Multiscale Materials Modeling Research Articles

Modeling of ice-matrix composite fracture

This article discusses the results of a study that used the structural approach to conduct multiscale modeling of composite materials. These materials are composed of an ice matrix that has been enhanced with high-strength basalt fibers. The research involved numerical modeling to analyze the fracture process of composite materials made by freezing fresh water with added basalt fibers. The analysis included experimental data from samples of pure ice and composites with different amounts of filler. The effective modulus of elasticity of the composites was determined by considering the quantity of basalt fiber reinforcement. The discrepancy between the strength obtained by finite element complex ANSYS numerical calculation and the experimental data was revealed by a series of macroscopic test calculations of the composite material sample, according to which the effective modulus of elasticity of the composite was recalculated and corrections were introduced into the Voight and Reuss models, taking into account the non-uniform distribution of the fibers and the non-ideal adhesion between the fibers and water ice. A stochastic model of crack growth at the micro level was also used with the data on the diameter and length of basalt fibers and their random distribution in the layers of the composite material. Using the newly acquired effective elastic moduli and the SmartCrackGrowth algorithm, a satisfactory agreement of the crack growth rate with the obtained by stochastic calculation was achieved. The refined method of effective elastic moduli and multilevel model of stress-strain state calculation of composite materials are recommended for assessing the strength of ice cover and designing winter roads with high load-bearing capacity and long operational duration in the Arctic and Subarctic environments.

Design of polycrystalline metallic alloys under multi-scale uncertainty by connecting atomistic to meso‑scale properties

Uncertainty quantification plays a pivotal role in advancing the development of reliable and high-performance material designs via multiscale materials modeling. This study focuses on modeling the uncertainty of meso‑scale mechanical properties, e.g. modulus of elasticity and yield strength of Ti-7Al, by incorporating the inherent randomness of substitutional atoms of the alloy and its microstructural texture. A molecular dynamics approach is employed to probe the epistemic uncertainty of single-crystal properties. Moreover, the aleatoric uncertainty is quantified using the experimental microstructural texture data of a previous investigation. The propagation of the epistemic and aleatoric uncertainty on the homogenized properties is investigated using an analytical uncertainty quantification method. Subsequently, the Ti-7Al alloy microstructures are designed to improve meso‑scale mechanical properties under uncertainty by integrating the analytical method into the optimization scheme.

Multi-layer perceptron-based data-driven multiscale modelling of granular materials with a novel Frobenius norm-based internal variable

One objective of developing machine learning (ML)-based material models is to integrate them with well-established numerical methods to solve boundary value problems (BVPs). In the family of ML models, recurrent neural networks (RNNs) have been extensively applied to capture history-dependent constitutive responses of granular materials, but these multiple-step-based neural networks are neither sufficiently efficient nor aligned with the standard finite element method (FEM). Single-step-based neural networks like the multi-layer perceptron (MLP) are an alternative to bypass the above issues but have to introduce some internal variables to encode complex loading histories. In this work, one novel Frobenius norm-based internal variable, together with the Fourier layer and residual architecture-enhanced MLP model, is crafted to replicate the history-dependent constitutive features of representative volume element (RVE) for granular materials. The obtained ML models are then seamlessly embedded into the FEM to solve the BVP of a biaxial compression case and a rigid strip footing case. The obtained solutions are comparable to results from the FEM-DEM multiscale modelling but achieve significantly improved efficiency. The results demonstrate the applicability of the proposed internal variable in enabling MLP to capture highly nonlinear constitutive responses of granular materials.

A new open-source framework for multiscale modeling of fibrous materials on heterogeneous supercomputers

A new open-source framework for multiscale modeling of fibrous materials on heterogeneous supercomputers

Microstructure generation algorithm and micromechanics of curved fiber composites with random waviness

During multiscale modeling and analysis of composite materials, accurately capturing the distinctive microstructural features of the material is essential. This is achieved by generating a representative volume element (RVE). Fiber reinforcements in composites can exhibit various shapes, including straight, slightly wavy, or complex shapes, depending on the inherent properties or the manufacturing process. Fibers are characterized based on their tortuosity, spread, and orientation distribution. It is crucial to account for these geometrical attributes during the microstructure generation and subsequent micromechanics modelling as they significantly influence the effective properties of the composite. The present work describes a novel algorithm capable of modeling a broad range of 3D periodic microstructures with fibers having random waviness. The effects of various parameters in the algorithm are studied to understand their influence on fiber shapes. This is followed by finite element analysis of the generated RVEs using the embedded element technique to quantify the microstructure- mechanical properties relationships. Finally, guidelines on the usage of the proposed model to generate fibers with desired microstructure is elucidated. A comprehensive framework for modeling and analyzing microstructures with complex fiber geometry is outlined.

