Random Microstructure Research Articles

Twinning in porous elastomers

It has been known for some time that constitutive models for the large-deformation response of porous elastomers can develop ‘macroscopic’ instabilities as a consequence of loss of strong ellipticity. Indeed, constitutive models obtained by homogenization methods for porous elastomers with periodic and random microstructures can lose strong ellipticity under appropriate loading conditions. For periodic microstructures, it has been shown theoretically, and verified experimentally and numerically, that ‘microscopic’ instabilities consisting in solutions that are periodic on ensembles of unit cells tend to occur before the long-wavelength ‘macroscopic’ instabilities that are captured by the loss of strong ellipticity of the homogenized response. But what about the response of porous elastomers with random microstructures? In this case, microscopic instabilities can be excluded, and the question then arises as to what happens after the onset of a macroscopic instability. Building on earlier work for reinforced elastomers, it is shown here that porous elastomers can undergo twinning after the onset of a macroscopic instability. For this purpose, use is made of a generalized Maxwell-type construction arising from the theory of relaxation and applied to linear comparison variational homogenization estimates for a certain class of two-dimensional porous elastomers consisting of aligned cylindrical pores in a rubber matrix subjected to plane strain loadings. It is shown that such porous elastomers recover Legendre-Hadamard stability by twinning after the onset of a macroscopic instability. Interestingly, the porous elastomers behave like elastic fluids in the twinned region, losing their ability to support shear stresses.

Epitaxially Growing 2D RGB Trichromatic Cocrystal Nanomeshes to Trigger Cross‐Modulation White Light Emission

Comprehensive SummaryConsidering their oriented crystalline structure and high luminescent efficiency, the exploration of multi‐component organic cocrystal systems with tunable supramolecular nanostructures and potential RGB light emission has emerged as a captivating but challenging subject. Here, we propose a straightforward synthetic strategy to precisely govern the assembly, structure and structure‐property relationship of organic cocrystals. By employing the single‐crystalline template‐assisted epitaxial growth (SCT‐EG) method, the two‐dimensional (2D) highly‐aligned cocrystal nanomeshes are firstly developed to afford an exceptional RGB trichromatic system, triggering cross‐modulation white light emission (WLE) with remarkable stability and regeneration capacity over six months. The transformation from random 1D microstructures to uniformly‐oriented 2D nanomeshes can be attributed to the regulatory competitive intermolecular π‐π, CT interactions, and partial H bond interactions among cocrystals. Moreover, the successful construction of 2D RGB trichromatic cocrystal nanomeshes system holds promise to generate full‐color display, which can function as multicolor inks for photonic dynamic recognition, information encryption, and decryption.

Freeze-thaw cycling of nano-SiO2-modified recycled aggregate in concretes: Hydro-thermal-mechanical modeling

The freeze-thaw cycling in the cold region causes severe damage to the concrete, which seriously affects the durability of concrete. In this paper, nano-SiO₂ (NS) modified RAC (NS-RAC) specimens were prepared by impregnating RCA with a 3 % NS dispersion for 48 h with following frost resistance assessed experimentally. To further fully understand the performance of NS-RAC under freeze-thaw (F-T) cycles, a comprehensive hydro-thermal-mechanical coupling model was established to simulate the damage behavior of NS-RAC under F-T conditions. A random polygon microstructure model of RAC was developed, and the characteristics of RCA and three types of ITZs were discussed. The damage control equation for RAC during the F-T process was defined based on the coupling effects of percolation, temperature, and stress in a porous medium. The F-T cycle tests show that the compressive strength of NS-RAC samples after 100 F-T cycles is 9.04 MPa higher than that of RAC. Numerical simulation results indicate that, compared to RAC without NS, the maximum pore pressure, crystallization pressure, and maximum principal stress of samples with 3 % NS after the first F-T cycle are reduced by 3.84 %, 4.36 %, and 2.26 %, respectively. During the F-T cycle, with increases in ITZ width, aggregate gradation range, RCA replacement rate, and temperature difference, the internal stress of NS-RAC specimens increased to varying degrees. This study provides insights into the F-T damage of RAC in severe cold regions and promotes the practical engineering application of RAC in such environments.

Lightweight Calcium-Silicate-Hydrate Nacre with High Strength and High Toughness.

