Material Model Research Articles

Hierarchical Bayesian modeling for calibration and uncertainty quantification of constitutive material models: Application to a uniaxial steel material model

Constitutive material models play an integral role in finite element (FE) modeling of structural components and systems and are governed by a set of parameters. The values of the material model parameters are important for the FE model to be able to predict the real structural behavior as closely as possible. Realistic cyclic material constitutive models well calibrated to experimental data are critical when predicting the nonlinear dynamic response of structural systems to extreme loads (e.g., earthquakes, high winds, blast). Hence, this study focuses on the inference and uncertainty quantification of material model parameters from an experimental dataset consisting of data from experiments on multiple specimens of the same kind, which is a topic of great interest to the structural modeling and simulation community. Traditionally, Bayesian inference is performed by pooling the data from all the specimens, or by considering the data from a single specimen, disregarding the inherent variability (aleatory uncertainty) among specimens of the same kind. Consequently, traditional approaches fail to capture the population distribution of material model parameters, which represents the aleatory specimen-to-specimen variability that is essential for conducting reliability analysis and uncertainty propagation studies. Moreover, these approaches cannot accurately simulate the response of new specimens. To overcome these limitations, this study introduces a novel application of hierarchical Bayesian inference for calibrating material model parameters. By simultaneously considering experimental data from multiple specimens of the same kind, hierarchical Bayesian modeling quantifies both epistemic uncertainty and aleatory specimen-to-specimen variability. In this study, the parameters of the well-known Giuffré-Menegotto-Pinto (GMP) uniaxial material model for reinforcing steel are calibrated and validated based on a dataset of experimental cyclic tests conducted on thirty-six steel specimens, or coupons, originating from three different manufacturing mills, complying to two different manufacturing standards, and subjected to different strain histories. These strain histories are similar to those experienced during seismic events by reinforcing steel bars within reinforced concrete structures. The material model parameters are calibrated using both the traditional and the hierarchical Bayesian approach and the results are compared. Based on the experimental dataset employed in this study, a joint probability distribution of the GMP material model parameters that quantifies both epistemic (due to finite sample size) and aleatory (coupon-to-coupon) variability or uncertainty is provided which can be used for uncertainty propagation in reliability and risk analyses of nonlinear dynamic systems.

A methodology for direct parameter identification for experimental results using machine learning — Real world application to the highly non-linear deformation behavior of FRP

In this work, we demonstrate how Machine learning (ML) techniques can be employed to externalize the knowledge and time intensive process of material parameter identification. This is done on the example of a recent data driven material model for the non-linear shear behavior of glass fiber reinforced polypropylene (GF/PP) (Gerritzen, 2022). A convolutional neural network (CNN) based model architecture is trained to predict material modeling parameters based on the input of stress–strain-curves. The optimal model architecture and training setup are determined by hyperparameter optimization (HPO). Solely virtual data, generated using the target material model, is used throughout the training and HPO. The final CNN is capable of calculating model parameter combinations from experimental stress–strain-curves which lead to excellent agreement between experimental and associated model curve.

Topology Optimization of Hard-Magnetic Soft Phononic Structures for Wide Magnetically Tunable Band Gaps

Abstract Hard-magnetic soft materials, which exhibit finite deformation under magnetic loading, have emerged as a promising class of soft active materials for the development of phononic structures with tunable elastic wave band gap characteristics. In this paper, we present a gradient-based topology optimization framework for designing the hard-magnetic soft materials-based two-phase phononic structures with wide and magnetically tunable anti-plane shear wave band gaps. The incompressible Gent hyperelastic material model, along with the ideal hard-magnetic soft material model, is used to characterize the constitutive behavior of the hard-magnetic soft phononic structure phases. To extract the dispersion curves, an in-house finite element model in conjunction with Bloch’s theorem is employed. The method of moving asymptotes is used to iteratively update the design variables and obtain the optimal distribution of the hard-magnetic soft phases within the phononic structure unit cell. Analytical sensitivity analysis is performed to evaluate the gradient of the band gap maximization function with respect to each one of the design variables. Numerical results show that the optimized phononic structures exhibit a wide band gap width in comparison to a standard hard-magnetic soft phononic structure with a central circular inclusion, demonstrating the effectiveness of the proposed numerical framework. The numerical framework presented in this study, along with the derived conclusions, can serve as a valuable guide for the design and development of futuristic tunable wave manipulators.

