Representation Of Microstructure Research Articles

Quantitative representation of directional microstructures of single-crystal superalloys in cyclic crystal plasticity based on neural networks

Nickel-based single-crystal alloys undergo microstructural degradation induced by thermal exposure. The directional rafting of microstructures significantly affects the mechanical properties and makes the material anisotropic. For structural design, establishing a quantitative description of microstructural effects in a constitutive model becomes essential and is still a tough research topic in multi-scale materials modeling. In the present work, the fabric tensor was correlated with the anisotropic cyclic crystal plasticity of nickel-based single-crystal alloys with the help of neural networks. The microstructural representative volume elements with various single-crystal morphologies were generated by the phase-field method and the deformation behaviors were studied under different crystal orientations and loading configurations. The neural network analysis confirmed that the fabric tensor can present anisotropic single-crystallographic microstructural features and describe mechanical behavior under both monotonic and cyclic multi-axial loading conditions. The history-dependent anisotropic cyclic hardening or softening behavior of the material can be captured by the introduced microstructural state variable. A principal component analysis (PCA) aided gradient-based attribution method was proposed to evaluate the importance of input variables. The characterization of different material components and their contribution to the stress–strain relationships are investigated and validated. The fabric tensor was verified to be an effective microstructural indicator for the continuum plasticity of single-crystal alloys.

Microstructure evolution and mechanical properties of pulse high current diffusion bonding γ-TiAl alloy to Ti2AlNb alloy

The development of lightweight high-temperature materials and their processing methods are receiving increasing attention as the need for improved performance and energy efficiency in aero-engines increase. In this study, the γ-TiAl alloy was successfully soundly bonded to Ti2AlNb alloy by pulsed high current (PHC) diffusion welding. The effect of different high level (HL)/low level (LL) of composite pulse current on the microstructure and mechanical properties of the joints have been studied. The representative interface microstructure of PHC-950 °C TiAl/Ti2AlNb joint was γ-TiAl substrate/diffusion bonding zone/Ti2AlNb impacted zone/Ti2AlNb substrate. The diffusion bonding zone was composed of continuous equiaxed α2 grains and a small amount of B2 and O phases. The α2 phase in the diffusion bonding zone was mainly transformed from the γ phase in γ-TiAl substrate and the B2 and O phase in Ti2AlNb substrate. The composite pulse current has a significant promoting effect on the diffusion of elements and joint formation. The diffusion coefficients of DAl and DNb in hot-pressing (HP, without current effect) diffusion welding joint at interface were 2 × 10−14 m2/s and 0.92 × 10−14 m2/s, respectively. In the representative PHC-950 °C joint with HL/LL = 12/2 cycles (single cycle duration 3.3 ms), diffusion coefficients of DAl-12/2, DNb-12/2 at interface were 19.62 × 10−14 m2/s, 13.34 × 10−14 m2/s, respectively. Increasing the duration of LL would weaken the current effect. The current waveform parameters were tuned to HL/LL = 12/4 and 12/6 cycles, the diffusion coefficients of DAl-12/4, DNb-12/4DAl-12/6 and DNb-12/6 were reduced to 15.69 × 10−14 m2/s, 12.49 × 10−14 m2/s, 15.31 × 10−14 m2/s and 10.99 × 10−14 m2/s, respectively. The PHC-950 °C joints have the highest shear strength of 257.3 MPa at HL/LL = 12/2 cycles, reaching 83.3% of the base material strength. The HP-950 °C TiAl/Ti2AlNb joint has a shear strength of 230.5 MPa, reaching 74.6% of the base material strength. The shear strength of PHC-950 °C joints at HL/LL = 12/4 and 12/6 reduced to 205.3 MPa, 195.8 MPa due to insufficient element diffusion and damages the bonding quality. This work provides a strategy that contributes to reduce the thermal damage of base metal and improve the joint forming efficiency.

Feasibility of postoperative diffusion-weighted imaging to assess representations of spinal cord microstructure in cervical spondylotic myelopathy.