Extended tensor decomposition model reduction methods: Training, prediction, and design under uncertainty

This paper introduces an extended tensor decomposition (XTD) method for model reduction. The proposed method is based on a sparse non-separated enrichment to the conventional tensor decomposition, which is expected to improve the approximation accuracy and the reducibility (compressibility) in highly nonlinear and singular cases. The proposed XTD method can be a powerful tool for solving nonlinear space–time parametric problems. The method has been successfully applied to parametric elastic–plastic problems and real time additive manufacturing residual stress predictions with uncertainty quantification. Furthermore, a combined XTD-SCA (self-consistent clustering analysis) strategy is presented for multi-scale material modeling, which enables real time multi-scale multi-parametric simulations. The efficiency of the method is demonstrated with comparison to finite element analysis. The proposed method enables a novel framework for fast manufacturing and material design with uncertainties.

Data-driven multiscale modelling of granular materials via knowledge transfer and sharing

Machine learning approaches have found immense potential to revolutionise the constitutive modelling of granular materials. However, data scarcity poses a significant challenge to this emerging paradigm. This study aims to tackle this issue by presenting two transfer learning-based strategies that harness well-established constitutive knowledge and similar material data to reduce data demands for data-driven material modelling. The first approach utilises phenomenological constitutive models to generate massive synthetic data which reflect the targeted material behaviour to train a base model. This base model is then repurposed for a new task based on numerical simulation data via transfer learning. The other approach involves using available material data to train a base model, which is then applied to other new materials that are similar but with limited data. The proposed transfer learning methods are tested on both particle-scale simulations of representative volume elements (RVEs) and hierarchical multiscale modelling of boundary value problems (BVPs) of granular materials. The trained data-driven material model is embedded in numerical simulations with the finite element method (FEM) to validate its accuracy, efficiency, and stability. The results demonstrate that transfer learning can effectively achieve high-quality machine learning predictions with limited data. The transfer learning strategy presented in this study is expected to be widely applicable to small data-driven material modelling.

A hybrid algorithm of particle swarm optimization and finite element method to identify local mesoscopic damage of concrete-like materials

Meso-scale material modeling and parameter identification are still unsettled issues in the current multi-scale methods for the field of computational mechanics. In this investigation, a hybrid algorithm of particle swarm optimization and finite element method coupled with continuum damage mechanics is proposed to forecast local mesoscopic elasticity modulus and damage of concrete-like materials based on the macroscopic stress-strain relationship data curve. The algorithm establishes a bridge between mesoscopic mechanical analysis and macroscopic mechanical analysis, which can also guarantee the consistency of analysis in different scales. A representative numerical case is conducted to support the algorithm. Additionally, the effect of different divisions of representative volume element is analyzed based on the algorithm, and the recommended size of representative volume element is 5 mm. The prediction results match well with the corresponding macroscopic experimental results and mesoscopic experimental results based on the chosen recommended size of representative volume element. The effectiveness of the algorithm is verified, which can support an effective numerical tool to optimize and identify mesoscopic mechanical parameters and damage for multi-scale material modeling and analysis.

Quantitative representation of directional microstructures of single-crystal superalloys in cyclic crystal plasticity based on neural networks

Nickel-based single-crystal alloys undergo microstructural degradation induced by thermal exposure. The directional rafting of microstructures significantly affects the mechanical properties and makes the material anisotropic. For structural design, establishing a quantitative description of microstructural effects in a constitutive model becomes essential and is still a tough research topic in multi-scale materials modeling. In the present work, the fabric tensor was correlated with the anisotropic cyclic crystal plasticity of nickel-based single-crystal alloys with the help of neural networks. The microstructural representative volume elements with various single-crystal morphologies were generated by the phase-field method and the deformation behaviors were studied under different crystal orientations and loading configurations. The neural network analysis confirmed that the fabric tensor can present anisotropic single-crystallographic microstructural features and describe mechanical behavior under both monotonic and cyclic multi-axial loading conditions. The history-dependent anisotropic cyclic hardening or softening behavior of the material can be captured by the introduced microstructural state variable. A principal component analysis (PCA) aided gradient-based attribution method was proposed to evaluate the importance of input variables. The characterization of different material components and their contribution to the stress–strain relationships are investigated and validated. The fabric tensor was verified to be an effective microstructural indicator for the continuum plasticity of single-crystal alloys.

