Micromechanical Model Research Articles

Continuous damage of concrete structures due to reinforcement corrosion: A micromechanical and multi-physics based analysis

Deterioration of concrete and composite structures due to the corrosion of embedded steel components (rebar, structural steel components, and steel fiber, etc.) is a self-accelerating process involving multiple chemophysical processes that occur concurrently in the heterogeneous structure of concrete. The multiple-inclusion matrix of concrete and the multi-chemophysics nature of steel corrosion synergistically challenge an accurate analysis and evaluation of the deterioration process using homogeneity-based continuum mechanics. This study presents a three-dimensional micromechanical model developed for quantifying the continuous deterioration of concrete by steel corrosion. Continuous damage theory of solid-state materials was applied to a steel-concrete sample that consists of mortar, aggregate, and steel phases as were reconstructed from high-resolution X-ray CT images. With due consideration of the variations in environmental temperature and moisture, the complex chemophysical processes involved in corrosion-induced deterioration of concrete were solved concurrently using finite element analysis. Results of the study indicate that capillary suction in a variably saturated concrete plays an important role in steel corrosion and that removal of chloride by an externally applied electrical field can effectively mitigate steel corrosion and the incurred concrete deterioration.

Research regarding the influence of size on the compressive strength of spontaneous combustion coal gangue concrete utilizing the diffusion model

This passage employs the U2-Net model to segment images of spontaneous combustion gangue coarse aggregate (SCGCA) concrete cross-section and randomly placed aggregate library. These methods are used to construct the dataset and subsequently establish and train the diffusion model. Based on this model, a two-dimensional micro-mechanical model of SCGCA concrete was constructed, accurately reproducing the distribution, grading, and shape of the aggregate in the concrete. The size effect of SCGCA concrete is analyzed through experimentation and numerical simulation of two-dimensional micro-models. The findings of the study reveal that the dimension conversion factors for the 100 mm and 200 mm cubic specimens are 0.92 and 1.12 respectively, which demonstrates the evident size effect of SCGCA concrete. The remarkable coherence between the empirical results and the computational simulation results serves as a powerful validation of the durability and efficacy of the model delineated in this paper. In accordance with the theory of Bažant's size effect, this paper elucidates the size effect law of uniaxial compressive strength in SCGCA concrete models ignited spontaneously at different dimensions.

Analysis of rolling contact and tooth root bending fatigue in a new high-strength steel: Experiments and micromechanical modelling

To find materials that meet the future requirements of increasing load density in wind turbine gear structures, the commonly used reference material, 18CrNiMo7-6, and another high-strength steel were analysed. Their fatigue properties were studied through rolling contact fatigue (RCF) and gear tooth root bending fatigue (TRBF) tests. The reference steel exhibited better fatigue performance under RCF conditions compared to the new steel; however, it was outperformed by the new steel under TRBF conditions. This study aims to understand gear contact fatigue at the microscopic level, moving beyond the macroscopic focus that dominates current research literature. To establish the causal link between the varied fatigue performance observed in these materials, we proposed a multiscale modelling workflow based on crystal plasticity. This crystal plasticity framework is combined with the fatigue indicator parameter (FIP) to explore the fatigue resistance of materials subjected to RCF and TRBF conditions. Emphasis has been placed on the role of retained austenite (RA) in fatigue performance. Utilizing representative elementary volumes (REVs) generated based on statistically representative crystallographic features and measured size distribution of RA, we examined the effects of various RA levels on fatigue resistance. Our findings reveals that the fatigue damage accumulation is significantly influenced by the level of RA. Different fatigue damage accumulation behaviours were observed under RCF and TRBF conditions. These insights offer new perspectives on RA’s role in fatigue resistance and highlight its complex influence under varied loading conditions.

