Two-phase Materials Research Articles

Multiscale modeling of cancellous bone considering full coupling of mechanical, electric and magnetic effects

Modeling of cancellous bone has important applications in the detection and treatment of fatigue fractures and diseases like osteoporosis. In this paper, we present a fully coupled multiscale approach considering mechanical, electric and magnetic effects by using the multiscale finite element method and a two-phase material model on the microscale. We show numerical results for both scales, including calculations for a femur bone, comparing a healthy bone to ones affected by different stages of osteoporosis. Here, the magnetic field strength resulting from a small mechanical impact decreases drastically for later stages of the disease, confirming experimental research.

Microstructural integrity characterization of cement-based construction materials

In this paper, a new micromechanical framework to characterize the microstructural integrity and predict the effective properties of multi-phase particulate composites is presented. Within the framework, a new scalar micromechanical parameter is identified and used to derive new expressions for the effective elastic properties of particulate composites using the mean-field homogenization technique. The derived equations are then generalized for composites with multiple phase constituents. The generality of the proposed framework is demonstrated by combining the derived equations with the existing homogenization techniques such as the Mori–Tanaka method and the Generalized Maxwell’s Approach (GMA). The results show that the theory delivers consistent estimates of the effective properties of two-phase elastic composite materials. The new scalar micromechanical parameter is also used to characterize the microstructural integrity of both asphalt mixtures and Portland cement concrete. The results show that the new scalar micromechanical parameter correlates well with multiple key fundamental properties of asphalt concrete mixture, including the creep rate, the fracture energy density, the endurance limit, and the damage rate parameters. The results also show that the new micromechanical framework can be used to accurately predict the effective modulus properties of Portland cement concrete mixtures.

Proposing a three-phase model for predicting the mechanical properties of mortar and concrete

The interfacial transition zone (ITZ) around aggregates is known as the weakest zone in mortar and concrete, which highly influences the mechanical properties. In this study, the influence of ITZ on mechanical properties such as Young’s modulus and Poisson’s ratio of cementitious materials is evaluated using a multi-scale model (developed in five hierarchical levels: nano-scale cement hydrates∼ scale of concrete). In the proposed model, the microstructure of mortar/ concrete is considered as a three-phase material: fine/ coarse aggregates, ITZ of aggregates and bulk paste/ mortar. The primary input is the microstructure of cement paste and ITZ, which are predicted as the function of curing time using coupled cement hydration-thermodynamic model. The ITZ volume fraction is analytically computed based on aggregate particle size distribution. Multi-level homogenization methods (based on three-phase sphere model for two-phase composite material) are finally implemented to predict the effective properties of mortar and concrete. Here, the equivalent matrix consisted of fine/ coarse aggregate, bulk paste/ mortar and ITZ are obtained with the first and second levels homogenization procedures for mortar/ concrete. To validate the predictability of the models for mortar and concrete, predicted values are compared with independent experimental data sets. The results show a reasonable agreement with experimental results of Poisson’s ratio and Youngs modulus (in the error range of 5 GPa). The influences of ITZ on properties of mortar and concrete are also discussed based on the outcomes.

Extensions of the two-phase double-point material point method to simulate the landslide-induced surge process

Landslide-induced surges, as a complex type of fluid-solid coupling problem, are widespread in mountain regions and cause disastrous consequences. In order to reproduce the entire process of landslide-induced surge, by taking full advantage of material point method (MPM) in simulating large deformation of soil and gravity-driven flow of water, the two-phase double-point material point method (TPDP-MPM) was extended: a new algorithm handling the boundary without setting boundary particles was proposed. The classical submarine block-induced surge test and sand column collapse experiment were numerically simulated by the MPM and verified the effectiveness of the program. After that, the multiphase coupling process of Lituya Bay landslide-induced surge was simulated and verified the reliability of the TPDP-MPM code, which have achieved parallel computing by making use of OpenMP model. By comparing the results of numerical simulation with the model experiment, the two-phase double-point material point method can well simulate the starting, propagation, run-up and reflux stage of landslide-induced surge. Moreover, the extension mechanism of landslide-surge disaster chain in both time and space is revealed from the perspective of energy. This study provides a reliable tool for the analysis and assessment of landslide-induced surge disasters.