Second-order multi-scale modelling of natural and architected materials in the presence of voids: Formulation and numerical implementation

This contribution proposes a second-order computational homogenisation formulation for natural and architected materials in the presence of voids. The macro-scale is described by a second gradient continuum theory in the finite strain regime, and the micro-scale is modelled by the concept of representative volume element (RVE) within the classical first-order continuum mechanics. The Method of Multi-scale Virtual Power is employed to link the two scales, ensuring a variationally consistent scale transition. Unlike the multi-scale model proposed by Rodrigues Lopes and Andrade Pires (2022), the developed formulation allows the consideration of voids in the RVE domain and boundary, which is critical for modelling cellular materials, lattice structures, and metamaterials, among others. This is achieved by defining the kinematical quantities only in the solid domain of the RVE and postulating a new homogenisation relation for the second-order gradient. The kinematic constraints are imposed on the RVE by the Lagrange multiplier method and particularised for minimal (lower bound), periodic and direct (upper bound) conditions. It is demonstrated that the homogenised macroscopic stress tensors can be expressed in terms of the Lagrange multipliers. The finite element method is adopted for the numerical solution of the micro and macro equilibrium. The Newton–Raphson scheme is employed to solve the non-linear systems of equations at both scales and the consistent macroscopic tangents required for the FE2 framework are derived. Several numerical examples of porous solids, lattice structures and metamaterials illustrate the consistency and applicability of the formulation for two and three-dimensional problems.

A 3D multi-scale skeletal muscle model to predict active and passive responses. Application to intra-abdominal pressure prediction

Computational models have been used extensively to study the behavior of skeletal muscle structures, however few of these models are able to evaluate their 3D active response using as input experimental measurements such as electromyography. Hence, improving the activation mechanisms in simulation models can provide interesting and useful achievements in this field. Therefore, the purpose of this paper was to develop a multi-scale chemo-mechanical material model to consider the active behavior of skeletal muscle in 3D geometries. The model was used to investigate the response of abdominal muscles which represent a challenging scenario due to their complex geometry and anatomical conditions. Realistic muscle geometries and other tissues of the human abdomen, including transverse abdominis (TA), internal oblique (IO), external oblique (EO), rectus abdominis (RA), rectus sheath (RSH), linea alba (LA) and aponeurosis (APO) were considered. Since the geometry of these tissues was obtained from magnetic resonance images, an iterative algorithm was implemented to find the initial stress state that achieve the equilibrium of them with the intra-abdominal pressure. In order to investigate the functionality of the proposed model, the increase of intra-abdominal pressure was calculated during cough in the supine position while the Ca2+ signal for activating the muscles was set in regard to experimentally recorded electrical activity from previous studies. The amount of intra-abdominal pressure calculated by the model is consistent with reported experimental results. This model can serve as a virtual laboratory to analyze the role of the abdominal wall components in different conditions, such as the performance of meshes used for repairing hernia defects.

Uncertainty quantification and propagation in the microstructure-sensitive prediction of the stress-strain response of woven ceramic matrix composites

Hierarchical multiscale modeling of heterogeneous materials has traditionally relied upon a deterministic estimation of constitutive properties when making microstructure-sensitive predictions of effective response at each subsequent length-scale. Such an approach is wholly unsuitable for a variety of material classes, such as ceramic matrix composites, which exhibit large variability at multiple length-scales. This work demonstrates a framework for approaching two open problems towards improved microstructure-sensitive predictions, namely, (i) probabilistically calibrating complex constitutive models at the mesoscale to sparsely observed macroscale experimental data, and (ii) propagating this stochastic constituent behavior at the mesoscale towards low-cost homogenized predictions for unseen microstructures. The proposed stochastic scale-bridging framework displays a continuity of information flow where no portion of the experimental data is neglected out of convenience, facilitating the greatest information gain from oftentimes costly experiments. In this paper, suitable protocols were developed to address the challenges described above. The protocols were subsequently demonstrated on ceramic matrix composite’s uniaxial tensile stress–strain response, where constituent behavior at the mesoscale was described using continuum damage mechanics, and predictions encapsulating constitutive model parameter uncertainty were made for novel microstructures. The methodology presented in this work is broadly applicable to various material classes and constitutive models with high-dimensional parameter sets.