Transverse failure prediction of unidirectional carbon fiber reinforced polymer composites subjected to uniaxial and biaxial loading by stress-triaxiality-dependent computational micromechanics

Accurate characterizing the mechanical behavior of the component materials is crucial for failure predicting of unidirectional carbon fiber reinforced polymer (UD CFRP) composites. A stress-triaxiality-dependent micromechanics model is developed for the transverse failure prediction of the composites in this study, in which the stress triaxiality is innovatively adopted to define the plastic hardening behavior of the matrix material. Therefore, diverse hardening behaviors generated by heterostructures, accurate confirmation of biaxial failure, as well as hardening behavior evolution caused by stress status changes during loading process can be considered. The accuracy performance of the micromechanics model is provided by comparing the predicted results (stress–strain curves, RVE profiles and failure points) with existing experimental data and failure envelopes of failure criterion. The comparison results show that the micromechanics model can accurately capture the failure phenomenon and failure evolution mechanism of the composite under uniaxial and biaxial loadings.

Intra-yarn fibre hybridisation effect on homogenised elastic properties and micro and meso-stress analysis of 2D woven laminae: Two-scale FE model

In this paper, the effect of intra-yarn fibre hybridisation on the homogenised elastic properties and micro- and meso-scale matrix stress fields in 2D woven composite laminae (i.e. plain, 2/2 basket, 2/2 twill and 5-harness satin) is studied with a two-scale homogenisation scheme—employing a representative volume element model at micro-scale and a repeating unit cell model at meso-scale. The study is focused on S-glass/polypropylene/epoxy woven laminae with intra-yarn fibre hybridisation. A modified random sequential expansion algorithm generates microstructure for the micro-mechanical model, and a periodic meso-structure is used to generate the weave architecture for the meso-mechanical model. Both models are verified using analytical models. It is found that intra-yarn fibre hybridisation can significantly alter the homogenised properties as well as the micro- and meso-scale matrix stress fields—depending on the degree of hybridisation (i.e. the combination of S-glass and PP fibre volume fractions). Moreover, the homogenised lamina properties are found to be less sensitive to weave architecture and yarn thickness, but more so to the degree of intra-yarn fibre hybridisation, yarn width and yarn spacing. It is shown that the lamina properties can be tailored, and the micro- and meso-stress fields can be manipulated, by intra-yarn fibre hybridisation and weave architectures.

Micromechanical modeling of longitudinal tensile behavior and failure mechanism of unidirectional carbon fiber/aluminum composites involving fiber strength dispersion

This paper examines the longitudinal tensile behavior and failure mechanism of a new unidirectional carbon fiber reinforced aluminum composite through experiments and simulations. A Weibull distribution model was established to describe the fiber strength dispersion based on single-fiber tensile tests for carbon fibers extracted from the composite. The constitutive models for the matrix and interface were established based on the uniaxial tensile and single-fiber push-out tests, respectively. Then, a 3D micromechanical numerical model, innovatively considering the fiber strength dispersion by use of the weakest link and Weibull distribution theories, was established to simulate the progressive failure behavior of the composite under longitudinal tension. Due to the dispersion of fiber strength, the weakest link of the fiber first fractures, and stress concentration occurs in the surrounding fibers, interfaces, and matrix. The maximum stress concentration factor for neighboring fibers varies nonlinearly with the distance from the fractured fiber. Both isolated and clustered fractured fibers are present during the progressive failure process of the composite. The expansion of fractured fiber clusters intensifies stress concentration and material degradation which in turn enlarges the fractured fiber clusters, and their mutual action leads to the final collapse of the composite.

Symmetry-enforcing neural networks with applications to constitutive modeling

The use of machine learning techniques to homogenize the effective behavior of arbitrary microstructures has been shown to be not only efficient but also accurate. In a recent work, we demonstrated how to combine state-of-the-art micromechanical modeling and advanced machine learning techniques to homogenize complex microstructures exhibiting non-linear and history dependent behaviors (Logarzo et al., 2021). The resulting homogenized model, termed smart constitutive law (SCL), enables the adoption of microstructurally informed constitutive laws into finite element solvers at a fraction of the computational cost required by traditional concurrent multiscale approaches. In this work, the capabilities of SCLs are expanded via the introduction of a novel methodology that enforces material symmetries at the neuron level, applicable across various neural network architectures. This approach utilizes tensor-based features in neural networks, facilitating the concise and accurate representation of symmetry-preserving operations, and is general enough to be extend to problems beyond constitutive modeling. Details on the construction of these tensor-based neural networks and their application in learning constitutive laws are presented for both elastic and inelastic materials. The superiority of this approach over traditional neural networks is demonstrated in scenarios with limited data and strong symmetries, through comprehensive testing on various materials, including isotropic neo-Hookean materials and tensegrity lattice metamaterials. This work is concluded by a discussion on the potential of this methodology to discover symmetry bases in materials and by an outline of future research directions.