Insight on the structural changes of Glass-Ceramics during nanoindentation derived from Reactive Force-Field-Based molecular dynamic simulations

Glass-ceramics (GCs) are preferred over glass or ceramics in certain optical applications including those requiring lower porosity than ceramics and higher transition temperatures than glass. However, due to its material heterogeneity, it is difficult to precisely control the microstructure in GCs to meet specific property targets. The chemical mechanism behind the microstructural changes in the two-phase heterogeneity has not yet been clearly elucidated. In this work, the continuous Reactive Force Field molecular dynamics nanoindentation algorithm was developed and used to study the mechanism of structural evolution during nanoindentation. It was found that crystalline phases (CP) had the maximum load at the same indentation depth. The number of point defects of CP was more than glass-crystalline phase (GCP) at the end of loading. However, after total unloading, the opposite was observed with the number of point defects in GCP more than that in CP. The details in GCP bonding indicated that the formation of irreversible supersaturated bonds hindered the healing of defects while promoting the annihilation of pores. The evolution of pores and the typical chemical changes of GCP in the nanoindentation process had also been explored, which proves to be helpful in understanding the behaviors of two-phase heterogeneous materials at the nanoscale.

On the fracture mechanism of rock-like materials with interbedded hard-soft layers under Brazilian tests

The fracture of layered rocks subjected to tensile stress is involved in various subsurface energy-related activities. Many studies have numerically investigated the fracture evolution behaviour and Brazilian tensile strength (BTS) of layered rock in Brazilian tests. However, the fracture mechanism of layered rocks, especially those with interbedded hard-soft layers, is still not well understood. This is mainly due to the fact that the layered rocks were often modelled as two-phase materials only consisting of either rock matrix with layer interfaces or hard and soft layers without explicitly considering layer interfaces. In this study, rock-like discs interbedded with hard and soft layers are prepared with a dimension of 40 mm in diameter and 15 mm in thickness. The uniaxial compressive strength (UCS), BTS, and Young’s modulus of hard layers are 49 MPa, 6.7 MPa, and 10 GPa, respectively, while those of soft layers are 17 MPa, 3.2 MPa, and 8.0 GPa, respectively. The layered discs are tested with inclination angles between 0° and 90° at 15° interval under Brazilian tests with a loading rate of 0.24 mm/min. Then, three-dimensional layered models comprised of soft layers, hard layers, and layer interfaces are numerically established. Their mechanical behaviours are described by a newly developed constitutive model that can capture the tensile and compressive damage of rock-like materials under various loading scenarios. After validating against experimental results, the effects of Young’s modulus of layer interface and mechanical contrast of hard-to-soft layers on the stress distribution, crack initiation and propagation mechanisms, and peak load of layered discs with various inclination angles are numerically explored. It is observed that the effects of interface stiffness and mechanical contrast ratio on the peak load and fracture mechanism are layer orientation dependent.

Effect of nodes on mechanical properties and microstructure of laminated bamboo lumber units

Mechanical properties of laminated bamboo lumber (LBL) units with and without nodes were experimentally studied under various loading conditions such as compression along parallel and perpendicular to the grain as well as tension and shear along parallel to the grain direction. Small specimens were carefully manufactured from Moso bamboo investigate to the effect of nodes on key mechanical properties including strength, ductility, elastic modulus and failure modes under considered loading cases. Results showed that nodes clearly have some beneficial effect on compression resistance of LBL units, albeit the effect is dependent on grain direction. On the other hand, the presence of nodes showed an adverse effect on the tensile resistance but did not have any meaningful effect on shear resistance. Elastic modulus under different loading conditions was also affected due to the presence of nodes. The behavior of LBL units under compression and shear were nonlinear and showed good agreement with Ramberg-Osgood type analytical models when calibrated using obtained results. In addition, the microstructure of LBL units was scanned using an electron microscope and it was obvious that those units are a two-phase composite material like natural bamboo.

Effective Medium Model Applied to Biopolymer Solutions.

