Micromechanical Framework Research Articles

Effective flexoelectric properties of inclusion-based composites based on strain gradient theory and homogenization technique

This study focuses on enhancing flexoelectricity in composites and develops a new micromechanical analytical framework to determine the effective electromechanical properties of inclusion-based flexoelectric composites within the context of SGE. Initially, we specialize in studying isotropic materials and derive the governing Navier equations for the problem. Subsequently, we streamline these differential equations by introducing a Laplacian-type gradient state variable, departing from higher-order gradient-enrichment treatments. The study employs Green’s functions and stress polarization tensors for spherical inhomogeneities, deriving homogenized material properties through volumetric averages of microscopic properties weighted by displacement localization operators. The analytical scheme’s relevance is validated against results from reference models and experimental data. Effective composite properties are evaluated using numerical methods, with an emphasis on assessing the impact of reinforcement on these properties. Our findings lay the foundation for developing a micromechanical method to predict the electromechanical behavior of composites. Specifically, we demonstrate the efficacy of our proposed theory by deriving effective flexoelectric properties of particulate composites.

Micro to macro investigation of clays advising their constitutive modelling - part II

This paper reports the second part of the keynote lecture, whose part I has been already published in this journal, presenting extensive experimental research on the investigation of clay microstructure and its evolution upon loading. Whether the first part focused on the micro to macro behaviour of different reconstituted clays, this part instead concerns the microscale features of the corresponding natural clays, their changes under different loading paths and the ensuing constitutive modelling implications. The experimental investigation is carried out according to the methodology outlined in the part I-paper, hence micro-scale analyses are presented on natural clays subjected to macro-scale mechanical testing, with the purpose to provide experimental evidence of the processes at the micro-scale which underlie the clay response at the macroscale. As for the reconstituted clays in the part I-paper, original results on stiff Pappadai and Lucera clay, this time in their natural state, are compared to literature results on clays of different classes, either soft or stiff. The results presented in this paper, together with those discussed in the part I, allow for a conceptual modelling of the microstructure evolution under compression of natural versus reconstituted multi-mineral clays, providing microstructural insights into the macro-behaviour described by constitutive laws and advising their mathematical formalization in the framework of either continuum mechanics or micro-mechanics.

Morphology-Driven Nanofiller Size Measurement Integrated with Micromechanical Finite Element Analysis for Quantifying Interphase in Polymer Nanocomposites.

This study focused on an innovative practical method using computer vision for particle size measurement, which serves as a key precursor for predicting the elastic modulus of polymer nanocomposites. This approach involved the morphological segmentation of the nanodispersed phase. It aimed, for the first time, to address the impractical conditions resulting from the assumption of idealized single-particle sizes in a monodispersed system during modeling. Subsequently, a micromechanical finite element framework was employed to determine the interphase thickness and modulus in ultrahigh molecular weight polyethylene/nanozeolite composites, following the quantification of nanoparticle sizes. The size measurement approach relied on morphological images extracted from scanning electron microscopy micrographs of impact-fractured surfaces. To compute the interphase thickness, experimental data was fitted to an interphase-inclusive upper-bound Hashin-Shtrikman model, with the measured average particle size per composition serving as a crucial input. Subsequently, the interphase elastic modulus was computed based on its thickness, employing a hybrid modified-Hashin-Hansen and Maxwell model. These estimated interfacial variables were then utilized as inputs for the finite element model to determine the tensile modulus. A comparison between the model results and measured data revealed a maximum discrepancy of 3.29%, indicating the effectiveness of the methodology employed in quantifying interfacial properties.