Low flexural strength and toughness have posed enduring challenges to cementitious materials. As the main hydration product of cement, calcium silicate hydrate (C-S-H) plays important roles in the mechanical performance of cementitious materials while exhibiting random microstructures with pores and defects, which hinder mechanical enhancement. Inspired by the "brick-and-mortar" microstructure of natural nacre, this paper presents a method combining freeze casting, freeze-drying, in situ polymerization, and hot pressing to fabricate C-S-H nacre with high flexural strength, high toughness, and lightweight. Poly(acrylamide-co-acrylic acid) was used to disperse C-S-H and toughen C-S-H building blocks, which function as "bricks", while poly(methyl methacrylate) was impregnated as "mortar". The flexural strength, toughness, and density of C-S-H nacre reached 124 MPa, 5173 kJ/m3, and 0.98 g/cm3, respectively. The flexural strength and toughness of the C-S-H nacre are 18 and 1230 times higher than those of cement paste, respectively, with a 60% reduction in density, outperforming existing cementitious materials and natural nacre. This research establishes the relationship between material composition, fabrication process, microstructure, and mechanical performance, facilitating the design of high-performance C-S-H-based and cement-based composites for scalable engineering applications.

Crack Initiation in Compacted Graphite Iron with Random Microstructure: Effect of Volume Fraction and Distribution of Particles.

Thanks to the distinctive morphology of graphite particles in its microstructure, compacted graphite iron (CGI) exhibits excellent thermal conductivity together with high strength and durability. CGI is extensively used in many applications, e.g., engine cylinder heads and brakes. The structural integrity of such metal-matrix materials is controlled by the generation and growth of microcracks. Although the effects of the volume fraction and morphology of graphite inclusions on the tensile response of CGI were investigated in recent years, their influence on crack initiation is still unknown. Experimental studies of crack initiation require a considerable amount of time and resources due to the highly complicated geometries of graphite inclusions scattered throughout the metallic matrix. Therefore, developing a 2D computational framework for CGI with a random microstructure capable of predicting the crack initiation and path is desirable. In this work, an integrated numerical model is developed for the analysis of the effects of volume fraction and nodularity on the mechanical properties of CGI as well as its damage and failure behaviours. Finite-element models of random microstructure are generated using an in-house Python script. The determination of spacings between a graphite inclusion and its four adjacent particles is performed with a plugin, written in Java and implemented in ImageJ. To analyse the orientation effect of inclusions, a statistical analysis is implemented for representative elements in this research. Further, Johnson-Cook damage criteria are used to predict crack initiation in the developed models. The numerical simulations are validated with conventional tensile-test data. The created models can support the understanding of the fracture behaviour of CGI under mechanical load, and the proposed approach can be utilised to design metal-matrix composites with optimised mechanical properties and performance.

The Microstructure Characterization of a Titanium Alloy Based on a Laser Ultrasonic Random Forest Regression

The traditional microstructure detecting methods such as metallography and electron backscatter diffraction are destructive to the sample and time-consuming and they cannot meet the needs of rapid online inspection. In this paper, a random forest regression microstructure characterization method based on a laser ultrasound technique is investigated for evaluating the microstructure of a titanium alloy (Ti-6Al-4V). Based on the high correlation between the longitudinal wave velocity of ultrasonic waves, the average grain size of the primary α phase, and the volume fraction of the transformed β matrix of the titanium alloy, and with the longitudinal wave velocity as the input feature and the average grain size of the primary α phase and the volume fraction of the transformed β matrix as the output features, prediction models for the average grain size of the primary α phase and the volume fraction of the transformed β matrix were developed based on a random forest regression. The results show that the mean values of the mean relative errors of the predicted mean grain size of the native α phase and the volume fraction of the transformed β matrix for the six samples in the two prediction models were 11.55% and 10.19%, respectively, and the RMSE and MAE obtained from both prediction models were relatively small, which indicates that the two established random forest regression models have a high prediction accuracy.

