Multiscale Homogenization Model Research Articles

High-modulus engineered cementitious composites: Design mechanism and performance characterization

Engineered cementitious composites features with high tensile performance while relatively weak compressive stiffness. This study endeavors to address the inherent trade-off between tensile properties and elastic modulus in conventional Engineered Cementitious Composites (ECC). Utilizing the distinctive characteristics of iron ore aggregates, known for their relatively stiff nature, smooth surface and rounded shape, an Iron Sand-based ECC (IS-ECC) emphasizing both high elastic modulus and ductility is formulated. Guided by micromechanical design theory and multiscale homogenization model, this study systematically explores the impacts of aggregate types, water-to-binder (w/b) ratios, sand-to-binder (s/b) ratios, and sand particle sizes on ECC properties. Compared with Quartz Sand-based ECC (QS-ECC), IS-ECC exhibits notably enhanced matrix fluidity and elastic modulus, reduced matrix toughness, and more robust strain-hardening behavior. The proposed three-level multiscale homogenization model accurately predicts the elastic modulus of ECC and provides insights into the underlying mechanism contributing to the enhanced elastic modulus of IS-ECC. With a resulting high elastic modulus of 33.3–48.6 GPa and superior tensile properties, IS-ECC holds promise for widespread applications in structural engineering.

Effect of collagen fibril orientation on the anisotropic properties of peri-implant bone.

In orthopedic and dental surgery, the implantation of biomaterials within the bone to restore the integrity of the treated organ has become a standard procedure. Their long-term stability relies on the osseointegration phenomena, where bone grows onto and around metallic implants, creating a bone-implant interface. Bone is a highly hierarchical material that evolves spatially and temporally during this healing phase. A deeper understanding of its biomechanical characteristics is needed, as they are determinants for surgical success. In this context, we propose a multiscale homogenization model to evaluate the effective elastic properties of bone as a function of the distance from the implant, based on the tissue's structure and composition at lower scales. The model considers three scales: hydroxyapatite foam (nanoscale), ultrastructure (microscale), and tissue (mesoscale). The elastic properties and the volume fraction of the elementary constituents of bone matrix (mineral, collagen, and water), the orientation of the collagen fibril relative to the implant surface, and the mesoscale porosity constitute the input data of the model. The effect of a spatiotemporal variation in the collagen fibrils' orientation on the bone anisotropic properties in the proximity of the implant was investigated. The findings revealed a strong variation of the components of the effective elasticity tensor of the bone as a function of the distance from the implant. The effective elasticity appears to be primarily sensitive to the porosity (mesoscale) rather than to the collagen fibrils' orientation (sub-micro scale). However, the orientation of the fibrils has a significant influence on the isotropy of the bone. When analyzing the symmetry properties of the effective elasticity tensor, the ratio between the isotropic and hexagonal components is determined by a combination of the porosity and the fibrils' orientation. A decrease in porosity leads to a decrease in bone isotropy and, in turn, an increase in the impact of the fibrils' orientation. These results demonstrate that the collagen fibril orientation should be taken into account to properly describe the effective elastic anisotropy of bone at the organ scale.

A multiscale homogenization model on thermal conductivity of bio-based building composite considering anisotropy, imperfect interface and moisture

Bio-based materials are considered as one of the solutions to reduce energy consumption in buildings due to their excellent thermal insulation properties. However, previous studies often do not consider multiple complex microstructural characteristics in one model. In this study, a novel iterative multi-scale homogenization model was developed to predict the effective thermal conductivity of bio-based materials. This model is based on micro-geometric features at three scales and considers plant fiber orientation and shape, imperfect contact, moisture, and different pores’ size. Further, the model was verified by comparison with finite element models and experimental data from the literature. The results show that the present model demonstrates reliable predictions on the scale of binder, plant fiber, and bio-based composites. The application on hemp verified the accuracy of the imperfect contact in the model, while the application on wheat straw showed the non-negligibility of moisture. Additionally, this study also has good applicability to other plant fibers. In conclusion, this model links microstructure and macroscopic behavior, which can effectively predict and evaluate the thermal conductivity of a wide range of bio-based materials, and thus contribute to reducing building energy consumption.