Diffusion basis spectrum imaging (DBSI) has shown promise in evaluating cervical spinal cord structural changes in patients with cervical spondylotic myelopathy (CSM). DBSI may also be valuable in the postoperative setting by serially tracking spinal cord microstructural changes following decompressive cervical spine surgery. Currently, there is a paucity of studies investigating this topic, likely because of challenges in resolving signal distortions from spinal instrumentation. Therefore, the objective of this study was to assess the feasibility of DBSI metrics extracted from the C3 spinal level to evaluate CSM patients postoperatively. Fifty CSM patients and 20 healthy controls were enrolled in a single-center prospective study between 2018 and 2020. All patients and healthy controls underwent preoperative and postoperative diffusion-weighted MRI (dMRI) at a 2-year follow-up. All CSM patients underwent decompressive cervical surgery. The modified Japanese Orthopaedic Association (mJOA) score was used to categorize CSM patients as having mild, moderate, or severe myelopathy. DBSI metrics were extracted from the C3 spinal cord level to minimize image artifact and reduce partial volume effects. DBSI anisotropic tensors evaluated white matter tracts through fractional anisotropy, axial diffusivity, radial diffusivity, and fiber fraction. DBSI isotropic tensors assessed extra-axonal pathology through restricted and nonrestricted fractions. Of the 50 CSM patients, both baseline and postoperative dMR images with sufficient quality for analysis were obtained in 27 patients. These included 15 patients with mild CSM (mJOA scores 15-17), 7 with moderate CSM (scores 12-14), and 5 with severe CSM (scores 0-11), who were followed up for a mean of 23.5 (SD 4.1, range 11-31) months. All preoperative C3-level DBSI measures were significantly different between CSM patients and healthy controls (p < 0.05), except DBSI fractional anisotropy (p = 0.31). At the 2-year follow-up, the same significance pattern was found between CSM patients and healthy controls, except DBSI radial diffusivity was no longer statistically significant (p = 0.75). When assessing change (i.e., postoperative - preoperative values) in C3-level DBSI measures, CSM patients exhibited significant decreases in DBSI radial diffusivity (p = 0.02), suggesting improvement in myelin integrity (i.e., remyelination) at the 2-year follow-up. Among healthy controls, there was no significant difference in DBSI metrics over time. DBSI metrics derived from dMRI at the C3 spinal level can be used to provide meaningful insights into representations of the spinal cord microstructure of CSM patients at baseline and 2-year follow-up. DBSI may have the potential to characterize white matter tract recovery and inform outcomes following decompressive cervical surgery for CSM.

Evaluating the efficacy of alternative small scale test methodologies in deriving the mechanical properties of additive manufactured materials

With the continuous drive of the aerospace industry to implement additive manufactured (AM) components into the next generation of aero-engines, to benefit from the near net shape and weight saving potential that the technology has to offer, the requirement to understand their mechanical performance is also rising in parallel. This is further complicated by the highly localised and transient micro/macro structures that AM produced parts typically possess, raising a question mark over the suitability of more traditional mechanical test approaches where the bulk properties are heavily influenced by the presence of a single defect. As such, alternative experimental approaches, capable of establishing the properties of smaller more intricate structures and geometrically representative microstructures and cross sections, needs to be considered for process parameter down-selection. This paper will explore the suitability of several alternative mechanical test methodologies in characterising the mechanical behaviour of a nickel based superalloy, Inconel 718 (IN718), produced by laser powder bed fusion (LPBF), and establish which results correlate most favourably to those generated through more conventional means. For the first time, results will be presented from several mechanical test methodologies including small punch, shear punch, hardness, nano-indentation and profilometry based indentation plastometry experiments; a set of mechanical test approaches that have yet to be directly compared and discussed in a single study on an additively manufactured material. Findings will be supported by advanced microscopy in the form of field emission SEM and crystallographic texture maps produced through electron back-scattered diffraction.

Multiscale Modelling of Solid Oxide Cells Validated on Electrochemical Impedance Spectra and Polarization Curves

