only scaffold at static compressive stimulation. For dynamic compressive stimulation (15 min cyclic interval), cell proliferation in the composite scaffold was 2 times higher than that of in PLGA-only scaffold. In conclusion, NPR composite (HA/PLGA) scaffold was effective in isotropic compressive load delivery for osteogenic cell proliferation.ConclusionThis composite scaffold with stimulation can be used as tissue engineered scaffold and dynamic cell culture system for bone tissue regeneration.

Limit analysis and homogenization of porous materials with Mohr–Coulomb matrix. Part II: Numerical bounds and assessment of the theoretical model

This second part of the two-part study is devoted to the numerical Limit Analysis of a hollow sphere model with a Mohr–Coulomb matrix and its use for the assessment of theoretical results. Brief background and fundamental of the static and kinematic approaches in the context of numerical limit analysis are first recalled. We then present the hollow sphere model, together with its axisymmetric FEM discretization and its mechanical position. A conic programming adaptation of a previous iterative static approach, based on a piecewise linearization (PWL) of the plasticity criterion, was first realized. Unfortunately, the resulting code, no more than the PWL one, did not allow sufficiently refined meshes for loss of convergence of the conic optimizer. This problem was solved by using the projection algorithm of Ben Tal and Nemriovski (BTN) and the (interior point) linear programming code XA. For the kinematic approach, a first conic adaptation appeared also inefficient. Then, an original mixed (but fully kinematic) approach dedicated to the general Mohr–Coulomb axisymmetric problem was elaborated. The final conic mixed code appears much more robust than the classic one when using the conic code MOSEK, allowing us to take into account refined numerical meshes. After a fine validation in the case of spherical cavities and isotropic loadings (for which the exact solution is known) and comparison to previous (partial) results, numerical lower and upper bounds (a posteriori verified) of the macroscopic strength are provided. These bounds are used to assess and validate the theoretical results of the companion (part I) paper. Effects of the friction angle as well as that of the porosity are illustrated.

Measuring unsaturated soil deformations during triaxial testing using a photogrammetry-based method

When characterizing an unsaturated soil using the triaxial test apparatus, it is required to measure the soil deformation during loading. Recently, a photogrammetry-based method has been developed for total and localized volume change measurements on unsaturated soils during triaxial testing. In this study, more in-depth discussions on the photogrammetry-based method are addressed, such as system setup, the measurement procedure, accuracy self-check, data post-processing, and differences from conventional image-based methods. Also, an application of the photogrammetry-based method on unsaturated soil deformation measurements is presented through a series of undrained triaxial tests with different loading paths. After testing, three-dimensional (3D) models of the tested soils at different loading steps were constructed based on the 3D coordinates of measurement targets on the soil surface. Clear barreling processes for soils during deviatoric loading were observed through the constructed 3D models at different axial strain levels. Soil volume changes and volumetric strain nonuniformities during isotropic and deviatoric loadings were extracted based upon detailed analyses of different soil layers. Through a full-field strain distribution analysis, a shear band evolution process was captured for the soil during deviatoric loading at a low confining stress. The photogrammetry-based method proved to be very powerful for in-depth soil deformation characteristics investigation.

Pore-size changes and responses of kaolinite with different structures subject to consolidation and shearing

In this paper, the responses of kaolinite samples with two different soil structures, i.e., unwashed and pH7.8 samples, under 1-D consolidation, isotropic loading–unloading and triaxial shearing are examined. The focus is on the associated changes in the pore-size distribution. During isotropic consolidation, the unwashed sample, with an open, aggregated and flocculated structure, exhibits higher compressibility than the pH7.8 sample, which has a densely packed aggregated structure. The associated deformation in both samples primarily arises from the compression of the large inter-aggregate pores, which are not controlled by the suppression of the electrical double layer, and the intra-aggregate pores remain almost unchanged during consolidation. Similar behavior is observed in clay samples with different structures during 1-D consolidation and triaxial shearing that only the inter-aggregate pores are affected and the intra-aggregate pores stay almost the same. All of these findings suggest that the mechanical responses of kaolinite clay depend on aggregate-to-aggregate interactions rather than on particle-to-particle interactions. The aggregates of kaolinite clay can be considered analogous to sand particles.