Two-Scale analysis of fretting fatigue crack initiation in heterogeneous materials using Continuum Damage Mechanics

The phenomenon of fretting fatigue damage is related to tribological behaviour and commonly occurs at the contact interface between two bodies that sustain oscillation loads. Based on the complicated mechanical situation, several methods have been developed to predict the crack initiation location and life. The Continuum Damage Mechanics (CDM) approach in conjunction with Finite Element Method (FEM) is used in this paper. The fretting fatigue lifetime includes two parts, crack initiation lifetime and crack propagation lifetime, and this paper focuses on the crack initiation phase. Homogeneous materials are usually studied in fretting fatigue problems, and the influence of defects is necessary to be considered. In this study, the authors proposed several models to consider the effect of heterogeneity on crack initiation location and lifetime. The numerical model is a 2D one with plane strain assumption. To get more accurate numerical results with low computational cost, a Two-Scale Analysis approach is developed in this paper. Two macroscopic models and three microscopic models are proposed, including a Macroscopic homogeneous model (Macro-HOMO), a Multiscale Homogenization model with Direct Numerical Simulation (MH-DNS), a Microscopic homogeneous model (Micro-HOMO), a Microscopic Model with equivalent material properties by using Mean Field Homogenization method (Micro-MFH), and a microscopic model with Direct Numerical Simulation (Micro-DNS). The results obtained by using the CDM approach with different microscopic models are compared, and show that the prediction accuracy of the Micro-DNS is the best. In addition, in terms of computational cost, the Micro-DNS model shows great advantages as well comparing to the Macro-DNS model.

A machine-learning aided multiscale homogenization model for crystal plasticity: application for face-centered cubic single crystals

A machine-learning aided multiscale homogenization model for crystal plasticity: application for face-centered cubic single crystals

Role of micro fibres in tailoring the specific heat capacity of cementitious composites at elevated temperatures: Experimental characterisation and micromechanical modelling

The temperature dependency of specific heat capacity is crucial for thermo-mechanical analysis of fibre reinforced cementitious composites. In this study, a combined experimental and theoretical analysis was conducted to characterise the role of micro fibres in tailoring the specific heat capacity of cementitious composites at elevated temperatures. The specific heat capacity of cement mortar reinforced with four types of fibres, including polypropylene, basalt, carbon and glass fibres, was measured by means of a transient method at up to 400 °C. Based on the effective medium theory, a multiscale homogenization model was developed to predict the specific heat capacity evolution of cementitious composite with temperature from micro to macro level. The results indicate that within the measured temperature range, the addition of 2.0 vol% polypropylene and glass fibres lead to the maximum rise or drop in specific heat capacity of mortar by 8.7% and 14.1%, respectively. In addition, the thermal expansion of polymer fibre was proved to effectively enhance the specific heat capacity of mortar due to thermal expansion coupling effect. The parametric analysis suggests that stiffer inclusions with high thermal expansion govern the effective specific heat capacity coupled with thermal expansion, while the composite incorporated with softer inclusions is insensitive to the variation in thermal properties of inclusions.

Optimization of mechanical properties in anisotropic bio-based building materials by a multiscale homogenization model

Bio-based building material is derived mainly from waste agricultural by-products and has been intensively studied for its role in mitigating carbon emissions. This study aims to optimize its mechanical properties of bio-based building materials by a multiscale model based on micro-geometric characteristics. This model considered three common agricultural by-products: hemp, sunflower, and maize. Then the predicted results were compared with the experimental data. Moreover, the influence of the following parameters on the effective mechanical properties was investigated: volume fraction, modulus of binder and aggregate, shape, and orientation. In order to quantify the priority of each parameter in the optimization, a weight evaluation method was proposed. The analysis of the weight of these parameters shows that the modulus of the binder and the volume fraction of the plant aggregates have the greatest influence on improving the mechanical properties of the composites. When the aspect ratio of the plant particles is greater than 8, the change in their shape almost does not affect the results. Furthermore, this weight evaluation method was used in the case of bio-aggregates with high and low aspect ratios and volume fractions. The analysis shows that in the composite with a low aspect ratio, the optimization by orientation can take into account the performance in both vertical and horizontal directions. The higher the volume fraction, the better the optimization by shape and orientation. These findings provide a theoretical reference to improve the mechanical properties of bio-based building materials containing different agricultural by-products.