A review on computational modeling of instability and degradation issues of halide perovskite photovoltaic materials

AbstractHybrid halide perovskite solar cells have been recognized as one of the most promising future photovoltaic technologies due to their demonstrated high‐power conversion efficiency, versatile stoichiometry and low cost. However, degradation caused by environmental exposure and structural instability due to ionic defect migration hinders the commercialization of this technology. While the experimental studies try to understand the phenomenology of the degradation mechanisms and devise practical measures to improve the stability of these materials, theoretical studies have attempted to bridge the gaps in our understanding of the fundamental degradation mechanisms at different time and length scales. A deeper understanding of the physical and chemical phenomena at an atomic level through multiscale materials modeling is going to be crucial for the knowledge‐based prognosis and design of future halide perovskites. There have been increased efforts in this direction in the last few years. However, the instability fundamentals explored through atomistic modeling and simulation methods have not been reviewed comprehensively in the literature yet. Therefore, this paper is an attempt to present a critical review, while identifying the existing gaps and opportunities in the investigation of the degradation and instability issues of the halide perovskites using computational methods. The review will primarily focus on the instability caused due to the intrinsic ionic defect migration and degradation due to thermal, moisture and light exposure. The findings from the simulation studies conducted primarily using density functional theory, ab initio molecular dynamics, classical molecular dynamics and machine learning methods will be presented.This article is categorized under: Software > Molecular Modeling Structure and Mechanism > Computational Materials Science Data Science > Artificial Intelligence/Machine Learning

The non-affine fiber network solver: A multiscale fiber network material model for finite-element analysis

Multiscale mechanical models in biomaterials research have largely relied on simplifying the microstructure in order to make large-scale simulations tractable. The microscale simplifications often rely on approximations of the constituent distributions and assumptions on the deformation of the constituents. Of particular interest in biomechanics are fiber embedded materials, where simplified fiber distributions and assumed affinity in the fiber deformation greatly influence the mechanical behavior. The consequences of these assumptions are problematic when dealing with microscale mechanical phenomena such as cellular mechanotransduction in growth and remodeling, and fiber-level failure events during tissue failure. In this work, we propose a technique for coupling non-affine network models to finite element solvers, allowing for simulation of discrete microstructural phenomena within macroscopically complex geometries. The developed plugin is readily available as an open-source library for use with the bio-focused finite element software FEBio, and the description of the implementation allows for the adaptation to other finite element solvers.

English

Recently, there has been a high interest in using lightweight aluminum foams for automotive, railway and aerospace operations. Because of its high ductility and deformability, Aluminum foam is generally used for energy absorption for crashworthiness applications. To keep safe and avoid occupant injuries, it is necessary to absorb the kinetic energy generated during impact. Thus, to absorb high kinetic energy, the crash box material needs a special material microstructure, which is light in weight and can absorb further energy than the being one like CaCo3, CBC, or SiC. B4C etc. In particular, the analysis of energy absorption of aluminum foam in automotive for energy absorption applications is limited. The main objective of this exploration is to analyze and optimize the porosity size and voids percentage on impact energy absorption of aluminum foam using a numerical approach. For this purpose, first, fifteen CAD Al foam samples were developed by using Digimat multi-scale material modeling software. Second, cubic elements with circular bubble shape at 5, 10 and 15 void percentage and at 1.5 mm, 2 mm,2.5 mm, 3 mm and 3.5 mm bubble sizes were modeled. Finally, the numerical analysis of impact energy by using ANSYS workbench19.2 Explicit dynamics by applying initial low velocity was performed. The parameters were compared to each other to optimize the proper percentage composition and cell size for the best energy absorption applications. The effects of bubble shape, foaming agent and percentage composition on energy immersion were discussed. In this study, the analysis was fulfilled by determining and comparing the energy absorptions of all the models and, finally, comparing them with existing foaming agents.

Efficient multiscale modeling of heterogeneous materials using deep neural networks

Material modeling using modern numerical methods accelerates the design process and reduces the costs of developing new products. However, for multiscale modeling of heterogeneous materials, the well-established homogenization techniques remain computationally expensive for high accuracy levels. In this contribution, a machine learning approach, convolutional neural networks (CNNs), is proposed as a computationally efficient solution method that is capable of providing a high level of accuracy. In this work, the data-set used for the training process, as well as the numerical tests, consists of artificial/real microstructural images (“input”). Whereas, the output is the homogenized stress of a given representative volume element mathcal {RVE}. The model performance is demonstrated by means of examples and compared with traditional homogenization methods. As the examples illustrate, high accuracy in predicting the homogenized stresses, along with a significant reduction in the computation time, were achieved using the developed CNN model.