Studying dielectric properties of heterogeneous systems is challenged by a problem of uncertainty of the ratio between dielectric permittivity of the system and dielectric permittivities of its components. Such ratios can be obtained in some cases using theoretical effective medium models. However, such models have not yet been developed for all the systems possible. Particularly, there is no effective medium model with filamentary inclusions. Such a theoretical model elaborated based on the fundamental principles of electrodynamics of continuous media is suggested in the present work. Any point of a filamentary inclusion with a length that is significantly greater than the thickness can be regarded as being located in a long cylinder-like fragment of the inclusion with stochastic direction of the cylinder axis relative to the external electric field. With this regard, electric field strength and electric induction values were averaged across the entire volume of a two-phase dielectric material. As a result, a model linking the dielectric permittivity of the two-phase system and the dielectric permittivities of both phases was elaborated. The model appears to be highly relevant for studying solutions of biopolymers, such as nucleic acids, fibrillar proteins and protein aggregates, polysaccharides, by means of electrical impedance spectroscopy, dielectric spectroscopy, and terahertz time-domain spectroscopy. The suggested theoretical model was successfully validated on a DNA solution within the terahertz region.

Numerical simulation of NEPCM series two-layer solidification process in a triple tube with porous fin

In this paper, the solidification of two-phase change materials (PCM) in a triple tube with porous fins and nanoparticles is investigated. RT35 and RT50 are considered as the PCM. The enthalpy-porosity method is used for simulating the solidification. The effects of the storage chamber geometry, non-Newtonian PCM, placement of PCMs with different melting points in the tubes, porous fins, and nanoparticles on the PCM solidification are evaluated. The results show that the finned triple tube has a better solidification performance than the finned double tube. The solidification rate of PCM is decreased by increasing the radius of the middle tube and decreasing the length of the fins attached to this tube. In the case of applying two PCM layers, the solidification time is decreased using RT35 in the middle tube and RT50 in the outer one. The addition of a nanoparticle, increasing its volume fraction and using porous fins improve the solidification. Decreasing the Darcy number and porosity coefficient also enhances the solidification by 7%–27%. The solidification rate is increased by 37% and 47% using the non-Newtonian PCM and Al2O3 nanoparticles, respectively.

Two deterministic methodologies for estimation of OGIP by production dynamics diagnostic of gas-condensate reservoir

This study presents two independent methodologies for estimation of original gas in place (OGIP) by production dynamics diagnostic of gas-condensate reservoir with no-flow outer boundary based on black-oil concept. Classic Blasingame decline-type curves are also extended to apply in gas-condensate reservoir to calculate kh . Both numerically simulated case and field data are used to demonstrate the applicability and validity of proposed methodologies. One method develops a novel analytical model to obtain average reservoir pressure, OGIP and Diatz shape factor at the same time by coupling flow equation of gas-condensate reservoir for boundary dominated flow (BDF) and general material balance equation (GMBE). The two-phase variable-rate flow equation at late time for BDF is clearly and concisely derived in this study in terms of defined two-phase pseodopressure and two-phase material balance pseudotime. In addition, another innovative, simple and effective method for estimation of OGIP is proposed in this study requiring input data of only cumulative production of well and reservoir fluid PVT characteristics of Constant Volume Depletion (CVD) experiment. The fundamental concept of this method suggests that transient cumulative production GOR is determined by only current gas recovery degree and fluid PVT characteristics of the reservoir. Due to the accurate, simple and relaxed data-requiring nature of this method, widespread use in field to estimate OGIP of gas-condensate reservoir is potentially encouraging. On the contrary, if OGIP is already known, an intermediate equation of the method can also be applied to check accuracy of CVD experiment results from laboratory. The first methodology extends OGIP estimation to gas-condensate reservoir from Blasingame and Lee (1988)’s method for dry-gas reservoir. Often used two-phase z factor, which is inconvenient to evaluate and easy to yield error, for gas-condensate reservoir in material balance equation is avoided in this methodology by applying more analytical and accurate Walsh et al. (1994)’s GMBE instead. The second methodology, to the authors’ knowledge, is the first proposed allowing OGIP estimation of gas condensate reservoir without requiring bottom hole flowing pressure (BHFP), pressure tests and complex calculation.