Multiscale modeling for food drying: A homogenized diffusion approach

Fruits and vegetables have a heterogeneous microstructure which dynamically changes during drying. Currently, food drying models approximate the material's structure through utilizing a representative elementary volume which adopts a larger scale of description and considers the fluid phases as fictitious continuums. This assumption limits the ability of the models to capture the heterogeneity of food material. The multiscale modeling is considered to have the ability to overcome this limitation and advance the understanding of the micro level transport processes. This research aims to develop a multiscale homogenization model for food drying. The homogenization was performed on the cellular structure of apple tissue considering intracellular (bound) water and free water separately to calculate the effective diffusivity for convective drying. The simulation was performed at three different drying temperatures (45 °C, 60 °C and 70 °C), and the results were validated using experimental data. The homogenized diffusivity approach described the experimental data well and provides new insight into how to consider the heterogeneous structure of food material utilizing knowledge of the microstructural evolution. • A multiscale model was developed to consider the heterogeneously distributed water. • Microscale domains were created using knowledge of the microstructural evolution. • The model was able to describe convective drying at low/medium temperatures. • The results were validated and compared with two existing diffusivity methods.

Development of Multiscale Homogenization Model to Predict Thermo-Mechanical Properties of Nanocomposites including Carbon Nanotube Bundle

Development of Multiscale Homogenization Model to Predict Thermo-Mechanical Properties of Nanocomposites including Carbon Nanotube Bundle

Effective piezoelectric coefficients of cement-based 2–2 type piezoelectric composites based on a multiscale homogenization model

The effective piezoelectric properties of the cement-based 2–2 type piezoelectric composites have been investigated both experimentally and theoretically. The two-scale asymptotic expansion method is employed to develop a homogenized model for the effective properties calculation. The validity of the theoretical solution is confirmed through the comparison with the experimental results. The influence of the volume fraction of the piezoelectric phase on the effective piezoelectric coefficients is then examined. It is found that higher volume fraction will induce obvious increment of the magnitude of the effective piezoelectric strain coefficients d31Eff, d32Eff, and d33Eff, however, the hydrostatic piezoelectric strain coefficient dhEff will reach a maximum value at a lower volume fraction.

A multi-scale homogenization model for fine-grained porous viscoplastic polycrystals: II – Applications to FCC and HCP materials

In Part I of this work (Song and Ponte Castañeda, 2018a), a new homogenization model was developed for the macroscopic behavior of three-scale porous polycrystals consisting of random distributions of large pores in a fine-grained polycrystalline matrix. In this second part, the model is used to investigate both the instantaneous effective behavior and the finite-strain macroscopic response of porous FCC and HCP polycrystals for axisymmetric loading conditions. The stress triaxiality and Lode parameter are found to have significant effects on the evolution of the substructure, which in turn have important implications for the overall hardening/softening behavior of the porous polycrystal. The intrinsic effect of the texture evolution of the polycrystalline matrix is inferred by appropriate comparisons with corresponding results for porous isotropic materials, and found to be significant, especially at low triaxialities. In particular, the predictions of the model identify, for the first time, two disparate regimes for the macroscopic response of porous polycrystals: a porosity-controlled regime at high triaxialities, and a texture-controlled regime at low triaxialities. The transition between these two regimes is found to be quite sharp, taking place between triaxialities of 1 and 2.

A multi-scale homogenization model for fine-grained porous viscoplastic polycrystals: I – Finite-strain theory

We make use of the recently developed iterated second-order homogenization method to obtain finite-strain constitutive models for the macroscopic response of porous polycrystals consisting of large pores randomly distributed in a fine-grained polycrystalline matrix. The porous polycrystal is modeled as a three-scale composite, where the grains are described by single-crystal viscoplasticity and the pores are assumed to be large compared to the grain size. The method makes use of a linear comparison composite (LCC) with the same substructure as the actual nonlinear composite, but whose local properties are chosen optimally via a suitably designed variational statement. In turn, the effective properties of the resulting three-scale LCC are determined by means of a sequential homogenization procedure, utilizing the self-consistent estimates for the effective behavior of the polycrystalline matrix, and the Willis estimates for the effective behavior of the porous composite. The iterated homogenization procedure allows for a more accurate characterization of the properties of the matrix by means of a finer “discretization” of the properties of the LCC to obtain improved estimates, especially at low porosities, high nonlinearties and high triaxialities. In addition, consistent homogenization estimates for the average strain rate and spin fields in the pores and grains are used to develop evolution laws for the substructural variables, including the porosity, pore shape and orientation, as well as the “crystallographic” and “morphological” textures of the underlying matrix. In Part II of this work has appeared in Song and Ponte Castañeda (2018b), the model will be used to generate estimates for both the instantaneous effective response and the evolution of the microstructure for porous FCC and HCP polycrystals under various loading conditions.