A Dynamic Damage Constitutive Model of Rock-like Materials Based on Elastic Tensile Strain

To accurately characterize the damage of rock-like materials under simultaneous or alternating tensile and compressive loading, a dynamic damage constitutive model for rock-like materials based on elastic tensile strain is developed by integrating the classical compressive plastic damage model and the tensile elastic damage model. The model is based on the Holmquist–Johnson–Cook (HJC) and Kuszmaul (KUS) models, categorizing the element stress state into tensile and compressive states through positive and negative elastic volumetric strain. It utilizes elastic tensile strain to enhance the calculation method for tensile cracks, determining the tensile strength of the principal direction based on the contribution rate of tensile principal stress for uniaxial/multiaxial loading. Additionally, it establishes a maximum elastic tensile strain rate function to rectify the model’s effect on the tensile strain rate. Through the LS-DYNA subroutine development, the model proficiently delineates the distribution of ring-shaped cracks on the frontal side and strip-shaped cracks on the rear side of the reinforced concrete slab subjected to impact loading. Numerical simulations demonstrate that the model provides more accurate damage prediction results for stress conditions involving simultaneous or alternating compression and tension, offering valuable insights for damage analysis in engineering blasting or impact penetration.

Stress Representations for Tensor Basis Neural Networks: Alternative Formulations to Finger–Rivlin–Ericksen

Abstract Data-driven constitutive modeling frameworks based on neural networks and classical representation theorems have recently gained considerable attention due to their ability to easily incorporate constitutive constraints and their excellent generalization performance. In these models, the stress prediction follows from a linear combination of invariant-dependent coefficient functions and known tensor basis generators. However, thus far the formulations have been limited to stress representations based on the classical Finger–Rivlin–Ericksen form, while the performance of alternative representations has yet to be investigated. In this work, we survey a variety of tensor basis neural network models for modeling hyperelastic materials in a finite deformation context, including a number of so far unexplored formulations which use theoretically equivalent invariants and generators to Finger–Rivlin–Ericksen. Furthermore, we compare potential-based and coefficient-based approaches, as well as different calibration techniques. Nine variants are tested against both noisy and noiseless datasets for three different materials. Theoretical and practical insights into the performance of each formulation are given.

Two-dimensional migration characteristics of contaminant through composite liner with arbitrarily distributed defects

Previous studies indicate that liner defects can significantly accelerate contaminant migration in landfill, shortening the migration time by orders of magnitude. Although the effect of defects upon contaminant migration and barrier capacity of liner system has been investigated based on several theoretical models, they are always limited to one-dimensional scopes. Here a two-dimensional (2-D) model was established for contaminant transport through composite liner to the soil layer, with geomembrane (GM) defects arbitrarily distributed along the horizontal direction, and then Laplace transform, Fourier transform, and boundary transform method were utilized to derive its semi-analytical solution, which was verified by experimental data and numerical results. The obtained solution can take nonuniformly distributed defects into account and demonstrates the 2-D contaminant concentration and flux profiles in the spatiotemporal domain. Computational results of the solution are employed to illustrate the roles of material coefficients and modeling sizes upon the variations of contaminant concentration and flux. Results support that contaminant migration is expedited by the GM defect in landfill, and geosynthetics clay liner can reduce the pollution level caused by GM failure. Moreover, the contaminant flux will not be significantly influenced by the defect positions, which, however, leads to non-negligible impact on concentration profiles.

FSGe: A fast and strongly-coupled 3D fluid–solid-growth interaction method

Equilibrated fluid–solid-growth (FSGe) is a fast, open source, three-dimensional (3D) computational platform for simulating interactions between instantaneous hemodynamics and long-term vessel wall adaptation through mechanobiologically equilibrated growth and remodeling (G&R). Such models can capture evolving geometry, composition, and material properties in health and disease and following clinical interventions. In traditional G&R models, this feedback is modeled through highly simplified fluid solutions, neglecting local variations in blood pressure and wall shear stress (WSS). FSGe overcomes these inherent limitations by strongly coupling the 3D Navier–Stokes equations for blood flow with a 3D equilibrated constrained mixture model (CMMe) for vascular tissue G&R. CMMe allows one to predict long-term evolved mechanobiological equilibria from an original homeostatic state at a computational cost equivalent to that of a standard hyperelastic material model. In illustrative computational examples, we focus on the development of a stable aortic aneurysm in a mouse model to highlight key differences in growth patterns between FSGe and solid-only G&R models. We show that FSGe is especially important in blood vessels with asymmetric stimuli. Simulation results reveal greater local variation in fluid-derived WSS than in intramural stress (IMS). Thus, differences between FSGe and G&R models became more pronounced with the growing influence of WSS relative to pressure. Future applications in highly localized disease processes, such as for lesion formation in atherosclerosis, can now include spatial and temporal variations of WSS.