Solid Oxide Cells (SOCs) are high temperature energy-conversion devices which have attracted a growing interest in the recent years. Indeed, this technology presents a high efficiency and a good reversibility in fuel cell (SOFC) and electrolysis (SOEC) modes. Thanks to its flexibility, SOCs can offer technical solutions for the development of a clean hydrogen economy. Nevertheless, SOCs durability is still insufficient for large scale commercialization. Therefore, it is still required to improve the SOCs lifetime by maintaining high performances. For this purpose, it is necessary to better understand the impact of global operating conditions on the local processes taking place in the cell components. Besides, the role of the electrode microstructure on the reaction mechanism is still not precisely understood. From this point of view, the modelling can be an efficient tool to unravel and better analyze all the microscopic processes involved in the cell operation.In this context, a physical-based model has been proposed to investigate the impact of operating conditions on the electrodes reaction mechanisms and cell performances. This model takes into account (i) a 3D representation of the electrode microstructure [1], (ii) a description of the reaction mechanisms in full elementary steps [2,3] and (iii) the SOC geometry with the gas flow configuration [4,5]. This multiscale model has been developed considering a typical cell composed of a dense electrolyte in Y0.148Zr0.852O1.926 (8YSZ) sandwiched between an O2 electrode in La0.6Sr0.4Co0.2Fe0.8O3- d-Ce0.8Gd0.2O2-δ (LSCF-GDC) and an H2 electrode made of Ni and YSZ (Ni-YSZ). The model has been validated using a specific experimental setup which was developed to measure the local polarization curves along the cell length. For this purpose, a specific design of the interconnect has been proposed in order to probe the local current density on the standard studied cells (Fig. 1a) [6]. It has been found that the model is able to reproduce accurately the global and local polarizations curves in SOFC and SOEC modes (Fig. 1a and 1b). The stationary model has been also extended to compute electrochemical impedance spectra by keeping the full description of the reaction mechanisms in elementary steps. This dynamic model, which is able to compute the impedance diagrams at Open Circuit Voltage (OCV) and under polarization, has been compared to the experimental data. As shown in Fig. 1c and 1d, a reasonable agreement has been found between the measurements and the simulations without any fitting.The validated stationary and dynamic model has been used to analyze the cell operation in electrolysis and fuel cell modes. The activated reaction pathways associated with the elementary steps in the active layers have been investigated depending on the position along the cell length. The different contributions arising in the impedance spectra have been also identified and discussed.

DL-MSTO+: A deep learning-based multi-scale topology optimization framework via positive definiteness ensured material representation network

A multi-scale approach to topology optimization has recently emerged due to its lightweight, robust, and multi-functional characteristics. Considering material diversity, an increasing number of materials leads to a computational burden due to numerous design variables and homogenization equations. This study proposes DL-MSTO+, a deep learning-based multi-scale topology optimization framework. The framework consists of two distinct deep neural networks for multi-scale topology optimization problems to reduce the dimensionality of design variables and predict homogenized material properties. First, a generator network learns the low-dimensional representation of a material microstructure in an unsupervised manner. Thus, the trained generator produces a micro-structural image from a low-dimensional vector. Second, a predictor network is trained in a supervised manner to predict the homogenized elasticity matrix for a given micro-structural image. Additionally, the predictor is specifically designed to ensure the positive definiteness of the predicted elasticity matrix. Lastly, the networks are integrated into the algorithm to improve the efficiency of multi-scale topology optimization. The numerical experiments demonstrate higher efficiency for the proposed algorithm than the conventional multi-scale approach. Moreover, the proposed method provides connectable multi-scale designs, and the low-dimensional latent representation enables semantic interpolation between solutions.

Computational homogenization of histological microstructures in human prostate tissue: Heterogeneity, anisotropy and tension-compression asymmetry.

Human prostatic tissue exhibits complex mechanical behaviour due to its multiphasic, heterogeneous nature, with hierarchical microstructures involving epithelial compartments, acinar lumens and stromal tissue all interconnected in complex networks. This study aims to establish a computational homogenization framework for quantifying the mechanical behaviour of prostate tissue, considering its multiphasic heterogeneous microstructures and the mechanical characteristics of tissue constituents. Representative tissue microstructure models were reconstructed from high-resolution histology images. Parametric studies on the mechanical properties of the tissue constituents, particularly the fibre-reinforced hyper-elasticity of the stromal tissue, were carried out to investigate their effects on the apparent tissue properties. These were then benchmarked against the experimental data reported in literature. Results showed significant anisotropy, both structural and mechanical, and tension-compression asymmetry of the apparent behaviours of the prostatic tissue. Strong correlation with the key microstructural indices such as area fractions of tissue constituents and the tissue fabric tensor was also observed. The correlation between the stromal tissue orientation and the principal directions of the apparent properties suggested an essential role of stromal tissue in determining the directions of anisotropy and the compression-tension asymmetry characteristics in normal human prostatic tissue. This work presented a homogenization and histology-based computational approach to characterize the apparent mechanical behaviours of human prostatic or other similar glandular tissues, with the ultimate aim of assessing how pathological conditions (e.g., prostate cancer and benign prostatic hyperplasia) could affect the tissue mechanical properties in a future study.