Micromechanical Modeling of Cement-Treated Base Materials Considering Recycled Crushed Aggregate Morphology from Construction and Demolition Waste Using Three-Dimensional Discrete Element Method

Abstract This study established a three-dimensional discrete element method (3D DEM) of cement-treated base materials (CTBM), considering the morphology of recycled crushed aggregates (RCAs) derived from construction and demolition waste. Coarse RCA morphology was obtained using X-ray computed tomography and integrated into the DEM model. The linear contact model and linear parallel bond model were selected and key microparameters were determined. The developed 3D DEM model was verified through the actual indirect tensile test of CTBM. Micromechanical analysis, encompassing contact force and displacement fields of particles, was subsequently evaluated based on the virtual uniaxial compression test. The findings revealed that particles near the loading plate exhibited relatively higher contact force, gradually decreasing with distance from the loading position. Regarding the displacement field, the particles closer to the edge of the cross-section and the loading plate on the longitudinal section experienced greater displacement, whereas those in the middle of the specimen and farther from the loading plate had smaller displacements. Furthermore, it was observed that increasing the cement content effectively enhanced the internal contact force and the ability of CTBM to resist uniaxial deformation.

Improved energy method and agglomeration influence of carbon nanotubes on polymer composites

In this paper, the geometric analysis of carbon nanotubes (CNTs) without external loading is carried out by energy method. Based on the theory of molecular mechanics, an improved mechanical model is proposed to predict the energy of armchair carbon nanotubes under stress-free conditions, and the diameter of CNTs is estimated according to the principle of minimum energy. The results show that the diameter obtained by the improved model is larger, but basically consistent with that obtained by conformal mapping. The inversion energy term is added to the modified model, and the inversion energy term related to atomic curvature is characterized by the conization angle. It can be seen from the error that the inversion energy of carbon nanotubes can not be neglected in the stress-free state, especially in the case of small diameter. The agglomeration of nanotubes is one of the important factors, which affects the effective elastic modulus of nanocomposites. Here, a new micro-mechanics model consisting of both agglomeration of CNTs and pure matrix is also presented to analyze its effect on the effective elastic modulus. It is noted from the results that the stiffness of nanocomposites is very sensitive to the CNTs agglomeration.

Experimentally Verified Hybrid Spatial Structure Micromechanical Model for MR Fluid Prepared by the Drying-Free Process

Experimentally Verified Hybrid Spatial Structure Micromechanical Model for MR Fluid Prepared by the Drying-Free Process

Effect of Micromechanical Models on Mechanical Behavior of Functionally Graded Plates Based on a Quasi-3D Hyperbolic Shear Deformation Theory

Five alternative micromechanical models (Voigt, Reuss, Tamura, LRVE, Hashin) are used to predict the valid material properties of a simply-supported functionally graded materials (FGM) plate. The free vibration and static behavior are studied based on a quasi-3D hyperbolic shear deformation theory considering the stretching effect. The profile of an FGM plate is assumed by the power-law, Sigmoid and exponential functions. The numerical results of an FGM plate behavior reveal via Navier-type solution. The temperature effects of the micromechanical models on the fundamental frequency and transverse displacement for an FGM plate are also discussed. By analyzing the influence of different micro-models on the mechanical behavior of an FGM plate, researchers can objectively understand the establishment and differences of structural micromechanical models. And considering the actual high temperature situation, the deformation prediction ability of the structure is predicted. This study provides theoretical guidance for the analysis and modeling of FGM structures for the purpose of engineering practice.