Elastoplastic damage model and numerical implementation of nano‐silica incorporated concrete

AbstractAn energy‐based isotropic elastoplastic damage model is developed for investigating the elastoplastic damage responses and stress–strain relationships of nano‐silica incorporated concrete. The formulation employs a multiscale micromechanical framework to determine the effective elastic properties of composites at different scales. The stress–strain constitutive relation is derived by splitting the strain tensor into “elastic‐damage” and “plastic‐damage” parts while introducing the homogenized free potential energy function and the undamaged potential energy function. The elastoplastic damage response of the material is further characterized by elastic–plastic‐damage coupling. To construct realistic 3D three‐phase concrete mesostructures in numerical simulations, this paper introduces an encapsulation placement method that avoids particle overlap checking when placing aggregates. This methodology allows adjustments for the aggregate compactness as needed and enhances computational efficiency in concrete mesostructure construction. The numerical results of the modeling show good agreement with the experimental values in the open literature. Further, the influence of nano‐silica addition contents and ITZ (interfacial transition zone) thicknesses on the elastoplastic damage response of nano‐silica incorporated concrete are quantitatively and qualitatively investigated for the optimization of nano‐silica incorporated cementitious composites. The proposed model facilitates simulating and optimizing the mechanical characteristics of nano‐silica incorporated concrete and enhances the computational efficiency of 3D concrete modeling with the introduced encapsulation placement method.

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.

Hygroscopic damage of fiber–matrix interface in unidirectional composites: A computational approach

The mechanical properties of fiber-reinforced composites are significantly affected by hygroscopic exposure. Recent experimental findings reveal that the diffusion of water molecules results in void formation at the fiber–matrix interface, contributing to ∼1% increase in porosity. This paper presents a computational micromechanics framework to analyze the damage behavior of unidirectional composites under hygroscopic aging and transverse loads. First, a mathematical relation for the porosity evolution with moisture content in the composite is obtained. Leveraging this correlation, the aged composite is modeled as a porous microstructure consisting of fiber, matrix, and voids at the fiber–matrix interface in finite element simulations. The fiber is considered elastic, and the matrix is modeled as an elastoplastic material using a pressure-dependent yield model to capture tension–compression asymmetry. A cohesive interface is considered between the fiber and matrix. Simulation results indicate that a void at the interface significantly influences plastic strain evolution and stress distribution, leading to early damage initiation and reduced strength. Previous works have indicated that matrix and inter-fiber voids do not have a significant impact on the strength of composites when their combined porosity is below 1%. On the contrary, this study demonstrates that a porosity of as low as 0.1% at the fiber–matrix interface can result in an 11% decrease in the transverse tensile strength of the composite. A parametric study is conducted to understand the fundamental effects of pore size, location, and relative position on the transverse tension, compression, and shear loading responses of a unidirectional composite. For a given moisture content, the predicted strength of the hygroscopic aged composite exhibits a lower and upper bound. The strengths observed in the experiments fall within the model-predicted range. Additionally, a computational method is proposed that incorporates the effects of porosity at the fiber–matrix interface into a modified cohesive strength. This method allows efficient computations and failure predictions for water or moisture-aged strength degradation of unidirectional composites.

A multiscale bifurcation analysis using micromechanical-based constitutive tensor for granular material

The current study presents a multiscale approach that investigates material instability and localization phenomena in plastic granular materials and the discrete-continuum duality. A bifurcation and stability analysis in continuum mechanics usually requires the material’s tangent (stiffness) operator, the computation of which in a micromechanical approach such as Discrete Element Modeling (DEM) requires specific treatment. To bridge the discrete and continuum worlds, a new computational approach incorporating strain probing is proposed to reconstruct the elastoplastic constitutive tensor and its spectral characteristics from DEM simulations. The probing technique permits the computation of the tangent operator that inherits microstructural information from the discrete world to analyze bifurcation in elastoplasticity at the macro level. An incrementally linear constitutive tensor is computed, distinct for each of the ensemble of probing directions belonging to a particular tensorial zone or sector of incremental stress or strain space, thus making it directionally non-linear. Following such an approach, material instability can be evaluated from the spectral characteristics of the tangent constitutive tensor deduced from DEM probing calculations belonging to an identified tensorial zone. A meso-scale analysis is finally offered to detect shear band localization through the well-known Rice’s criterion as a continuum-based concept extended to a micromechanical discrete modeling framework. These new numerical results show that the multiscale proposed approach, which allows access to microstructural information, is consistent with a continuum one such as when predicting the localization angle during shear banding in a granular specimen in DEM.