Probabilistic analysis of homogenized elastic property for resin products fabricated by additive manufacturing based on three-dimensional random field modeling of microstructure

Additive manufacturing (AM) techniques have been used in several fields of science and industry, and fabrication techniques are being updated. For this fact, especially, for industrial use, mechanical property evaluation methodologies for AM products and standards for product quality assessment should also be well established. In this paper, a probabilistic evaluation of the homogenized elastic properties of a resin product fabricated by a material extrusion-based AM technique is attempted by considering the randomness of both material and microscopic geometrical quantities. This AM method fabricates a resin structure by piling up melted resin, and to decrease consumed material and influence of thermal deformation, the inner structure of the fabricated products will include many pores and its geometry is difficult to be well controlled. From this fact, the products will be regarded as a heterogeneous material with complex random microstructure. This will cause difficulty in the evaluation of its apparent material properties and therefore a probabilistic homogenization analysis is attempted for their quantitative estimation in this study. In particular, to investigate probabilistic properties of microscopic geometry, a random field modeling technique is employed for the evaluation of autocorrelation of the microscopic geometrical parameter, and the results of the autocorrelation identified by experimental observation are introduced to the probabilistic homogenization analysis. The two-dimensional or three-dimensional random field modeling is attempted, and the effectiveness of this approach is investigated by comparing it with the experimental result.

High fidelity FEM based on deep learning for arbitrary composite material structure

Due to the outstanding performance, composite materials are widely used and analyzing their properties and designing them based on performance has become a crucial task in the field of many manufacturing industries. Composite materials possess complex multiscale structures, and traditional fine-scale finite element modeling and analysis may lead to severe computational resource challenges. To overcome this difficulty, breakthroughs in key technologies of multiscale accelerated analysis algorithms are required. In this study, an innovative approach based on artificial intelligence and multiscale finite element method is presented. This approach involves partitioning the entire composite material structure into coarse grids that resemble homogenous structures of similar size, providing results consistent to fine-grid finite element analysis. By utilizing CNN for image feature recognition and employing the CGAN adversarial method, coarse-grid equivalent stiffness matrices and multiscale shape functions from completely random microstructures of composite materials can be obtained. Consequently, this enables a rapid response process from microstructure to low-resolution grid to high-resolution physical field, with remarkably accurate physical field results. Moreover, compared to traditional fine-grid finite element methods, this approach significantly reduces memory usage and computation time. This method is applicable to composite materials with varying shaped inclusions, different component properties, and diverse geometric distributions, allowing these materials to perform high-fidelity finite element calculations on coarse grids and predict their mechanical behavior. Furthermore, this breakthrough opens avenues for accelerating the optimization design of composite materials with diverse mechanical functionalities, by employing a bottom-up approach.

Application of ultrasound-assisted compression and 3D-printing semi-solid extrusion techniques to the development of sustained-release drug delivery systems based on a novel biodegradable aliphatic copolyester

The purpose of this study was to investigate the ability of two advanced hot-processing technologies, Ultrasound-Assisted Compression (USAC) and 3D-printing Semi-solid Extrusion (SSE), to manufacture sustained-release drug delivery systems based on a novel biodegradable aliphatic copolyester. The copolymer was synthesized from ω-pentadecalactone (PDL), 1,4-cyclohexanedimethanol (CHDM) and dimethyl succinate (DMS) (monomer ratio PDL/CHDM/DMS 70/30/30) by enzymatic ring opening polymerization and two-step melt polycondensation processes and has a random microstructure, a high molecular weight (107,100 g mol−1) and a relatively low melting point (∼65 °C). The antibacterial agent metronidazole (MTZ) was chosen as model drug and binary physical mixtures copolymer:drug were prepared at 90:10 and 70:30 w/w ratios. Thermal analysis studies evidenced that the formulations could be processed below their degradation temperatures. Drug delivery devices with dense and meshed structures were manufactured using USAC and SSE techniques, respectively, with USAC devices exhibiting more reproducible physical properties than the SSE systems. Powder X-ray diffraction and scanning electron microscopy studies showed a partial sintering of the copolyester during USAC processing while MTZ remained mostly crystalline. In contrast, the copolymer melted and the drug underwent some amorphization when processed using SSE. In vitro drug release studies in phosphate buffer (pH 6.8) showed that, after an initial burst release of metronidazole, USAC and SSE devices exhibited a prolonged and/or sustained drug release over 20 days. The initial burst release was dependent on the manufacturing technique and the drug/polymer ratio, being minimized for SSE devices containing 10 wt% MTZ. The whole drug release profiles fitted well to the Peppas-Sahlin model, being drug diffusion the predominant release mechanism. After the burst release, the sustained release period of USAC and SSE devices containing 10 wt% MTZ showed a good fit to the zero-order kinetic model, with faster drug release from the SSE devices due to the larger surface area of their meshed structure. In conclusion, this work demonstrates that processing the aliphatic copolyester by both USAC and SSE technologies provides an attractive strategy to manufacture biodegradable drug delivery systems for long-term release of metronidazole.