Uniaxial material model with softening for simulating the cyclic behavior of steel tubes in concrete‐filled steel tube beam‐columns

AbstractThis paper presents a new uniaxial constitutive material formulation with softening for simulating the inelastic behavior of steel rectangular tubes in concrete‐filled steel tube (CFST) members. The primary behavioral characteristics of the steel tube in CFST members are isolated and pronounced through a carefully designed experimental campaign with CFST specimens subjected to uniaxial strain‐based loading protocols. The model is expressed in an effective stress–strain domain, where the effective uniaxial strain is defined as the uniaxial displacement within a dissipative zone over a predefined length. In the pre‐peak state, the proposed model can effectively capture the combined kinematic/isotropic hardening and Bauschinger effect—characteristic of mild structural steels—within the framework of rate‐independent plasticity. In the post‐peak state, the proposed model traces strength deterioration due to outward local buckling, which is a characteristic nonlinear geometric instability in CFST members due to the presence of the filled concrete in the steel tube. The proposed constitutive formulation incorporates a softening branch that exponentially decays to trace the stabilization of the outward buckling wave within the buckling region in successive inelastic loading cycles. Cyclic deterioration of the effective stress is explicitly considered via an energy‐based rule. The proposed model is calibrated to a CFST dataset. Regression equations are proposed for predicting the input model parameters. These equations cover a wide range of geometric parameters and structural steel materials in CFST members. Comparisons with prior tests on actual CFST beam‐columns under planar symmetric cyclic loading suggest that conventional 2‐dimensional displacement‐based beam‐column elements can predict the full‐range of the hysteretic behavior of the CFST members with the proposed constitutive formulation including cases where the post‐peak response of CFST members exhibits negative stiffness.

Three-dimensional solidification modeling of various materials using the lattice Boltzmann method with an explicit enthalpy equation

Three-dimensional solidification modeling of various materials using the lattice Boltzmann method with an explicit enthalpy equation

Crystal Composition Transformer: Self-Learning Neural Language Model for Generative and Tinkering Design of Materials.

Self-supervised neural language models have recently achieved unprecedented success from natural language processing to learning the languages of biological sequences and organic molecules. These models have demonstrated superior performance in the generation, structure classification, and functional predictions for proteins and molecules with learned representations. However, most of the masking-based pre-trained language models are not designed for generative design, and their black-box nature makes it difficult to interpret their design logic. Here a Blank-filling Language Model for Materials (BLMM) Crystal Transformer is proposed, a neural network-based probabilistic generative model for generative and tinkering design of inorganic materials. The model is built on the blank-filling language model for text generation and has demonstrated unique advantages in learning the "materials grammars" together with high-quality generation, interpretability, and data efficiency. It can generate chemically valid materials compositions with as high as 89.7% charge neutrality and 84.8% balanced electronegativity, which are more than four and eight times higher compared to a pseudo-random sampling baseline. The probabilistic generation process of BLMM allows it to recommend materials tinkering operations based on learned materials chemistry, which makes it useful for materials doping. The model is applied to discover a set of new materials as validated using the Density Functional Theory (DFT) calculations. This work thus brings the unsupervised transformer language models based generative artificial intelligence to inorganic materials. A user-friendly web app for tinkering materials design has been developed and can be accessed freely at www.materialsatlas.org/blmtinker.