Mechanical properties of soft sedimentary rock under <i>K</i><sub>0</sub> and isotropic cyclic loading conditions

Mechanical properties of soft sedimentary rock under <i>K</i><sub>0</sub> and isotropic cyclic loading conditions

Interpreting measurements of small strain elastic shear modulus under unsaturated conditions

Bender element testing of unsaturated isotropically compacted speswhite kaolin samples was used to investigate the variation of small strain elastic shear modulus G under unsaturated conditions. Testing was performed in a suction-controlled triaxial cell and involved combinations of isotropic loading and unloading stages and wetting and drying stages. Analysis of the experimental results indicated that the variation of G could be represented by a simple expression involving only mean Bishop’s stress p* and specific volume v , with the only significant mismatches between measured and predicted values of G occuring at the end of final unloading. No significant improvement of fit was achieved by incorporating additional dependency on degree of saturation Sr or a bonding parameter ζ . The proposed expression for G reverts to a well-established form for saturated soils as Sr tends to 1.

Anisotropic behaviour of compacted clayey silt subjected to hydromechanical paths

Compaction induces anisotropy on soil deformational response due to preferential straining associated with the fabrication process. An experimental insight into the stress-strain response of Barcelona clayey silt is provided here. The material was statically compacted at low dry density to induce high collapsibility upon wetting (dry density 1.48 Mg/m3 , water content 12%). Two types of controlled-suction tests were carried out: a) constant suction radial paths on as-compacted samples following different stress ratios (deviator stress / mean net stress: q/p″ , including isotropic and K0 stress paths; and b) the same type of radial stress paths but performed after saturation under low confining stress. These paths were intended to define the as-compacted and saturated yield surfaces. The experimental data on as-compacted state is satisfactorily interpreted adopting an anisotropic yield surface with an inclination linked to the compaction under oedometer conditions. Development of shear strain was observed during isotropic loading of the compacted samples. This anisotropy that the soil exhibits at the end of the compaction vanishes after collapse by saturation and as plastic volumetric straining develops.

Elastoplastic homogenization of particulate composites complying with the Mohr–Coulomb criterion and undergoing isotropic loading

This work aims at determining the overall response of a two-phase elastoplastic composite to isotropic loading. The composite under investigation consists of elastic particles embedded in an elastic perfectly plastic matrix governed by the Mohr–Coulomb yield criterion and a non-associated plastic flow rule. The composite sphere assemblage model is adopted, and closed-form estimates are derived for the effective elastoplastic properties of the composite either under tensile or compressive isotropic loading. In the case when elastic particles reduce to voids, the composite in question degenerates into a porous elastoplastic material. The results obtained in the present work are of interest, in particular, for soil mechanics.

Hydro-mechanical behavior of undisturbed collapsible loessial soils under different stress state conditions

A conventional triaxial test device was modified to characterize the hydro-mechanical behavior of a loessial soil during isotropic and shear loadings. This device is capable of precise and continuous measurements of water outflow during the application of loading. The tests were performed on “undisturbed” cylindrical specimens, which were taken from loessial deposits in Gorgan, a city in the northeast of Iran. Experimental measurements indicate that the hydro-mechanical behavior of loess is highly affected by the extent of applied mean net stress and the level of suction. During both isotropic and shearing stages of loading, the tested specimens may exhibit collapse, abrupt decrease in volume or sudden positive volumetric strain, upon wetting or applied loading. However, the magnitude and extent of collapse are different depending on the applied state of the stress and the hydro-mechanical loading path. The results of the experiments reveal that the peak shear strength of the soil increases, as the applied mean net stress during isotropic loading or the applied matric suction increases. The shearing test results are also used to investigate the efficiency of suction stress in describing the state of stress for unsaturated loessial soils. The outcome indicated a unique critical state line for unsaturated specimens under different stress paths and loading conditions. Furthermore, considering the effective stress concept, a hardening constitutive law is presented in this study to demonstrate the hardening/softening behavior of the collapsible loessial soils.

Interaggregate Forces and Energy Potential Effect on Clay Deformation

This study aims to propose a new model for clay behavior by incorporating physical–chemical effects acting between clay clusters using the Chang and Hicher micromechanical approach. Local mechanisms are thus introduced through repulsive and attractive forces similar to double-layer van der Waals forces, which are obtained from the derivation of energy potentials. A specific study of local parameters and their evolution is conducted using experimental data from the mineralogy variation provoked by the variation of a remolded saturated reconstituted clayey mixture consisting of kaolinite and montmorillonite ranging from 0 to 100% montmorillonite. Using scale transition, the results of micro–macrocalculations under an isotropic loading path show a very good agreement with experimental results.