Plastic energy-based analytical approach to predict the mechanical response of two-phase materials with application to dual-phase steels

A composite made of two phases is considered with a perfect disorder of the phases, and isotropic behavior. The strain hardening behavior of such a composite is modeled under axisymmetric tension. The approach is based on using the strain hardening behavior of the two constituent phases together with a relation between the plastic energy of the two phases. The newly developed analytical model was applied to several dual-phase steel alloys and on iron-silver composite metal. These case studies revealed that the equal-power approach reproduces faithfully the strain hardening behavior of the composite, together with the strain partitioning between the two phases, in good agreement with experiments.

Conditional generative adversarial network driven approach for direct prediction of thermal stress based on two-phase material SEM images

A conditional generative adversarial network (cGAN)-driven approach for the direct prediction of thermal stress is proposed. Synthetic two-phase structure images of ceramic top coat (TC) with CaO–MgO–Al2O3–SiO2 (CMAS) inclusions are established, and the TC matrix and CMAS inclusions are semantically segmented by grayscale. The thermal stresses of the two-phase structure are calculated using image-restoration finite element models (FEMs) under the isothermal process. The training database is established based on a small-scale original dataset of integral structures and their stresses. Each integral TC–CMAS structure and its corresponding stress distribution are partitioned into many local images, using which the cGAN model is trained. The model stresses are generated by the trained cGAN directly from the structure images. The deviations between the predicted stress and the FEM stress are small in most areas of the images. In terms of computing time, the proposed approach has higher stress evaluation efficiency than does the FEM.

Prediction of the mechanical properties of isotropic pure metal-based and two-phase alloy-based porous materials using modified analytical models

This work investigates the applicability and accuracy of the five fundamental analytical models commonly used to estimate the thermophysical properties of porous materials for the prediction of the mechanical behaviour, both compressive and tensile, of isotropic pure metal-based and two-phase alloy-based porous materials. In literature, the prediction of the mechanical behaviour of these advanced engineering materials requires the development of semi-empirical models, which are material-specific and, thus, require empirical constants. The significance of the current investigation is the possibility to optimise the mechanical behaviour of porous metallic materials through the rapid and accurate prediction of their mechano-physical behaviour using non-empirical physically-based prediction models. The work is complemented with the derivation of new combined models with increased accuracy prediction of up to approx. 90% with respect to fundamental models. Although developed for porous materials, the derived combined models could be applied for the accurate and rapid prediction of the thermophysical and mechanical properties of multi-phase materials with unknown microstructure such as two-ductile-phase alloys, nanocomposites, hetero- and harmonic-structured materials, and immiscible alloys.

Estimation of Local Strain Fields in Two-Phase Elastic Composite Materials Using UNet-Based Deep Learning

Estimation of Local Strain Fields in Two-Phase Elastic Composite Materials Using UNet-Based Deep Learning

Analysis of thermal stresses in FGM-matrix media induced by a constant heat generation

The three-dimensional thermal stress field is derived for an elastic medium that contains a spherical inclusion made of an functionally graded material (FGM) embedded in a matrix phase. The material properties in the inclusion phase are assumed to vary linearly while the material properties in the matrix phase are uniform. The presence of a uniform heat source in the inclusion introduces the temperature distribution which generates thermal stresses. The temperature distribution is derived analytically by solving the heat conduction equation. Based on the temperature distribution, the differential equations for the displacement field are derived for both the inclusion and matrix phases. The displacement for the matrix phase is solved analytically while the displacement for the FGM inclusion phase is solved semi-analytically using the method of weighted residuals. Only a single differential equation needs to be solved. To the authors’ best knowledge, this is the first attempt to express the thermal stress field semi-analytically. Unlike the conventional two-phase composite materials in which the von Mises stress is discontinuous at the interface of the inclusion and the matrix, the von Mises stress in this model shows continuity at the interface.