MODIFICATION OF THE EXTENDED TUBE MODEL (METM) FOR THE CHARACTERIZATION OF FILLED VULCANIZATES

ABSTRACT The aim of this study is to develop a material model for filled vulcanizates that is physically justifiable. This model builds upon the established extended tube model and is incorporated into a finite element program. The research demonstrates that the intrinsic deformation concept is inadequate for describing nonlinear deformation behavior under the assumption of incompressible, isotropic materials. Consequently, an alternative approach is proposed, employing a strain function rather than direct use of principal strains, to characterize reinforcement behavior. This strain function aligns with the first invariant of the right Cauchy-Green strain tensor over a wide deformation range. At minor deformations, the entanglements’ contribution is considered through an additional reinforcement term. The novel reinforcement function is depicted as a sum of three elements, each representing reinforcement at different strain levels: low, medium, and high. Experimental comparisons show that the Modified Extended Tube Model (METM) effectively captures the stress-strain response of filled systems across all deformation levels. Furthermore, the reinforcement function parameters, derived from fitting the METM to experimental data, offer a quantitative assessment of the fillers’ reinforcing effects, while the extended tube model parameters reflect the network characteristics.

Piezoresistive modeling of orthotropic 3D-printing composite line extrusions with non-affine reorientation of fibers

This work introduces a micromechanical semi-analytical model to estimate piezoresistive constants in 3D-printable short-fiber composites, extending the Mori–Tanaka scheme with two innovative components. Firstly, the model incorporates non-affine reorientation of fibers, controlled by a parameter η, which significantly impacts texture coefficients. This parameter introduces an additional layer of complexity, modifying texture coefficients beyond traditional affine fiber reorientations. Observational data illustrate a linear relationship between piezoresistivities and η, leading to the development of a statistical model that calculates η based on the fiber aspect ratio. Secondly, the model accounts for preferential fiber orientation in the undeformed state, resulting in an orthotropic material model. This anisotropy is quantified using an Orientation Distribution Function (ODF) derived from X-ray scans, which is parameterized to maintain symmetry across three orthogonal planes. Initial investigations indicate that the inherent anisotropy introduced by the printing process substantially affects the initial resistivity of 3D-printed composites. Utilizing a Gaussian transversely isotropic model, we find that neglecting this anisotropy could lead to significant errors in understanding and predicting piezoresistive behavior. The model’s incorporation into advanced nanocomposite frameworks offers preliminary reconciliation with experimental data. Additionally, our results emphasize the necessity to refine wavy fiber models by incorporating non-affine rotations, particularly crucial for fibers with small aspect ratios, thereby enhancing predictive accuracy. The findings lay a robust foundation for future research, emphasizing the need for comprehensive experimental validation and setting the stage for nuanced applications in piezoresistive composite materials.

Visco-hyperelastic material model fitting to experimental stress–strain curves using a genetic algorithm and its application to soft tissue simulants

Ballistic impacts on human thorax without penetration can produce severe injuries or even death of the carrier. Soft tissue finite element models must capture the non-linear elasticity and strain-rate dependence to accurately estimate the dynamic human mechanical response. The objective of this work is the calibration of a visco-hyperelastic model for soft tissue simulants. Material model parameters have been calculated by fitting experimental stress–strain relations obtained from the literature using genetic algorithms. Several parametric analyses have been carried out during the definition of the optimization algorithm. In this way, we were able to study different optimization strategies to improve the convergence and accuracy of the final result. Finally, the genetic algorithm has been applied to calibrate two different soft tissue simulants: ballistic gelatin and styrene–ethylene–butylene–styrene. The algorithm is able to calculate the constants for visco-hyperelastic constitutive equations with high accuracy. Regarding synthetic stress–strain curves, a short computational time has been shown when using the semi-free strategy, leading to high precision results in stress–strain curves. The algorithm developed in this work, whose code is included as supplementary material for the reader use, can be applied to calibrate visco-hyperelastic parameters from stress–strain relations under different strain rates. The semi-free relaxation time strategy has shown to obtain more accurate results and shorter convergence times than the other strategies studied. It has been also shown that the understanding of the constitutive models and the complexity of the stress–strain objective curves is crucial for the accuracy of the method.

Multiscale modeling for viscoelasticity of woven CFRP considering preforming and curing effects via finite element and long-short term memory analysis

The constitutional model is crucial to model the complex response of woven carbon fiber reinforced plastics (CFRPs) during curing. This study developed a multiscale modeling method to describe the viscoelastic behavior of preformed woven CFRP parts during curing. The essence of the viscoelastic modeling lies in the stiffness matrix, which was predicted via the long-short term memory (LSTM) model. A library of viscoelastic stiffness components for the LSTM model was created through finite element method (FEM) on mesoscopic representation volume elements (RVEs). Specifically, FEM models for RVEs with different configurations were established first, and then utilized for virtual relaxation tests to build the stiffness component library for the woven CFRP. Afterwards, the LSTM model was embedded into the material model for FEM at the part-level. Finally, the prediction accuracy of the multiscale modeling method for viscoelasticity of the woven CFRP samples was validated by experiments with the average error of 6.62%.