Prediction of constrained modulus for granular soil using 3D discrete element method and convolutional neural networks

To efficiently predict the mechanical parameters of granular soil based on its random micro-structure, this study proposed a novel approach combining numerical simulation and machine learning algorithms. Initially, 3500 simulations of one-dimensional compression tests on coarse-grained sand using the three-dimensional (3D) discrete element method (DEM) were conducted to construct a database. In this process, the positions of the particles were randomly altered, and the particle assemblages changed. Interestingly, besides confirming the influence of particle size distribution parameters, the stress-strain curves differed despite an identical gradation size statistic when the particle position varied. Subsequently, the obtained data were partitioned into training, validation, and testing datasets at a 7:2:1 ratio. To convert the DEM model into a multi-dimensional matrix that computers can recognize, the 3D DEM models were first sliced to extract multi-layer two-dimensional (2D) cross-sectional data. Redundant information was then eliminated via gray processing, and the data were stacked to form a new 3D matrix representing the granular soil's fabric. Subsequently, utilizing the Python language and Pytorch framework, a 3D convolutional neural networks (CNNs) model was developed to establish the relationship between the constrained modulus obtained from DEM simulations and the soil's fabric. The mean squared error (MSE) function was utilized to assess the loss value during the training process. When the learning rate (LR) fell within the range of 10-5–10-1, and the batch sizes (BSs) were 4, 8, 16, 32, and 64, the loss value stabilized after 100 training epochs in the training and validation dataset. For BS = 32 and LR = 10-3, the loss reached a minimum. In the testing set, a comparative evaluation of the predicted constrained modulus from the 3D CNNs versus the simulated modulus obtained via DEM reveals a minimum mean absolute percentage error (MAPE) of 4.43% under the optimized condition, demonstrating the accuracy of this approach. Thus, by combining DEM and CNNs, the variation of soil's mechanical characteristics related to its random fabric would be efficiently evaluated by directly tracking the particle assemblages.

Acoustic emission applied to stochastic modeling of microdamage in compact bone

Exploring the stochastic intricacies of bone microstructure is a promising way to make progress on the practical issue of bone fracture. This study investigates the fracture of human complete ribs subjected to bending and using acoustic emission (AE) for microfailure detection. As the strain increases, the number of AE signals per unit of time rises until, beyond a certain threshold, an avalanche of signals occurs, indicating the aggregation of numerous microfailures into a macroscopic fracture. Since microfailures appear randomly throughout the bending test, and given the lack of a deterministic law and the random nature of microfailures during the bending test, we opted to develop a stochastic model to account for their occurrence within the irregular and random microstructure of the cortical bone. Notable discoveries encompass the significant correlation between adjusted parameters of the stochastic model and the total number of microfailures with anthropometric variables such as age and body mass index (BMI). The progression of microfailures with strain is significantly more pronounced with age and BMI, as measured by the rate of bone deterioration. In addition, the rate of microfailures is significantly impacted by BMI alone. It is also observed that the average energy of the identified AE events adheres to a precisely defined Pareto distribution for every specimen, with the principal exponent exhibiting a significant correlation with anthropometric variables. From a mathematical standpoint, the model can be described as a double Cox stochastic and explosive (coxplosive process) model. This further provides insight into the reason why the ribs of older individuals are considerably less resilient than those of younger individuals, breaking under a considerably lower maximum strain (εmax\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon _{\\max }$$\\end{document}).

Large strain micromechanics of thermoplastic elastomers with random microstructures

Thermoplastic polyurethanes (TPU) are block copolymeric materials composed of plastomeric “hard” and elastomeric “soft” domains, by which they exhibit highly resilient yet dissipative large deformation features depending on volume fractions and microstructures of the two distinct domains. Here, we develop a new methodology to explore the microscopic deformation mechanisms in TPU materials with highly disordered microstructures. We propose new micromechanical models for randomly dispersed (or occluded) as well as randomly continuous hard domains (and mixtures of both dispersed and continuous hard domains), each within a continuous soft structure as widely found in representative TPU materials over a wide range of volume fractions, vhard = 26.9% to 52.2%. The micromechanical modeling results are compared to experimental data on the macroscopic large strain behaviors reported previously (Cho et al., 2017). We explore the role of the dispersed vs. continuous nature of the geometric features of the random microstructures on shape recovery and energy dissipation at the microstructural level in these phase-separated copolymeric materials.