Viscoelastic modelling and analysis of two-dimensional woven CNT-based multiscale fibre reinforced composite material system

Carbon nanotube (CNT) has fostered research as a promising nanomaterial for a variety of applications due to its exceptional mechanical, optical, and electrical characteristics. The present article proposes a novel and comprehensive micromechanical framework to assess the viscoelastic properties of a multiscale CNT-reinforced two-dimensional (2D) woven hybrid composite. It also focuses on demonstrating the utilisation of the proposed micromechanics in the dynamic analysis of shell structure. First, the detailed constructional attributes of the proposed trans-scale composite material system are described in detail. Then, according to the nature of the constructional feature, mathematical modelling of each constituent phase or building block’s material properties is established to evaluate the homogenised viscoelastic properties of the proposed composite material system. To highlight the novelty of this study, the viscoelastic characteristics of the modified matrix are developed using the micromechanics method of Mori–Tanaka (MT) in combination with the weak viscoelastic interphase (WI) theory. In the entire micromechanical framework, the CNTs are considered to be randomly oriented. The strength of the material (SOM) approach is used to establish mathematical frameworks for the viscoelastic characteristics of yarns, whereas the unit cell method (UCM) is used to determine the viscoelastic properties of the representative unit cell (RUC). Different numerical results have been obtained by varying the CNT composition, interface conditions, agglomeration, carbon fibre volume percentage, excitation frequency, and temperature. The influences of geometrical parameters like yarn thickness, width, and the gap length to yarn width ratio on the viscoelasticity of such composite material systems are also explored. The current study also addresses the issue of resultant anisotropic viscoelastic properties due to the use of dissimilar yarn thickness. The results of this micromechanical analysis provide valuable insights into the viscoelastic properties of the proposed composite material system and suggest its potential applications in vibration damping. To demonstrate the application of developed novel micromechanics in vibration analysis, as one of the main contributions, comprehensive numerical experiments are conducted on a shell panel. The results show a significant reduction in vibration amplitudes compared to traditional composite materials in the frequency response and transient response analyses. To focus on the aspect of micromechanical behaviour on dynamic response and for the purpose of brevity, only linear strain displacement relationships are considered for dynamic analysis. These insights could inform future research and development in the field of composite materials.

Identifying multiple synergistic factors on the susceptibility to stress relaxation cracking in variously heat-treated weldments

The 347H austenitic stainless steel has been widely used for pressure vessels and pipeline (PVP) applications due to its excellent creep and corrosion resistance, which fit ideally to the harsh conditions in petrochemical industries, fossil fuel or nuclear power plants, and modern energy storages. However, a failure mode has been commonly observed with cracks emerging at the heat affected zone (HAZ) of weldments during post-weld heat treatment (PWHT) or under intermediate to high temperature service conditions. This phenomenon is termed as Stress Relaxation Cracking (SRC) since the purpose of PWHT is to relieve the welding-induced residual stress fields, or as Stress Age Cracking (SAC) if failure happens during service. A leading literature explanation of this failure suggests that the residual stress relaxation and the precipitation dissolution and/or re-precipitation occur in the same temperature range, which can lead to locally high strains and thus to crack at the grain boundaries. Since in situ spatial measurements of residual stress fields, microstructural evolution, and failure processes are nearly infeasible, this work recourses to a micromechanical finite element framework that models the high temperature failure as the nucleation and growth of grain boundary cavities, whereas various parameters such as thermomechanical loading history and its evolution, the competition of grain-interior dislocation creep and grain-boundary diffusion in failure lifetime, and microstructural heterogeneities (such as the precipitate free zone near grain boundaries) can be quantitatively incorporated. It can be concluded from these microstructure-explicit simulations that an accurate knowledge of residual stress evolution and a carefully calibrated set of material constitutive parameters are the essential prerequisites for lifetime predictions. The understanding of individual governing factors also leads to a mechanistic interpretation of the observed SRC susceptibility C-curves. These results suggest that the criticality of residual stress evolution, but not the precipitation-induced local strains, be the leading factor for SRC.