Contribution to micromechanical modeling of the shear wave propagation in a sand deposit

The object of study is the vertical wave propagation in a sand deposit. This paper is aimed at analyzing the vertical wave propagation in a sand deposit through micromechanical modeling that inherently takes account of intergranular slips during deformation. Such a problem, which is part of the general framework of wave propagation in the soil, has long been analyzed using continuum models based on approximate behavior laws. For this purpose, a 2D Discrete Element Method (DEM) model is developed. The DEM model is based on molecular dynamics with the use of circular shaped elements. The intergranular normal forces at contacts are calculated through a linear viscoelastic law while the tangential forces are calculated through a perfectly plastic viscoelastic model. A model of rolling friction is incorporated in order to account for the damping of the grains rolling motion. Different boundary conditions of the profile have been implemented; a bedrock at the base, a free surface at the top and periodic boundaries in the horizontal direction. The sand deposit is subjected to a harmonic excitation at the base. Using this model, the fundamental and resonance frequencies of the deposit are first determined. The former is determined from the low-amplitude free vibration and the latter by performing a variable-frequency excitation test. It is noted that there is a significant gap between the two frequencies, this gap could be attributed to the degradation of the soil shear modulus in the vicinity of the resonance. Such degradation is well proven in classical soil dynamics. The effects of deposit height and confinement on resonance frequency and free-surface dynamic amplification factor are then investigated. The obtained results highlighted that the resonance frequency is inversely proportional to the deposit’s thickness whereas the dynamic amplification factor Rd increases with the deposit’s thickness. In the other hand, when the confinement increases the deposit becomes stiffer, which results in reducing the amplification. Such result is in accordance with theoretical knowledge which states that the most rigid profiles such as rocks do not amplify seismic movement.

Stretchable-thickness model for dynamic responses of graphene origami reinforced badminton sport plate

In this article, we organize a stretchable-thickness model to present a frequency analysis for a composite plate applicable in badminton court which is reinforced with origami graphene. A higher order kinematic model is extended in this work including three bending, shear, and stretching functions, where the stretching functions is responsible for satisfying the out of plane shear strains and stresses at top/bottom surfaces of the badminton equipment. The sport or composites plate is manufactured from a copper matrix reinforced with graphene origami where the effective material properties are calculated based on micromechanical models as a function of volume fraction and folding degree of graphene origami, material properties of matrix and reinforcement and temperature. The numerical results are presented with changes of volume fraction, folding degree of reinforcement, and thermal loading along the thickness direction. The main novelty of this work is accounting thickness stretching deformation for the analysis of a graphene origami reinforced plate and investigating the responses of graphene origami as a new reinforcement. A verification investigation is presented for approve of the methodology, and solution procedure. An investigation on the order of deformation is presented for various thickness ratio of the badminton sport plate.

Free vibration analysis of nanocomposite plate in contact with fluid using a novel quasi-3D shear deformation theory and artificial neural network

This article presents an analytical approach leveraging a novel quasi-three-dimensional shear deformation theory to analyze the free vibration response of functionally graded graphene platelet-reinforced composite (FG-GPLRC) plates in a liquid medium. The study meticulously determines material properties using the Halpin-Tsai micromechanical model, offering a thorough characterization of these advanced nanocomposite structures. Differential motion equations, incorporating transverse shear and normal stresses, are derived via Hamilton’s principle. The natural frequencies of the nanocomposite plates are computed using Galerkin’s method and validated against published results, affirming their accuracy and reliability. The key innovation of this research is introducing a new trigonometric shape function, which exhibits superior precision compared to previously proposed shape functions and existing theories. Furthermore, an artificial neural network (ANN) model is developed to train the computed results, enabling precise prediction of the natural frequencies without further computational runs. The Bayesian Regularization algorithm, implemented in Matlab, is utilized for this purpose. Across different GPLs patterns and varying input parameters, the error percentage between the ANN model predictions and the results from the Galerkin’s method is consistently low, often below 0.1%. The ANN model demonstrates robust generalization by effectively predicting outcomes with input data beyond its training range. Additionally, it provides immediate computational results, eliminating the delays of traditional methods. The article also examines the effects of various factors, including material characteristics, geometric parameters, and the fluid medium, on the free vibration behavior of FG-GPLRC plates.