On the effective properties of random microstructures and cross-property connections for them

Effective elastic and conductive properties of 2-D random (“disordered”) mixtures of several types are examined by computational means. It is found that an “equivalent” material of simple microgeometry – a continuous matrix with elliptical inhomogeneities – can be identified, that matches both the elastic and the conductive properties, in the entire range of property contrast between constituents. Moreover, the ellipse eccentricities are almost the same for different types of the random mixtures in the volume fraction range (0.3 – 0.7); in this range, there is no need in specifying the type of a mixture, as far as the effective properties are concerned. It is also found that the effective properties of the considered random mixtures are well described by the Mori-Tanaka-Benveniste model (in spite of the fact that this model was not intended for them).We also examined the effect of inhomogeneity interactions in a matrix composite on the cross-property connections between the elastic and conductive properties. Whereas the interactions generally produce strong effect on each of the properties, their effect on the connections is negligible (the latter can be taken from the non-interaction approximation).It is argued that most findings related to 2-D random mixtures should apply to 3-D ones as well.

Effect of microvariability on electrical rock properties

SUMMARY In petrophysics, physical rock properties are typically established through laboratory measurements of individual samples. These measurements predominantly relate to the specific sample and can be challenging to associate with the rock as a whole since the physical attributes are heavily reliant on the microstructure, which can vary significantly in different areas. Thus, the obtained values have limited applicability to the entirety of the original rock mass. To examine the dependence of petrophysical measurements based on the variable microstructure, we generate sets of random 2-D microstructure representations for a sample, taking into account macroscopic parameters such as porosity and mean grain size. For each microstructure produced, we assess the electrical conductivity and evaluate how it is dependent on the microstructure’s variability. The developed workflow including microstructure modelling, finite-element simulation of electrical conductivity as well as statistical and petrophysical evaluation of the results is presented. We show that the methodology can adequately mimic the physical behaviour of real rocks, showing consistent emulation of the dependence of electrical conductivity on connected porosity according to Archie’s law across different types of pore space (microfracture, intergranular and vuggy, oomoldic pore space). Furthermore, properties such as the internal surface area and its fractal dimension as well as the electrical tortuosity are accessible for the random microstructures and show reasonable behaviour. Finally, the possibilities, challenges and meshing strategies for extending the methodology to 3-D microstructures are discussed.

Surrogate modeling by multifidelity cokriging for the ductile failure of random microstructures

Surrogate modeling by multifidelity cokriging for the ductile failure of random microstructures

Regularized coupling multiscale method for thermomechanical coupled problems

The coupling effects in multiphysics processes are often neglected in designing multiscale methods. The coupling may be described by a non-positive definite operator, which in turn brings significant challenges in multiscale simulations. In the paper, we develop a regularized coupling multiscale method based on the generalized multiscale finite element method (GMsFEM) to solve coupled thermomechanical problems, and it is referred to as the coupling generalized multiscale finite element method (CGMsFEM). The method consists of defining the coupling multiscale basis functions through local regularized coupling spectral problems in each coarse-grid block, which can be implemented by a novel design of two relaxation parameters. Compared to the standard GMsFEM, the proposed method can not only accurately capture the multiscale coupling correlation effects of multiphysics problems but also greatly improve computational efficiency with fewer multiscale basis functions. In addition, the convergence analysis is also established, and the optimal error estimates are derived, where the upper bound of errors is independent of the magnitude of the relaxation coefficient. Several numerical examples for periodic, random microstructure, and random material coefficients are presented to validate the theoretical analysis. The numerical results show that the CGMsFEM shows better robustness and efficiency than uncoupled GMsFEM.

Rapid evaluation and prediction of cure-induced residual stress of composites based on cGAN deep learning model

In this piece of present work, we propose a deep learning model driven by conditional generative adversarial network (cGAN) for rapid evaluation and prediction of cure-induced residual stress (CRS) of composites. The CRS is evaluated by solving for the material behaviors of the cure kinetics, viscoelasticity, thermal expansion, and cure shrinkage under heat transfer condition using finite element (FE) method. The geometry and CRS fields are extracted from numerous simulations and subsequently utilized in the proposed cGAN training process. With this end-to-end unsupervised learning, the cGAN model can predict the CRS with high fidelity based on the fiber random distributed microstructure and capture the variation of fiber volume fraction. In qualitative measures, peak signal to noise ratio (PSNR) and structure similarity index (SSIM) are employed for accuracy verification. Moreover, the cGAN model can also significantly reduce the computational cost and provide some insights for optimizing the manufacturing process of composites.