Crystal plasticity based homogenized model for lamellar colonies of near-α and titanium alloys

The microstructure of near α and Ti-alloys consists of globular α grains, and transformed β colonies, which have a lamellar structure with alternating α hexagonal close packed and β body centered cubic laths. Due to the disparate length scales between the laths of the colonies and the globular α grains, a homogenized representation of the lath microstructure is necessary for computationally feasible and efficient crystal plasticity (CP) based full-field simulations of polycrystalline aggregates of these alloys. Thus, equivalent models of the lath microstructure based on iso-strain and virtual crystal (consisting of both α and β slip systems) assumptions were developed. However, these models fail to capture the response of the lath aggregate (colony), the individual phases (α and β laths), and slip systems, accurately. The deficiencies in the earlier models have been overcome in the equivalent model developed in this work in which the individual laths are allowed independent iso-stress and iso-strain conditions, while strain compatibility and stress equilibrium of the lath aggregate is ensured by enforcing periodic motion of the laths and traction balance at the interface. Additionally, an anisotropic size dependent CP constitutive model, due to the semi-coherent nature of the lath interfaces, is also developed for the α and β laths in the colony. The improvements of the present model are elucidated by comparing its response with the existing equivalent models and periodic CP finite element method simulations of a lath representative volume element for two different sets of Euler angles and four different deformation histories. The comparisons clearly show that the present model is significantly more accurate than the existing models in predicting the stress–strain response of the lath aggregate and the individual phases, as well as the slip activities on the various systems. The formulation of the developed model is generic and can also be applied to other materials with lamellar microstructure.

Multiscale modelling of irradiation damage behavior in high entropy alloys

The increasingly harsh environment of the nuclear reactors and the insurmountable flaws of in-service materials have created an urgent need for the development of the brand-new alloys. For last decade, the high-entropy alloys (HEAs), a novel composition-design strategy, have received much attention due to their promise for the nuclear fields. The application of the multiscale modelling is to explore the irradiation performance and underlying mechanisms of HEAs. Abundant results and data deepen the understanding of the irradiation response, and accelerate the development of advanced irradiation-resistant HEAs. This review introduces the state-of-art multiscale modelling used for studying the irradiated properties of HEAs. Representative irradiation-induced microstructures and properties, as well as damage, are summarized. By strengthening the application of multiscale modelling, a rational design of high irradiation-resistant HEAs is expected.

A versatile and highly efficient algorithm to generate representative microstructures for heterogeneous materials

In this study, a novel approach based on the maximum penetration-biased (MPB) algorithm is proposed to rapidly generate representative volume elements (RVEs) for advanced composites. This method is capable of handling various microstructural features such as nonuniform distribution of high-volume fractions, concave or convex inclusions and the control of inter-inclusion distances. Statistical functions from short-range to long-range demonstrate that the resulting microstructures are complete spatial random, and the microstructures observed in realistic composites can be reproduced by the proposed algorithm. Accurate prediction for the elastic properties and transverse isotropy of the generated microstructures with varying inclusion shapes using homogenization method further verify the validity of the developed method. A nonlinear damage study compared to the circular inclusion reveals that the capsule shape leads to a reduction of strength of unidirectional fiber reinforced composites under transverse tension or compression while the lobular inclusion presents a deterioration of strength under tension but an enhancement of strength in compression. The MPB algorithm provides an effective tool for micromechanical assessment, quantitative research and data-driven studies such as machine learning of composites.

Three-dimensional microstructure reconstruction for two-phase materials from three orthogonal surface maps

Introduction: A full three-dimensional (3D) microstructure characterization that captures the essential features of a given material is oftentimes desirable for determining critical mechanisms of deformation and failure and for conducting computational modeling to predict the material’s behavior under complex thermo-mechanical loading conditions. However, acquiring 3D microstructure representations is costly and time-consuming, whereas 2D surface maps taken from orthogonal perspectives can be readily produced by standard microscopic procedures. We present a robust and comprehensive approach for such 3D microstructure reconstructions based on three electron backscatter diffraction (EBSD) maps from orthogonal surfaces of two-phase materials.Methods: It is demonstrated that processing surface maps by spatial correlation functions combined with principal component analysis (PCA) results in a small set of unique descriptors that serve as a representative fingerprint of the 2D maps. In this way, the differences between surface maps of the real microstructure and virtual surface maps of a reconstructed 3D microstructure can be quantified and iteratively minimized by optimizing the 3D reconstruction.Results: To demonstrate the applicability of the method, the microstructure of a metastable austenitic steel in the two-phase region, where austenite and deformation-induced martensite coexist at room temperature, was characterized and reconstructed. After convergence, the synthetic 3D microstructure accurately describes the experimental system in terms of physical parameters such as volume fractions and phase shapes.Discussion: The resulting 3D microstructures represent the real microstructure in terms of their characteristic features such that multiple realizations of statistically equivalent microstructures can be generated easily. Thus, the presented approach ensures that the 3D reconstructed sample and the associated 2D surface maps are statistically equivalent.