A multiscale micromechanical progressive elastic-damage model for cementitious composites featuring superabsorbent polymer (SAP)

A multiscale micromechanics-based progressive damage model is developed to investigate the overall mechanical behavior and the interfacial microcrack evolutions of the cementitious composites featuring superabsorbent polymer (SAP) under uniaxial tension. Elastic properties, progressive damage process, and homogenization procedure of cementitious composites are systematically integrated in this model. The effective elastic moduli of the composites are determined based on a multiscale micromechanical framework. According to the small strain assumption, the total strain tensor and the elastic-damage compliance tensor are additively decomposed into elastic and damage-induced components. The damage-induced strains and compliances are then deduced from micromechanics. To characterize the progressive elastic-damage induced by microcracks, stages of microcrack propagation are identified from the interface contact stress and the matrix cleavage stress. The complex potentials and stress intensity factors for kinked interface cracks are derived from the distributed dislocations method. By implementing the homogenization process, the macroscopic mechanical behavior is obtained from the micro/mesoscale. The results indicate that the material parameters have clear mechanical significance. Different parameters, such as the SAP addition ratio, aggregate content, initial interfacial crack size, and initial interfacial crack location, are revealed to be influential in the overall mechanical behavior of the composites. The proposed model can be generalized to other particle-reinforced composites with different constituent properties, which can potentially contribute to the design and optimization of durable composites.

Experimental study and numerical simulation of transverse tensile behavior for thermoplastic glass fiber reinforced plastics

In order to predict the mechanical behavior of thermoplastic composites, the phases of glass fiber reinforced plastics (GFRP) were discretized within the computational micromechanics framework. This approach incorporated the random distribution of fibers, nonlinear matrix behavior, and interface damage behavior in a synergistic manner. Subsequently, a three-dimensional representative volume element (RVE) model was established. To verify the accuracy of the numerical model, macroscopic transverse tensile experiments on GFRP were designed. Building upon this foundation, a detailed study on the damage failure of GFRP under transverse tensile loads was conducted to reveal the damage evolution mechanisms. Furthermore, the influence of the random distribution of fibers, nonlinear characteristics of the matrix, and interfacial parameters on the transverse damage mechanical behavior of GFRP was elucidated. The results demonstrate that the random distribution of fibers significantly affects the damage initiation point and crack evolution path. Moreover, GFRP with higher interfacial performance exhibits substantially improved transverse tensile strength compared to those with lower interfacial performance.

Micro to macro investigation of clays advising their constitutive modelling - part I

This keynote lecture discusses the results of a long lasting experimental research, devoted to the investigation of clay microstructure and its evolution upon loading. Micro-scale analyses, involving scanning electron microscopy, image processing, mercury intrusion porosimetry and swelling paths to test the clay bonding, are presented on clays subjected to different loading paths, with the purpose of providing experimental evidence of the processes at the micro-scale which underlie the clay response at the macro-scale. Data from the literature on clays of different classes, either soft or stiff, are compared to original results on two stiff clays, Pappadai and Lucera clay, both in their natural state and after reconstitution in the laboratory. The results presented herein allow building a conceptual model of the evolution of clay microstructure upon different loading paths, providing microstructural insights into the macro-behaviour described by constitutive laws and advising their mathematical formalization in the framework of either continuum mechanics or micro-mechanics. For editorial purposes, the research results are presented in two parts. The first part, presented in this paper, concerns the results for reconstituted clays, whereas a second part, concerning the corresponding natural clays, is discussed in a second companion paper.