Micromechanics modeling of cement concrete considering the interaction among randomly oriented ellipsoidal inhomogeneities

To account for the random orientation of ellipsoidal inhomogeneities, the averaging process over two Euler angles has been widely used in existing micromechanics models. However, the interaction among various inhomogeneity orientations is often overlooked and may also affect the prediction of composite elastic modulus. In this work, to consider the interaction among randomly oriented aggregates and fibers in cement concrete, a micromechanics model, the orientation interaction model (OIM), is proposed. An orientation average model (OAM) is also proposed, and by comparing OIM and OAM predictions, the effect of inhomogeneity orientation interaction on the predicted elastic modulus is shown. In both models, geometries of coarse aggregates and fibers are approximated using ellipsoids with three different semiaxes and cylinders, respectively, and their orientations are described using three Euler angles. Compared with existing random orientation models using two Euler angles, the proposed models can capture the isotropy of composites with randomly oriented asymmetric ellipsoidal inhomogeneities. By comparing the predictions of OIM, OAM, composite sphere models and the Mori-Tanaka method with spherical inhomogeneities, it is found that with the increase of the stiffness contrast between the matrix and inhomogeneities, the effects of the inhomogeneity geometry and orientation interaction become more apparent. The model predictions agree well with the experimental data. By changing the value range of three Euler angles based on the inhomogeneity orientation distribution, both models are also suitable for transversely isotropic and anisotropic composites containing several types of inhomogeneities.

Predicting effective elastic modulus of CNT metal matrix nanocomposites: A developed micromechanical model with agglomeration and interphase effects

Agglomeration and interphase region of fillers are two important factors that affect the mechanical properties of metal matrix composites reinforced with carbon nanotubes (CNT-CMMs). However, most of the existing theoretical models predict an ascending linear in strength for composites with increasing filler content, which disagrees with the experimental results, especially at high filler loading. In fact, at high CNT concentrations, agglomeration and weak interphase region bonding reduce the strength and consequently degrade the mechanical properties of composites. Based on the mean-field theory, we present a novel micromechanical model to predict the elastic modulus of CNT-CMMs by considering the effects of these two factors. Furthermore, we investigate the effect of other parameters such as CNTs aspect ratio, agglomeration amount, interphase layer thickness and modulus, and matrix modulus on the elastic modulus of CNT-CMMs. Finally, we validate our model by comparing it with numerous experimental outcomes from the literature signifies good precision. Using this model, it is possible to optimize the filler value and also maximize the elastic modulus, which can be a powerful tool for designing the CNT-CMMs.

Micromechanical modeling of thermal conductivities of unidirectional carbon fiber/epoxy composites containing carbon nanotube/graphene hybrids

This article deals with the micromechanical modeling of thermal conductivities of the unidirectional carbon fiber (CF)-reinforced composites with carbon nanotube (CNT)/graphene nanoplatelet (GNP)-enriched epoxy matrix. The thermal conductivity of epoxy-based nanocompounds enriched through the incorporation of CNT/GNP hybrids is estimated within the framework of micromechanics. The significant contribution of several microstructures, including the volume fraction, dimension, and straightness of nanofillers, thermal resistance at the interface of the nanofillers and epoxy matrix, and the percolation effect on the nanocomposite thermal conductivity is considered. Furthermore, the method of cells (MOC) is used to anticipate the axial and transverse thermal conductances of unidirectional composites featuring CFs integrated into the CNT/GNP-enriched polymer nanocomposite matrix. The results reveal that incorporating a combination of GNTs and CNTs into the polymer matrix significantly increases the transverse thermal conduction of the multiphase compound. Several factors contribute to improved thermal conductance of the transverse direction in CF/CNT/GNP composites: (i) higher nanofiller concentration, (ii) presence of straight nanofillers, and (iii) use of larger nanofillers. The predictions of micromechanical modeling give good agreement with available experiments. This study compares the transverse and axial thermal conductivity of unidirectional compounds predicted by MOC method with results obtained using the finite element method.