Incorporating dynamic recrystallization into a crystal plasticity model for high-temperature deformation of Ti-6Al-4V

During hot deformation of (α+β) titanium alloys, the simultaneous action of strain and temperature in the (α+β) regime facilitates dynamic recovery, dynamic recrystallization (DRX), and phase transformations via non-equilibrium paths. DRX is manifested in the form of fine recrystallized α or β grains. In the present study, a two-phase crystal plasticity finite element framework (CP-DRX) has been developed which incorporates DRX kinetics into the crystal plasticity (CP) model to predict the flow characteristics of Ti-6Al-4V alloys during thermo-mechanical processing. The CP slip system parameters, as well as elastic properties from both α and β phases of Ti, are calibrated for different strain rate conditions. An EBSD-informed two-phase microstructure representation has been utilized in the CP-DRX framework to explore the time-dependent evolution of DRX microstructure and crystal orientation for different strain rate conditions. The proposed CP-DRX can capture the evolution of crystal orientation and plastic flow stress–strain response of polycrystalline Ti-6Al-4V during the deformation process. Furthermore, the proposed model is able to capture the softening behavior, observed in average stress–strain response from experiments performed using a Gleeble thermomechanical simulator and predict the recrystallization texture.

Creep-fatigue assessment of martensitic welds based on numerically determined local deformation

Abstract The low cycle fatigue and creep-fatigue behavior of base material and similar welded joints of martensitic steel Grade 92 were examined in this work. Several low cycle fatigue tests with different loading scenarios: fatigue tests with strain-controlled hold time, fatigue tests with strain-controlled amplitudes, and load-controlled hold times, were performed at 873 K. The tests were evaluated with regard to fatigue lifetime, peak stress, the evolution of relaxation stress or creep strain, and failure location. The effect of amplitude level, hold time modus and hold time length on the lifetime of the specimens was investigated using lifetime and damage assessment methods based on strain energy approaches. The numerical simulations for the determination of the evolution of local strains and stresses were done using a viscoplastic material model of Chaboche type, including a strain energy based damage formulation. For the parameter identification, tests were carried out on the specimens made of base metal, welded joint, weld metal, and with microstructure simulated specimens aiming to obtain representative microstructures of the fine grain, intercritical, and coarse grain heat affected zone. The numerical assessment of the local stress, strain, and damage distribution explains the smaller lifetime of the welded joint specimens.

Tuning selectivity and activity of the electrochemical glycerol oxidation reaction by manipulating morphology and exposed facet of spinel cobalt oxides

To further explore the electrooxidation mechanism of biomass-based compounds, it is highly desirable to regulate the proportion of reactive facets and identify facet-governing reactivity through crystal facet engineering. In this study, octahedral and cubic cobalt spinel oxide (Co3O4), each exclusively exposed by one specific type of facet, are selected as two representative microstructure models for tuning the selectivity and productivity of electrochemical glycerol oxidation reaction. The results indicate that the {111}-dominant octahedral Co3O4 plane with a higher population of Co2+ sites exhibits superior electrocatalytic activity for glycerol oxidation compared with the {001}-dominant cubic Co3O4, allowing nearly 65% of glycerol to be converted into a high-value-added dihydroxyacetone (DHA) compound. The average DHA production rate over octahedral Co3O4 (2.5 μmol cm−2h−1) are approximately 3.5 times greater than that over cubic Co3O4 (0.7 μmol cm−2h−1). Electrochemical studies and surface atomic configuration analysis reveal that {111}-dominant octahedral Co3O4 with a higher density of active cobalt ion yields unique reactant adsorption and charge transfer, leading to increased glycerol oxidation reactivity and productivity. The present study emphasizes the significance of controlling the highly active facet in developing efficient and selective electrocatalysts.