Integration of a Multi-scale Homogenization Model into Finite Element Software for Predicting Mechanical Properties of Bulk Moulding Compound (BMC) Composite

Bulk Moulding Compound (BMC) is a short fiber composite with random orientation, used in many industrial sectors such as automotive, electrical,... Design and optimization of composite structures made of BMC meet difficulties due to the nature of this material and thus have not been integrated in the finite element software. This paper introduces a method to build and integrate a new computational model into finite element software (ABAQUS). The chosen model is a multi-scale homogenization model, which helps to calculate mechanical properties of composite materials by using the properties of the components and orientation tensor. This integration can be applied for prediction of composite properties on many kinds of materials, reducing time and cost for suppliers when it comes to optimization of mechanical properties.

A multiscale homogenization model for strength predictions of fully and partially frozen soils

Soil freezing is often used to provide temporary support of soft soils in geotechnical interventions. During the freezing process, the strength properties of the soil–water–ice mixture change from the original properties of the water-saturated soil to the properties of fully frozen soils. In the paper, a multiscale homogenization model for the upscaling of the macroscopic strength of freezing soil based upon information on three individual material phases—the solid particle phase (S), the crystal ice phase (C) and the liquid water phase (L)—is proposed. The homogenization procedure for the partially frozen soil–water–ice composite is based upon an extension of the linear comparison composite (LCC) method for a two-phase matrix–inclusion composite, using a two-step homogenization procedure. In each step, the LCC methodology is implemented by estimating the strength criterion of a two-phase nonlinear matrix–inclusion composite in terms of an optimally chosen linear elastic comparison composite with a similar underlying microstructure. The solid particle phase (S) and the crystal ice phase (C) are assumed to be characterized by two different Drucker–Prager strength criteria, and the liquid water phase (L) is assumed to have zero strength capacity under drained conditions. For the validation of the proposed upscaling strategy, the predicted strength properties for fully and partially frozen fine sands are compared with experimental results, focussing on the investigation of the influence of the porosity and the degree of ice saturation on the predicted failure envelope.

Multiscale homogenization model for thermoelastic behavior of epoxy-based composites with polydisperse SiC nanoparticles

A multiscale statistical homogenization method based on a finite element analysis is proposed to predict the embedded filler size-dependent thermoelastic properties of nanoparticulate polymer composites. A molecular dynamics simulation is used to predict the particle size-dependent elastic constants and coefficient of thermal expansion (CTE) of nanocomposites. Because of the densified interphase zones formed in the vicinity of nanoparticles, and their relative dominance according to particle size, the thermoelastic properties are more prominently increased by smaller nanoparticles. The equivalent continuum microstructure of a nanocomposite is modeled as a three-phase periodic unit cell consisting of the nanoparticle, matrix, and effective interphase zone. An inverse numerical scheme is proposed to predict the thermoelastic properties of the effective interphase zone from the known properties of nanocomposites. In order to account for more realistic variation of the nanoparticle radius and spatial distribution in nanocomposites, statistical homogenization is performed by assigning randomness to the particle size using a beta distribution and to the spatial distribution through larger many-particle embedded representative volume elements (RVEs). Compared with the result from a regular homogenization method using a mono-particle RVE, the mean value of the elastic moduli increases, while that of the CTE decreases in the many-particle RVEs whose mean particle radius corresponds to that of the mono-particle RVE at the same volume fraction of nanoparticles.