Analytical estimates for deformation behavior of fluid-filled elastomers with random microstructures

Macroscopic response of fluid filled elastomers with random microstructures, is obtained for aligned, cylindrical pores with circular cross-section. Results are derived for mono-disperse as well as poly-disperse pores, for Newtonian fluids. The obtained estimates are validated for plain strain compression loadings using numerical simulations performed in commercial multiphysics software COMSOL. Good agreement is observed between the analytical estimates and numerical solutions for different initial porosities and loading rates. Standard deviation in numerical results is seen to be high for polydisperse pores. Nonetheless, the mean response in numerical solutions matches well with analytical estimates. The obtained results can form the basis for design and fabrication of a new class of materials which have the potential to replace conventional spring–damper systems, particularly where space is limited.

Impact induced compression and decompression waves in porous meta-materials modeled using a continuum theory of phase transitions

Porous meta-materials with both regular and random microstructure are of intense research interest today due to their interesting dynamical properties, including but not limited to, their acoustic band structure, shock absorption properties, and fracture toughness. Some of these materials can exist in a rarefied or densified state depending on the state of stress, and recover their original configuration after a cycle of loading and unloading. Often, they exhibit a hysteretic stress–strain response under quasistatic uniaxial compression. As such, many aspects of their mechanical behavior can be captured using a continuum theory of phase transitions. In this work, the dynamical behavior of such materials is explored. It is shown that the impact problem for these materials can result in propagating shocks, phase boundaries, and fans. The impact problems admit multiple solutions for the same set of initial and boundary conditions leading to non-uniqueness. This non-uniqueness can be remedied using a nucleation criterion and kinetic laws, as is known from the continuum theory of phase transitions. The fan solutions which arise in decompressive impact problems have not received much attention in the literature and may be regarded as a novel contribution of this work. The analysis presented here may have applications in the dynamic behavior of a broad class of porous materials including architected truss-like metastructures and random fiber networks.

Porosity-permeability tensor relationship of closely and randomly packed fibrous biomaterials and biological tissues: Application to the brain white matter

The constitutive model for the porosity-permeability relationship is a powerful tool to estimate and design the transport properties of porous materials, which has attracted significant attention for the advancement of novel materials. However, in comparison with other materials, biomaterials, especially natural and artificial tissues, have more complex microstructures e.g. high anisotropy, high randomness of cell/fibre dimensions/position and very low porosity. Consequently, a reliable microstructure-permeability relationship of fibrous biomaterials has proven elusive. To fill this gap, we start a mathematical derivation from the fundamental brain white matter (WM) formed by nerve fibres. This is augmented by a numerical characterisation and experimental validations to obtain an anisotropic permeability tensor of the brain WM as a function of the tissue porosity. A versatile microstructure generation software (MicroFiM) for fibrous biomaterial with complex microstructure and low porosity was built accordingly and made freely accessible here. Moreover, we propose an anisotropic poro-hyperelastic model enhanced by the newly defined porosity-permeability tensor relationship which precisely captures the tissues macro-scale permeability changes due to the microstructural deformation in an infusion scenario. The constitutive model, theories and protocols established in this study will both provide improved design strategies to tailor the transport properties of fibrous biomaterials and enable the non-invasive characterisation of the transport properties of biological tissues. This will lead to the provision of better patient-specific medical treatments, such as drug delivery. Statement of significanceDue to the microstructural complexity, a reliable microstructure-permeability relationship of fibrous biomaterials has proven elusive, which hinders our way of tuning the fluid transport property of the biomaterials by directly programming their microstructure. The same problem hinders non-invasive characterisations of fluid transport properties in biological tissues, which can significantly improve the efficiency of treatments e.g. drug delivery, directly from the tissues accessible microstructural information, e.g. porosity. Here, we developed a validated mathematical formulation to link the random microstructure to a fibrous material’s macroscale permeability tensor. This will advance our capability to design complex biomaterials and make it possible to non-invasively characterise the permeability of living tissues for precise treatment planning. The newly established theory and protocol can be easily adapted to various types of fibrous biomaterials.