A length-free phase field model for epoxy adhesive materials based on modified Drucker–Prager criterion

Characterizing the cracking behavior of epoxy adhesive material is of great importance for composite structures. Recently, the phase field model has emerged as the preferred method for predicting the crack propagation. This paper presents a length-free phase field model considering the characteristics of epoxy adhesive materials. The proposed model is formulated within a framework that decomposes the phase field fracture driving force, ensuring that it adequately considers the tension/compression asymmetry of the epoxy adhesive materials. The effects of hydrostatic pressure, deviational stress, and friction are incorporated into the model by employing a modified Drucker-Prager failure criterion. The failure criterion is included in the phase field model using the effective stress invariants. Furthermore, the internal length scale, previously considered to lack real physical meaning, is reformulated based on material strength. This model addresses the challenge of measuring the internal length of epoxy materials. It serves as a valuable reference for applying phase field models to epoxy materials. The accuracy of the model is validated through an L-shaped plate simulation, and an attempt using the model to predict the crack development in thick epoxy adhesive joints is undertaken. Several representative samples are simulated, including three double cantilever beams with different configurations. The numerical results demonstrate a good correlation with experimental data, highlighting the potential of the model in simulating the crack propagation in epoxy adhesive joints.

Development of a continuum-based, meshless, finite element modeling approach for representation of trabecular bone indentation

Implant subsidence into the underlying trabecular bone is a common problem in orthopaedic surgeries; however, the ability to pre-operatively predict implant subsidence remains limited. Current state-of-the-art computational models for predicting subsidence have issues addressing this clinical problem, often resulting from the size and complexity of existing subject-specific, image-based finite element (FE) models. The current study aimed to develop a simplified approach to FE modeling of subject-specific trabecular bone indentation resulting from implant penetration.Confined indentation experiments of human trabecular bone with flat- and sharp-tip indenters were simulated using FE analysis. A generalized continuum-level approach using a meshless smoothed particle hydrodynamics (SPH) approach and an isotropic crushable foam (CF) material model was developed for the trabecular bone specimens. Five FE models were generated with CF material parameters calibrated to cadaveric specimens spanning a range of bone mineral densities (BMD). Additionally, an alternative model configuration was developed that included consideration of bone marrow, with bone and marrow material parameters assigned to elements randomly according to bone volume (BV%) measurements of experimental specimens, owing to the non-uniform nature of trabecular bone tissue microstructure.Statistical analysis found significant correlation between the shapes of the numerical and experimental force-displacement curves. FE models accurately captured the bone densification patterns observed experimentally. Inclusion of marrow elements offered improved response prediction of the flat-tip indenter tests.Ultimately, the developed approach demonstrates the ability of a generalizable continuum-level SPH approach to capture bone variability using clinical bone imaging metrics without needing detailed image-based geometries, a significant step towards simplified subject-specific modeling of implant subsidence.

Research on ship-ice collision model and ship-bow fatigue failure Mechanism based on elastic-plastic ice constitutive relation

Collisions between sea ice and ships can damage the hull structure and pose a threat to crew safety in severe cases. The modelling of ice materials is crucial, but it is difficult to study ice-ship interactions. In this study, an ice constitutive model including the temperature factor was verified through experiments and numerical simulations of uniaxial and triaxial compression. Furthermore, the effects of salinity and porosity on the compressive strength of ice were studied using experiments and numerical simulations. The mechanical behaviour of sea ice was then simulated using the constitutive model mentioned above. A numerical model of collisions between polar ships and sea ice was established to investigate the ice-breaking processes of ships under different working conditions. The collision force and the level of structural damage were obtained. The influences of the initial pore size, hull speed, bow angle, and bow shape on the collision force and structural damage in the ship-ice collision process were analysed. Finally, fatigue damage to the bow structure at different ice thicknesses and speeds was calculated. The present results provide a reference for the structural design and optimisation of polar ships to a certain extent and improve the theory of ship-ice collisions.