3D DEM model simulation of asphalt mastics with sunflower oil

A three-dimensional particle model, based on the asphalt mastic micro-structure representation following a discrete element model framework, was developed to investigate the influence of sunflower oil (rejuvenator) on the rheological properties of asphalt mastic. Dynamic shear rheometer tests in laboratory, for a frequency range of 0.1–20 Hz and temperatures in a range between 20 and 80 ^{circ }C, were carried out in order to assess the viscoelastic behaviour of asphalt mastics containing different oil-to-bitumen content by mass proportions (2.5–20%). Master curves were constructed for two reference temperatures (30 ^{circ }C and 50 ^{circ }C). Experimental results showed that the increase in sunflower oil content resulted in a progressive decrease in viscosity. However, the rheological behaviour of the mastic containing the highest oil amount could not be properly represented in master curves, indicating that the specimen had a different rheological behaviour when compared with the lower oil contents responses. Numerical simulations of rheometer tests were carried out with an asphalt mastic particle assembly that emulated the experimental procedure. The viscoelastic contacts within the asphalt mastic assembly were simulated with a generalized Kelvin contact model. A calibration procedure was derived based on the fitting of laboratory data. The simulations were shown to have a good agreement with laboratory values. The average errors for the dynamic shear modulus and phase angle were 3.4% and 4.0%, respectively, considering both temperatures of analysis. Finally, a considerable improvement was accomplished in comparison with the numerical response obtained with the often-used Burgers model.

Quantum annealing for microstructure equilibration with long-range elastic interactions

We demonstrate the use and benefits of quantum annealing approaches for the determination of equilibrated microstructures in shape memory alloys and other materials with long-range elastic interaction between coherent grains and their different martensite variants and phases. After a one dimensional illustration of the general approach, which requires to formulate the energy of the system in terms of an Ising Hamiltonian, we use distant dependent elastic interactions between grains to predict the variant selection for different transformation eigenstrains. The results and performance of the computations are compared to classical algorithms, demonstrating that the new approach can lead to a significant acceleration of the simulations. Beyond a discretization using simple cuboidal elements, also a direct representation of arbitrary microstructures is possible, allowing fast simulations with currently up to several thousand grains.

A sequential mobile packing algorithm for micromechanical assessment of heterogeneous materials

A new non-uniform sequential mobile packing (NSMP) algorithm featuring an efficient collision detection scheme was developed to rapidly generate representative volume elements (RVEs) for advanced heterogeneous and/or composite material systems with either spherical or cylindrical inclusions and a broad range of microstructural characteristics (i.e., various inclusion orientations and sizes, and agglomerations). Statistical assessment of inclusion spatial dispersion using nearest neighbor-based and pair correlation functions revealed that the NSMP algorithm generated RVEs with realistic microstructures for all cases considered. Subsequent statistical finite element micromechanical modeling was conducted to compute the effective properties for each generated microstructure. A case study for a 3D-printed nanocomposite material revealed that a combination of aligned and misoriented rod inclusions was the most representative microstructure. Contour plots of normalized effective stiffness for the 3D-printed composites and normalized average hydrostatic stress in the matrix phase enabled comparison of RVEs with different microstructures. The material system with aligned rod inclusions benefited from simultaneous high effective stiffness and effective load transfer to the inclusions (at higher inclusion volume fractions), which is indicated by low average hydrostatic stress in the matrix. The microstructures comprising spherical inclusions exhibited moderate stiffness, while those with clustered misoriented rod inclusions had the lowest effective stiffness and load transfer to the inclusions. The NSMP algorithm can be used for further microstructural optimizations and assessments of renifornced or porous heterogeneous and/or composite materials using machine learning, while the generated contours can be used as general design guidelines.

Simulated diffusion spreadability for characterizing the structure and transport properties of two-phase materials