A micromechanical investigation of cement paste through a combination of the X-ray computed tomography and the phase field method

Micromechanical modeling could provide essential insights into the failure mechanisms within cement paste, which is important for assessing and enhancing the performance of concrete. This study proposes a novel micromechanical modeling framework manifesting itself as a combination of the X-ray computed tomography for characterizing and the phase field method for modeling. Different from previous attempts, the procedure of the phase segmentation in cement paste is not necessary herein, thus reducing uncertainty in the microstructural characterization as well as the parametric input of the micromechanical modeling. The micromechanical modeling framework is used to predict the entire fracture process of cement paste. The current results are compared with previous studies for the sake of validation. Two critical parameters reflecting the micromechanical behavior are extracted and discussed, i.e., Young's modulus and tensile strength. Special attention is spent on the size effect of these parameters.

Mechanical damage in porcine dermis: Micro-mechanical model and experimental characterization

Skin is subjected to extreme mechanical loading during needle insertion and drug delivery to the subcutaneous space. There is a rich literature on the characterization of porcine skin biomechanics as the preeminent animal model for human skin, but the emphasis has been on the elastic response and specific anatomical locations such as the dorsal and the ventral regions. During drug delivery, however, energy dissipation in the form of damage, softening, and fracture, is expected. Similarly, reports on experimental characterization are complemented by modeling efforts, but with similar gaps in microstructure-driven modeling of dissipative mechanisms. Here we contribute to the bridging of these gaps by testing porcine skin from belly and breast regions, in two different orientation with respect to anatomical axes, and to progressively higher stretches in order to show damage accumulation and stiffness degradation. We complement the mechanical test with imaging of the collagen structure and a micro-mechanics modeling framework. We found that skin from the belly is stiffer with respect to the breast region when comparing the calf stiffness of the J-shaped stress–stretch response observed in most collagenous tissues. No significant direction dependent properties were found in either anatomical location. Both locations showed energy dissipation due to damage, evident though a softening of the stress–stretch response. The microstructure model was able to capture the elastic and damage progression with a small set of parameters, some of which were determined directly from imaging. We anticipate that data and model fits can help in predictive simulations for device design in situations where skin is subject to supra-physiological deformation such as in subcutaneous drug delivery.

Energy and morphology of martensite–twinned martensite interface in CuAlNi shape memory alloy: A phase-field study

Needle-like twins are observed experimentally within the transition layer at the martensite–twinned martensite interface. We utilize a phase-field approach to investigate this microstructure. Our goal is to simulate the morphology of the transition layer and to perform a detailed analysis to characterize its interfacial and elastic micro-strain energy. To illustrate the micromechanical framework developed for that purpose, sample computations are carried out for a CuAlNi shape memory alloy undergoing a cubic-to-orthorhombic martensitic transformation. A particular focus of the study is on size-dependent morphology through examining the impact of twin spacing. Additionally, our results reveal that certain twin volume fractions lead to the emergence of twin branching as a way to minimize the total free energy stored in the microstructure.

A Coupled Electro-Mechanical Homogenization-Based Model for PVDF-Based Piezo-Composites Considering α → β Phase Transition and Interfacial Damage.

Polyvinylidene fluoride or polyvinylidene difluoride (PVDF) is a piezoelectric semi-crystalline polymer whose electro-mechanical properties may be modulated via strain-induced α → β phase transition and the incorporation of polarized inorganic particles. The present work focuses on the constitutive representation of PVDF-based piezo-composites developed within the continuum-based micromechanical framework and considering the combined effects of particle reinforcement, α → β phase transition, and debonding along the interface between the PVDF matrix and the particles under increasing deformation. The micromechanics-based model is applied to available experimental data of PVDF filled with various concentrations of barium titanate (BaTiO3) particles. After its identification and predictability verification, the model is used to provide a better understanding of the separate and synergistic effects of BaTiO3 particle reinforcement and the micromechanical deformation processes on the electro-mechanical properties of PVDF-based piezo-composites.