A multiscale material model for metallic powder compaction during hot isostatic pressing

The prediction of the distortions during Near-Net-Shape Hot Isostatic Pressing (NNS-HIP) is an intrinsic multiscale problem where the local interactions among particles determine the macroscopic distortions taking place during the sintering and densification of a component. In this work, a multiscale approach is proposed to solve this problem. In particular, a viscoplastic constitutive model capable of predicting macroscopic contractions during a HIP process with high accuracy has been developed, implemented and validated. The macroscopic model incorporates the mechanical behaviour predicted at the meso-scale by means of multiple-particle finite element models (MP-FEM) of an agglomerate of powder particles. The model is validated through the prediction of distortions during HIP of a full scale industrial case. It is concluded that adding the microscopic information of the HIP process to simulate the contractions at the macroscopic level results in a considerable improvement of the accuracy of the predictions.

Objectivity and accuracy enhancement within ANN‐based multiscale material modeling

AbstractNowadays, supervised machine learning (ML) via artificial neural network (ANN) is increasingly applied within multiscale material modeling and homogenization to generate data‐based, physics‐informed material models as an alternative to conventional material models. This application is associated with many benefits, such as increasing of computational efficiency and accuracy. However, the establishment of a reliable data‐based or ML‐based material model requires the availability of a proper and sufficiently large database from small‐scale simulations and appropriate processing of these data as part of the model building steps. In this connection, this contribution discusses the method to generate ML‐based material models, which strictly fulfill a number of restrictions, such as objectivity (or material frame‐indifference) and thermodynamic consistency (second‐law of thermodynamics) for an elasto‐plastic material response. While focusing in this contribution on anisotropic crystal plasticity, the two aforementioned restrictions can be fulfilled via the utilization of informed‐graph NN and the application of data representation in spectral form. The numerical results show that learning the ML model to explicitly predict the plastic strain as an intermediate step not only enhances the fulfillment of thermodynamic consistency but also improves the accuracy of the final prediction.

Multi-scale modelling and life prediction of aged composite materials in salt water

Tidal turbine infrastructure is currently in the large-scale prototype and short-term demonstration phase. However, the immediate requirement is to develop materials, processes and long-term life predictive facilities for tidal turbine plant that has decades of operational lifetime requirements. Computational modelling is a key tool to interpret the experimental data, understand the relevant mechanisms and provide a predictive capability for the performance of aged components for industries. The goal of this paper is a prediction of the long-term life of marine-based glass/epoxy and carbon/epoxy composite laminates aged in artificial seawater with 3.5% salinity based on Arrhenius degradation theory and tensile strength retention over 180 days ageing at room temperature and 60°C. Three different analytical models (linear and exponential) were implemented to calculate time shift factors and corresponding life in a real marine environment. Additionally, multi-scale modelling has been implemented via a representative volume element approach for square and hexagonal cells, and two-step homogenization of textile composites in accordance with nanoindentation testing for matrix/resin cells and fibre constraint cells after 90 days of immersion in saltwater. In general, the multi-scale modelling in ABAQUS and TexGen4SC was able to approximate (with about 10% difference) the mechanical properties of dry and aged composite laminates.

Vector-based damage-driven computational homogenization with localized gradient enhanced boundary conditions for multi-scale modelling of quasi-brittle materials

Although a lot of progress has been made in computational homogenization, it is still a difficult challenge to emerge and evolve localization bands robustly and to tackle the size dependency issue for brittle and quasi-brittle materials. In this paper, a vector-based damage-driven computational homogenization with localized gradient enhanced boundary conditions is proposed. In the homogenization, the crack band theory is used to up-scale the damage at the micro level to the macro level based on the unit cell size and element size. The vector-based homogenization introduces damage in the principal direction based on the smeared crack model. The updated localized displacement gradients are introduced in the boundary conditions of unit cells to localize crack propagation between adjacent unit cells. The localized displacement gradients are updated iteratively to consider crack open and closure as well as the influences of surrounding elements. Incremental sequentially linear analysis is used to guarantee computational robustness. Size objectivity and localization have been demonstrated for different unit cell sizes and element sizes compared with the direct simulation method (DSM). In addition, an array of voids is considered in the notched beam test for further validation.