Electrical conductivity of multifunctional cementitious composites reinforced by graphene derivatives: A finite element-based computational micromechanics model

Graphene derivatives (GDs) are known for their considerable conductivity and electron mobility, making them promising candidates for developing electrically conductive cementitious composites (CCs). Consequently, CCs reinforced with GDs (CRGDs) can serve a variety of applications in the construction industry. Despite several experimental studies on the conductivity of CRGDs, finite element (FE) models have rarely been developed to investigate the conductivity of CRGDs. Previous FE models primarily focused on one-dimensional fillers like carbon nanotubes within polymeric matrices, overlooking the distinctive anisotropic behaviour of GDs in cementitious matrices. This study introduces a computational micromechanics model (CMM), integrating the representative elementary volume (REV) concept with FE analysis, to investigate the electrical conductivity of CRGDs. This model is particularly noted for its computational efficiency, as it converts the problem dimensions from 3D to 2D while ensuring an acceptable degree of accuracy. The CMM captures the anisotropic conductivity of GDs and includes critical conductivity mechanisms such as conductive pathways, the tunnelling effect, and field emission. Subsequently, REV size sensitivity analysis is performed to ensure the statistical relevance of the REV, followed by the model's validation against experimental data from the literature. Afterwards, the model's sensitivity analysis clarifies how different parameters, including the constituent properties, influence prediction results. The sensitivity analysis results suggest that the aspect ratio of GDs has considerable impacts on the electrical conductivity and the percolation threshold of CRGDs. Ultimately, this study aims to provide insights into the optimization and design of electrically conductive CRGDs and lay the foundation for future research in this area.

Emergence of critical state in granular materials using a variationally‐based damage‐elasto‐plastic micromechanical continuum model

AbstractThe mechanical response of granular materials, exemplified by frictional grain interactions, is characterized by a critical state in which deformation occurs without change of material volume or stresses when subjected to large shear deformation. In this work, a granular micromechanics approach (GMA) based continuum model is used to investigate the emergence of such a critical state. The continuum description is constructed through mechanical concepts based upon elastic and dissipation energies defined for a generic grain‐pair interaction. A hemivariational principle provides the basis for considering the evolution of damage and plasticity phenomena comprising grain‐pair contact loss and irreversible deformation. As a consequence, the Karush–Kuhn–Tucker (KKT)‐type conditions are derived, which give the evolution equations for the irreversible phenomena. Notably, in this derivation there is no invocation of flow rules and other similar assumptions of classical phenomenological continuum damage and plasticity. Further, Piola's ansatz is elaborated to kinematically connect granular micromechanics of grain‐pair to the continuum description. While the concept of critical state analysis has been handled with either phenomenological approaches or discrete numerical frameworks, in the present paper this concept is examined within a micromechanics‐based continuum description. The constitutive model is established and the coupled damage and plastic irreversible quantities are assessed. The critical state is shown to emerge as grain‐pair related damage and plastic evolution in a competitive/collaborative manner during the imposed loading path.

The role of the fiber–matrix interface in the tensile properties of short fiber–reinforced 3D‐printed polylactic acid composites

AbstractIn this study, we investigate the relationship between structure and properties of fiber–matrix adhesion for material extrusion–based 3‐dimensional (3D) printed composites. We examine the influence of fiber length and fiber content on the tensile properties of glass, basalt, and carbon fiber–reinforced polylactic acid (PLA) composites. Short fiber–reinforced filaments were produced, then, simple micromechanical models were used to predict the in‐plane tensile properties. We found that interlayer tensile properties are strongly influenced by fiber–matrix adhesion. If adhesion is sufficient, the fibers and matrix deform together under tensile load. A second‐order relationship describes interlayer tensile strength in relation to fiber content between 5 and 25 w%, with a maximum at 15 w%, for carbon and basalt fiber–reinforced composites. If adhesion is weak, the crack propagates along the fiber–matrix interface, causing brittle fracture and low strength. This behavior was noted for the glass fiber composite, for which the calculated interface shear strength was the lowest (1.4 MPa). In this case, fiber content is inversely proportional to interlayer tensile strength. Our results show the role of fiber–matrix adhesion quality on tensile properties, which has a major impact on both the accuracy of predictions and the damage processes.Highlights Critical fiber length determines accuracy of tensile property estimates Quality of fiber–matrix adhesion governs interlayer damage process Poor adhesion causes brittle fracture and low strength Second‐order relationship of interlayer tensile strength and fiber content Loss of interlayer tensile strength in composite due to fiber–matrix interface