Effects of oxidation on the effective thermomechanical properties of porous ultra-high temperature ceramics in compression via computational micromechanics and MPM

Due to the harsh flight environment of hypersonic platforms, Ultra-High Temperature Ceramics (UHTCs) imbued with macroscale porosity have been introduced as candidates for providing thermal insulation of sensitive on-board components. This study employs an oxidized state approach for modeling the coupled effects of surface oxidation and continuum damage in the effective thermomechanical response of such materials within the framework of computational micromechanics. Using an in-house Material Point Method (MPM) computational tool, two-dimensional plane strain simulations were performed on representative hexagonal structures of TiB2 with 10%, 40% and 70% macroporosity. Oxide layers ranging from 5 to 50 μm were applied to the structures in place of a transient, diffusion-based oxidation solver. Simulations with applied compressive strains of up to 30% were then performed on hexagonal structures with and without the oxide layer present. A range of dynamic thermal gradients were also applied to investigate the damage due to thermal expansion coefficient mismatch. Finally, the oxidized state modeling approach was applied to large porous structures derived from micro computed tomography images of TiB2 foam.

Compressible cementitious composite materials: Multiscale modeling and experimental investigation

Tunnel linings installed in difficult geological conditions characterized by a high expansion potential, such as Opalinus Clay and rocks containing anhydrite, may exhibit a loss of integrity due to excessive ground deformations in case water penetrates the rocks. One of the potential remedies against lining deterioration and failure of the tunnel structure is the incorporation of a compressible cementitious layer around the tunnel. This compressible layer serves as a cushion that protects the tunnel structure by tolerating a certain amount of deformations prior to collapse. The deformation capacity of the compressible layer can be enhanced by introduction of various soft inclusions or air bubbles in the cementitious mix. However, such soft inclusions reduce the overall elasticity modulus and strength of the composite. Hence, it is crucial to determine the optimal mix that provides the required compaction potential without compromising on stiffness and strength. For this design purpose computational modeling can be adopted. The model should be able to account for the material properties of the individual components and their volume fraction, which strongly influence the overall behavior of the cementitious composite, and to capture the main features characterizing compressible composites, such as a yielding plateau after a certain threshold loading has been reached. The compaction process of such a composite is described by a voxel model with a discrete distribution of material properties, where the voxels are compacted by applying an Eigenforce when the local stress state reaches a threshold value. This threshold is determined within the framework of continuum micromechanics on the scale of individual inclusions. The model predictions are compared with data from experimental investigations on the compression behavior of different cementitious mixes.

Uncertainty analysis for prediction of elastic properties of unidirectional bamboo fiber-reinforced composites

This paper presents a virtual framework to obtain the elastic response of unidirectional (UD) continuous bamboo fiber-reinforced composites based on the micromechanical modeling approach. The virtual framework involves the development of an algorithm for the generation of stochastic Representative Volume Elements (RVEs), taking into account the micro-structural uncertainty and variability of the bio-based bamboo fibers and their composites. The developed algorithm and model are validated with experimental characterizations and theoretical models. Different statistical micro-structural realizations with random fiber packing, fiber geometries, and variable RVE sizes are compared to investigate the effects of these parameters on the accuracy of the prediction of the elastic properties of bamboo fiber-reinforced composites. All models and loading scenarios are applied automatically through Python scripting in the Abaqus finite element (FE) solver. The uncertainty analysis of input parameters is carried out through parametric studies. This virtual micromechanical framework can be further linked in the future to macroscale models of bamboo or other natural fiber composites for multiscale prediction of the behavior of biocomposite structures under in-service loading.

Study of the effect of strain rate on the in-plane shear and transverse compression response of a composite ply using computational micromechanics

The use of composite materials for structures subjected to impacts requires a deep understanding about the dynamic behaviour of the material. To this end, a physically-based computational micromechanics simulation tool has been developed to predict failure initiation in a composite ply over a wide range of strain rates. The computational micromechanics framework incorporates constitutive models for the fibre, matrix and fibre-matrix interface, which are partly calibrated with novel micromechanical testing techniques. The simulation tool was applied to two matrix-dominated deformation modes of the ply: transverse compression and in-plane shear. The comparison of simulation and experimental results at coupon level have revealed a change in failure initiation mechanism of the composite ply with strain rate, which was then corroborated through observation of the fracture surfaces on the samples.