Minimization of the p-Laplacian first eigenvalue for a two-phase material

We study the problem of minimizing the first eigenvalue of the p-Laplacian operator for a two-phase material in a bounded open domain Ω⊂RN, N⩾2 assuming that the amount of the best material is limited. We provide a relaxed formulation of the problem and prove some smoothness results for these solutions. As a consequence we show that if Ω is of class C1,1, simply connected with connected boundary, then the unrelaxed problem has a solution if and only if Ω is a ball. We also provide an algorithm to approximate the solutions of the relaxed problem and perform some numerical simulations.

Effect of the heat treatment of CH3NH3PbI3 perovskite on its electrical and photoelectric properties

The effect of the annealing of CH3NH3PbI3 perovskite on its electrical, photoelectric and optical properties has been estimated. The annealing leads to a two-phase structure consisting of perovskite and lead iodide, whose relative concentrations depend on the annealing temperature. The formation of a PbI2 phase in a perovskite film upon heating leads to a decrease in the conductivity and photoconductivity of two-phase material, which contradicts the assumption of a decrease in recombination associated with PbI2, obtained by measuring the parameters of a solar cell.

Electrochemical Oscillation during Galvanostatic Charging of LiCrTiO4 in Li-Ion Batteries.

In the late 1960s, the establishment of Prigogine’s dissipative structure theory laid the foundation for the (electro)chemical oscillation phenomenon, which has been widely investigated in some electrochemical reactions, such as electro-catalysis and electro-deposition, while the electrochemical oscillation of Li-ion batteries has just been discovered in spinel Li4Ti5O12 a few years before. In this work, spinel LiCrTiO4 samples were synthesized by using a high-temperature solid-state method, characterized with SEM (Scanning electron microscope), XRD (X-ray diffraction), Raman and XPS (X-ray photoelectron spectroscopy) measurements, and electrochemically tested in Li-ion batteries to study the electrochemical oscillation. When sintering in a powder form at a temperature between 800 and 900 °C, we achieved the electrochemical oscillation of spinel LiCrTiO4 during charging, and it is suppressed in the non-stoichiometric LiCrTiO4 samples, especially for reducing the Li content or increasing the Cr content. Therefore, this work developed another two-phase material as the powder-sintered LiCrTiO4 exhibiting the electrochemical oscillation in Li-ion batteries, which would inspire us to explore more two-phase electrode materials in Li-ion batteries, Na-ion batteries, etc.

Stochastically homogenized peridynamic model for dynamic fracture analysis of concrete

Dynamic compact tension tests in concrete are investigated using an intermediately-homogenized peridynamic (IH-PD) model, and the results are compared with a fully-homogenized peridynamic (FH-PD) model as well as with experimental data from the literature. In the IH-PD model, concrete is considered as a two-phase material composed of aggregate and mortar, partially homogenized via a stochastic procedure. Both the FH and IH-PD models capture well the experimentally measured reaction-force time-evolution and crack paths for a wide range of dynamic loading rates, without the need for an explicit representation of microstructure geometry of the concrete material or of rate-dependent parameters. The IH-PD model is more accurate than the FH-PD in reproducing the peak loads and produces crack path tortuosity and randomness, similar to what is observed experimentally. These benefits come from the preservation of some micro-scale heterogeneity, stochastically generated to match the concrete’s aggregate volume fraction. We also find that it matters where one measures the reaction force when trying to connect it to fracture and damage progression in the sample: only when measured on the dynamically loaded side of the pre-notch are features in the reaction-force profile matching critical moments like crack initiation, crack branching, and sample final failure. These results provide guidance for future experiments seeking best placement of damage detection sensors and using elastic wave signal analysis in structural health-monitoring of concrete structures.

Random Auxetic Porous Materials from Parametric Growth Processes

We introduce a computational approach to optimize random porous materials via parametric growth processes. We focus on the problem of minimizing the Poisson’s ratio of a two-phase porous random material, which results in an auxetic material. Initially, we perform a parametric optimization of the growth process. Afterward, the optimized parametric growth process implicitly generates an auxetic random material. Namely, the growth process intrinsically entails the formation of an auxetic material. Our approach enables the computation of large-scale auxetic random materials in commodity computers. We also provide numerical results indicating that the computed auxetic materials have close to isotropic linear elastic behavior and physical tests revealing auxetic behavior.