Macroscopic Material Behavior Research Articles

Boosting machine learning algorithms for predicting the macroscopic material behavior of continuous fiber reinforced composite

Boosting machine learning algorithms for predicting the macroscopic material behavior of continuous fiber reinforced composite

Tracking the movement of quartz sand particles with neural networks

Tracking the movement of particles is of paramount significance for studying the impact of particle breakage on the macroscopic mechanical behaviour of granular materials and remains a persistent challenge to date. This paper presents a novel particle tracking method that integrates Pointon and PointNetLK networks, enabling an accurate tracking of both intact and broken Leighton Buzzard sand (LBS) particles. Initially, morphological information of LBS particles was extracted from X-ray micro-tomography (CT) data collected from a miniature triaxial test. Various image processing techniques were applied to the raw CT images to achieve a realistic three-dimensional (3D) reconstruction. Subsequently, particle point cloud data was processed through sampling, Gaussian noise injection, and grouping for training and testing the Poynton and PointNetLK networks. Next, the correspondences among particles across different scans were established by PointConv, and the transformation matrix between two mutually matched particles was predicted using PointNetLK. Finally, an examination of the changes in the spatial distribution and morphological parameters of both tracked and untracked particles throughout the shearing process was conducted and followed by an analysis of particle kinematics.

R‐Vine Copulas for Data‐Driven Quantification of Descriptor Relationships in Porous Materials

AbstractLocal variations in the 3D microstructure can control the macroscopic behavior of heterogeneous porous materials. For example, the permittivity through porous sheets or membranes is governed by local high‐volume pathways or bottlenecks. Due to local variations, unfeasibly large amounts of microstructure data may be needed to reliably predict such material properties directly from image data. Here it is demonstrated that a vine copula approach provides parametric models for local microstructure descriptors that compactly capture the 3D microstructure including its local variations and efficiently probe it with respect to selected, measurable properties. In contrast to common methods of complexity reduction, the proposed approach creates parametric models for the multivariate probability distribution of high‐dimensional descriptor vectors that inherently contain the complex, nonlinear dependencies between these descriptors. Therein, material properties are offered in physically motivated distributions of microstructure descriptors rather than as normally distributed data. Applied to porous fiber networks (paper) before and after unidirectional compression, it is shown that the copula‐based models reveal material‐characteristic relationships between two or more microstructure descriptors. In this way, the presented modeling approach can provide deeper insight into the microscopic origin of effective macroscopic properties of heterogeneous porous materials.

From micro to macro: Physical-chemical characterization of wheat starch-based films modified with PEG200, sodium citrate, or citric acid

Needing to extend the shelf-life of packaged food and the evolving consumer demands led researchers to seek innovative, eco-friendly, and biocompatible packaging solutions. Starch is among the most promising natural and renewable alternatives to non-degradable plastics. Here, we deeply study the structural features of starch films modified by adding citric acid (CA) or sodium citrate (SC) as a cross-linker and polyethylene glycol 200 (PEG200) as a plasticizer and obtained through solvent casting. The substances' influence on starch films was evaluated through Attenuated Total Reflection Fourier Transform Infrared (ATR-FTIR) and Solid-state Nuclear Magnetic Resonance (ss-NMR) spectroscopies. Films' macroscopic properties, such as swelling index, solubility, thermo-mechanical features, and moisture absorption, were also assessed to foresee potential applications. Proper amounts of CA, CS, and PEG200 improve film properties and inhibit starch chains' retrogradation and recrystallization. Besides, the chemical neighbourhood of nuclei observed through ss-NMR significantly changed alongside the polymer chains' mobility. The latter result indicates a different polymer chain structural organization that could justify the film's higher resistance to thermal degradation and elongation at the break. This methodological approach is effective in predicting the macroscopic behaviour of a polymeric material and could be helpful for the application of such products in food preservation.

Efficient thermomechanically coupled FE‐FFT‐based multiscale simulation of polycrystals

AbstractIn general, the overall macroscopic material behavior of any structural component is directly dependent on its underlying microstructure. For metal components, the associated microstructure is given in terms of a polycrystal. To enable the simulation of the related microstructural and overall elasto‐viscoplastic material behavior, a two‐scale simulation approach can be used. In this context, we use a FE‐FFT‐based two‐scale method, which is an efficient alternative to the classical FE2 method for the simulation of periodic microstructures. In addition, we consider a thermomechanically coupled framework to account for both thermal and mechanical loads. Finally, we incorporate a model order reduction technique based on a coarsely discretized microstructure to develop an efficient two‐scale simulation technique. As a demonstration of the feasibility of the proposed simulation framework, a numerical example will be investigated.