A profound study of damage behavior for Al 2024-T3 alloy worksheet produced by constrained groove pressing in the superior practical condition

Constrained groove pressing (CGP) process is one of the most efficient and novel methods of severe plastic deformation to manufacture ultra-fine sheet metal. The present research work is related to the study of CGP process of 2024-T3 Aluminum alloy sheet. The empirical and numerical simulation of CGPed- specimens have been examined at both room and elevated temperatures. In order to simulate the constrained groove pressing process in Abaqus software, the Johnson–Cook material model has been employed. The geometrical variables of the CGP process include the teeth number, teeth angle, and sheet thickness, and the criterion for the superiority of the numerical test is the maximum reduction of two equivalent strain and equivalent force factors, simultaneously. To determine the weight’s coefficients of the target factors and select the superior test, the Shannon’s Entropy and Simple Additive Weighting (SAW) methods have been used, respectively. After validating the numerical findings, the variation of damage parameter, stress triaxiality and the equivalent plastic strain distribution in the superior practical condition have been evaluated in detail. Based on the Entropy-SAW hybrid technique, the weight’s coefficients of equivalent strain and equivalent force target factors were computed to, in turn, 0.38 and 0.62. Also, the results revealed that the CGP process could not be performed at room temperature based on high damage evolution. But, at elevated temperature, the damage parameter (D) doesn't exceed 0.26. Also, the maximum stress triaxiality and equivalent plastic strain (PEEQ) at this process temperature reached to 0.5 and 0.1, respectively.

A Modeling Framework for the Thermoforming of Carbon Fiber Reinforced Thermoplastic Composites

A comprehensive modeling framework for the thermoforming of polymer matrix woven laminate composite was developed. Two numerical indicators, the slip path length and traction magnitude, have been identified to be positively correlated to matrix smearing and wrinkling defects. The material model has been calibrated with picture-frame experimental results, and the prediction accuracy for intra-ply shear and thickness distribution was examined with measurements of the physically formed parts. Specifically, thickness prediction for most locations on the formed parts was accurate within an 11.6% error margin. However, at two points with significant intra-ply shear, the prediction errors increased to around 20%. Finally, a parametric study was conducted to determine the relationship between various process parameters and the quality of the formed part. For the trapezoidal part, orienting the laminate at 45 degrees to the mold axis reduces the likelihood of matrix smear and wrinkling defects. Although this laminate orientation yielded a greater spatial variation in part thickness, the thickness deviation is lower than that for the 0-degree orientation case. Two forming analyses were conducted with ramp rates of 25 mm/s and 80 mm/s to match the equipment’s operational limits. It was observed that higher forming rates led to a greater likelihood of defects, as evidenced by a 15% and 10% increase in the formed part areas with longer slip paths and higher traction magnitudes, respectively. It was discovered that shallower molds benefit from faster ramp rates, while deeper molds require slower rates to manage extensive shearing, stretching and bending. Faster forming rates lead to smaller thickness increases at high intra-ply shear regions, indicating a shift from intra-ply shear to out-of-plane bending due to the visco-plastic effect of the molten laminate and can negatively impact part quality. Lastly, it was shown that a well-conceived strategy using darts could improve the part quality by reducing the magnitude of the defect indicators.

Examining the adaptive elastic anisotropy of granular materials

Changes of granular material anisotropy with stress are a function of numerous microscale attributes, such as contact network, particle size uniformity and shape. Such influences are often represented with fabric variables. Although multiple choices for fabric exist, the question of which variable best explains why and how granular materials adapt to stress is still open. In this study, the effectiveness of different fabric variables in tracking stress-induced anisotropy is compared. The analysis is restricted to a simple, yet fundamental, range of behavioir: elastic deformation. Both particle-scale simulations and continuum analyses are deployed. Analyses based on the discrete-element method (DEM) reveal that, depending on the contact behaviour, anisotropy may emerge even if the topology of the grain contact network is unchanged. The inspection of these results through a continuum-scale hyperelastic constitutive law further reveals that the computed trends cannot be captured without an evolving fabric variable. A comparison between such fabric and multiple microstructural indicators extracted from DEM simulations suggests that elastic stress-induced anisotropy is primarily a manifestation of changes in the anisotropic particle contact area distribution in response to the current magnitude and orientation of force chains. These results not only offer opportunities to enhance current continuum elastic models for granular materials, but can also be used to design testing strategies quantifying changes in fabric anisotropy through multi-scale measurements.