Multiscale homogenization modeling for thermal transport properties of polymer nanocomposites with Kapitza thermal resistance

In this study, multiscale homogenization modeling to characterize the thermal conductivity of polymer nanocomposites is proposed to account for the Kapitza thermal resistance at the interface and the polymer immobilized interphase. Molecular dynamics simulations revealed that the thermal conductivity dependent on the embedded particle size originated from the structurally altered interphase zone of surrounding matrix polymer in the vicinity of nanoparticles, and clearly indicate strong dominance of interfacial phonon scattering and dispersion. To account for both the thermal resistance and the immobilized interphase, a four-phase equivalent continuum model composed of spherical nanoparticles, Kapitza thermal interface, effective interphase, and bulk matrix phase is introduced in a finite element-based homogenization method. From the given thermal conductivity of the nanocomposites obtained from MD simulations, the thermal conductivity of the interphase is inversely and numerically obtained. Compared with the micromechanics-based multiscale model, the thermal conductivity of the interphase can be obtained more accurately from the proposed homogenization method. Using the thermal conductivity of the interphase, the random distribution and radius of nanoparticles to describe real nanocomposite microstructure are considered, and the results confirm the applicability of the proposed multiscale homogenization model for further stochastic approaches to account for geometric uncertainties in nanocomposites.

Multiscale prediction of viscoelastic properties of softwood under constant climatic conditions

This paper covers the development and validation of a multiscale homogenization model for linear viscoelastic properties of wood. Starting point is the intrinsic structural hierarchy of wood, which is accounted for by several homogenization steps. Using the correspondence principle, an existing homogenization model for the prediction of elastic properties of wood is adapted herein for upscaling of viscoelastic characteristics. Accordingly, self-consistent, Mori–Tanaka, and unit-cell-based techniques are employed, leading to pointwise defined tensorial creep and relaxation functions in the Laplace-Carson domain. Subsequently, these functions are back-transformed into the time domain by means of the Gaver-Stehfest algorithm. With this procedure the orthotropic macroscopic creep behavior of wood can be derived from the isotropic shear behavior of the lignin-hemicellulose phase. A comparison of model predictions for viscoelastic properties of softwood with corresponding experimentally derived values yields very promising results and confirms the suitability of the model.

Modified Polylactide Microfiber Scaffolds for Tissue Engineering

ABSTRACTPhysical properties of porous membranes made of biocompatible and biodegradable polymers have been studied. The membranes are intended to be used as scaffolds for the regeneration of soft and hard tissues. Polylactides, polycaprolactone and some of their derivates are biocompatible as well as biodegradable materials, and are used for the preparation of nanofibers and nanoporous membranes. These membranes also have comparative advantages as cellular scaffolds for tissue engineering since they can be prepared to mimic the morphology of the extra cellular matrix.Chemical, physical, and biological properties of microfibers and scaffolds of polylactic acid (PLLA), as well as PLLA modified with hydroxyapatite nanoparticles and collagen (Col) are reported in this paper. The microfibers and the scaffolds were prepared by electrospinning. Morphology, diameter and porosity of the scaffold were determined by scanning electron microscopy and an image analyzer program. The microfibers are semicrystalline showing a shell of crystalline nanofibrils. The diameter of the fibers varied between 100 and 800 nm and the porous area of the membrane is between 60 and 80%. The mechanical properties of the microfibers and scaffolds were evaluated by microtensile tests and their behavior was simulated by using an original multiscale asymptotic homogenization model. Cultures of mesenchymal stem cells were used to evaluate their biological activity. Cell adhesion was observed in the modified PLLA scaffolds with grafted hydroxyapatite.

Effect of the variations of clinker composition on the poroelastic properties of hardened class G cement paste

The effect of the variations of clinker composition on the poroelastic properties of class G oil-well cement pastes is studied using a multiscale homogenization model. The model has been calibrated in a previous work based on the results of a laboratory study. Various compositions of class G cements from literature are used in a hydration model to evaluate the volume fractions of the microstructure constituents of hardened cement paste. The poroelastic parameters such as drained bulk modulus, Biot coefficient, and Skempton coefficient are evaluated using the homogenization model. The results show that the variations in chemical composition of class G cements have no important effect on the variations of the poroelastic properties.

Micromechanics analysis of thermal expansion and thermal pressurization of a hardened cement paste

The results of a macro-scale experimental study of the effect of heating on a fluid-saturated hardened cement paste are analysed using a multi-scale homogenization model. The analysis of the experimental results revealed that the thermal expansion coefficient of the cement paste pore fluid is anomalously higher than the one of pure bulk water. The micromechanics model is calibrated using the results of drained and undrained heating tests and permits the extrapolation of the experimentally evaluated thermal expansion and thermal pressurization parameters to cement pastes with different water-to-cement ratios. It permits also to calculate the pore volume thermal expansion coefficient α ϕ which is difficult to evaluate experimentally. The anomalous pore fluid thermal expansion is also analysed using the micromechanics model.