Time-dependent diffusion processes between phases of heterogeneous materials are ubiquitous in a variety of contexts in the physical, chemical, and biological sciences. Examples of such materials include composites, porous materials, geological media, cellular solids, polymer blends, colloids, gels, and biological media. The recently developed diffusion spreadability, S(t), provides a direct link between time-dependent interphase diffusive transport and the microstructure of two-phase materials across length scales (Torquato, 2021); thus making S(t) a powerful dynamic means for classifying all statistically homogeneous microstructures, spanning from anti-hyperuniform to hyperuniform. It was shown that the small-, intermediate-, and long-time behaviors of S(t) are directly determined by the small-, intermediate-, and large-scale structural features of the material. Moreover, the spreadability can be applied as a physical-property based tool for microstructural characterization in the absence of or as supplement to scattering information. In this work, we develop a computationally efficient algorithm for ascertaining S(t) directly from digitized representations of material microstructures via random-walk techniques. Our algorithm yields the time-dependent local walker concentration field c(x,t), a quantity not previously examined in the context of the spreadability, enabling us to compute the entropy production rate ṡ(t) of the associated diffusion process, which is a quantity related to the rate of energy dissipation. We also derive exact analytical expressions for ṡ(t), and find that hyperuniform materials have smaller dissipation than any nonhyperuniform materials. Lastly, we use our algorithm to compute, for the first time, the more general case of the spreadability in which the phase diffusion coefficients are distinct and provide a method for extracting the effective diffusion coefficient of the two-phase material from such data. We apply our algorithm to a variety of two- and three-dimensional simulated model (non)hyperuniform microstructures to assess their large-scale structures and diffusion properties. Given previously identified connections between the spreadability and certain nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) procedures, our algorithm is also pertinent to such experimental studies. Overall, our algorithm has practical use in the discovery and design of heterogeneous materials with desirable time-dependent diffusion properties.

Effect of biomaterial stiffness on cardiac mechanics in a biventricular infarcted rat heart model with microstructural representation of in situ intramyocardial injectate.

Intramyocardial delivery of biomaterials is a promising concept for treating myocardial infarction. The delivered biomaterial provides mechanical support and attenuates wall thinning and elevated wall stress in the infarct region. This study aimed at developing a biventricular finite element model of an infarcted rat heart with a microstructural representation of an in situ biomaterial injectate, and a parametric investigation of the effect of the injectate stiffness on the cardiac mechanics. A three-dimensional subject-specific biventricular finite element model of a rat heart with left ventricular infarct and microstructurally dispersed biomaterial delivered 1 week after infarct induction was developed from ex vivo microcomputed tomography data. The volumetric mesh density varied between 303 mm-3 in the myocardium and 3852 mm-3 in the injectate region due to the microstructural intramyocardial dispersion. Parametric simulations were conducted with the injectate's elastic modulus varying from 4.1 to 405,900 kPa, and myocardial and injectate strains were recorded. With increasing injectate stiffness, the end-diastolic median myocardial fibre and cross-fibre strain decreased in magnitude from 3.6% to 1.1% and from -6.0% to -2.9%, respectively. At end-systole, the myocardial fibre and cross-fibre strain decreased in magnitude from -20.4% to -11.8% and from 6.5% to 4.6%, respectively. In the injectate, the maximum and minimum principal strains decreased in magnitude from 5.4% to 0.001% and from -5.4% to -0.001%, respectively, at end-diastole and from 38.5% to 0.06% and from -39.0% to -0.06%, respectively, at end-systole. With the microstructural injectate geometry, the developed subject-specific cardiac finite element model offers potential for extension to cellular injectates and in silico studies of mechanotransduction and therapeutic signalling in the infarcted heart with an infarct animal model extensively used in preclinical research.

A deep learning convolutional neural network and multi-layer perceptron hybrid fusion model for predicting the mechanical properties of carbon fiber

Recently, deep learning methods have become one of the hottest topics in predicting material properties, however, one bottleneck in current research is the simultaneous analysis of heterogeneous data. In this study, a deep learning fusion model is developed for the first time to predict the material properties of carbon fiber monofilament using textual (macroscopic properties of composites and matrix) and visual (two-point statistics of microstructures) data. For this, 1200 stochastic microstructures are generated using the greedy-based generation (GBG) algorithm. Then, the statistical representations of microstructures are determined using two-point statistics and the macroscopic properties are calculated based on a micro-scale finite element (FE) simulation. Finally, the visual and textual data are fed into the convolutional neural network (CNN) and multi-layer perceptron (MLP) fusion model for predicting the mechanical properties of carbon fibers. The developed hybrid CNN-MLP fusion model achieves encouraging average testing R2 of longitudinal modulus, transverse modulus, in-plane shear modulus, major Poisson’s ratio, and out-of-plane shear modulus of carbon fibers with values of 0.991, 0.969, 0.984, 0.903, and 0.955, respectively. Thus, the proposed strategy provides a promising framework for predicting material properties via multisource heterogeneous data and is expected to accelerate the smart design and optimization of materials.