Isothermal annealing of radiation defects in silicon bulk material of diodes from 8” silicon wafers

The high luminosity upgrade of the LHC will provide unique physics opportunities, such as the observation of rare processes and precision measurements. However, the accompanying harsh radiation environment will also pose unprecedented challenged to the detector performance and hardware. In this paper, we study the radiation induced damage and its macroscopic isothermal annealing behaviour of the bulk material from new 8” silicon wafers using diode test structures. The sensor properties are determined through measurements of the diode capacitance and leakage current for three thicknesses, two material types, and neutron fluences from 6.5· 1014 to 1 · 1016 neq/cm2.

Semi‐crystalline polymers at finite strains: A thermo‐coupled constitutive model for varying degrees of crystallinity and temperatures

AbstractThermoplastics are gaining interest for various industrial applications, since they can be widely used for thermoforming and injection moulding processes due to their thermostable material behavior. In combination with the material's low density and high strength to mass ratio, they are especially of interest in times where an improved environmental balance is more and more important. Hence, why they are for example frequently used in the automotive industry to reduce the weight of automotive components.Semi‐crystalline polymers as a subcategory of thermoplastics, partly crystallize after cool‐down from the molten state. During the thermoforming process, they are subjected to large deformations as well as thermal loads and show strong thermo‐mechanical coupling effects in addition to the influence of the evolution of the crystalline phase on the macroscopic material behavior. Therefore, computational models are needed to predict the complex material response reliably and minimize production errors.This work presents a thermomechanically consistent material formulation at finite strains. In order to account for the highly nonlinear material behavior, elasto‐plastic and visco‐elastic contributions are combined in the Helmholtz free energy and a dependency on temperature as well as the degree of cristallinity (DOC) is incorporated. Special attention is devoted to the choice of yield function and hardening behavior.A comparison of the simulation results to experiments at varying degrees of crystallinity and temperatures is presented to review the changes in the formulation. Therefore a special blending technique is used to ensure stable crystallinity conditions in the test samples.

Direct stress minimization in electro‐mechanical metamaterials

AbstractMetamaterials are artificially created multiscale materials with many different applications [1]. We assume periodic microstructure. No specific length scale is demanded for the differentiation between the scales. Instead, we consider the microscale as consisting of repeating unit cells, whereas the macroscale is the scale, where desired and sometimes unusual physical effects occur. The precise arrangement and geometry at the microscale level is responsible for the macroscopic material behavior, which can substantially differ from the original components it is made from. This way, unique material properties otherwise not found in nature (e.g. negative refractive materials [2]) are possible. Most previous research regarding metamaterials concentrated only on a single physical branch in each case, e.g. electromagnetic or acoustic metamaterials [3,4].In this contribution we present a class of theoretical electro‐mechanical metamaterials by combining insulating and conducting materials. Our aim is to directly control and reduce the resulting total stress of insulating materials by counteracting the mechanical stress through the application of an electric field, which is created by a conducting material. The solution of the resulting minimization problem is related to the eigenvalues of the mechanical stress tensor. Additionally, we discuss the constrained cases of tension and compression and cover the plane stress case. We show numerical results for all cases and discuss the limits of such a material.

Constitutive Modeling with Single and Dual Internal Variables.

Phenomenological constitutive models with internal variables have been applied for a wide range of material behavior. The developed models can be classified as related to the single internal variable formalism based on the thermodynamic approach by Coleman and Gurtin. The extension of this theory to so-called dual internal variables opens up new avenues for the constitutive modeling of macroscopic material behavior. This paper reveals the distinction between constitutive modeling with single and dual internal variables using examples of heat conduction in rigid solids, linear thermoelasticity, and viscous fluids. A thermodynamically consistent framework for treating internal variables with as little a priori knowledge as possible is presented. This framework is based on the exploitation of the Clausius-Duhem inequality. Since the considered internal variables are "observable but not controllable", only the Onsagerian procedure with the use of the extra entropy flux is appropriate for the derivation of evolution equations for internal variables. The key distinctions between single and dual internal variables are that the evolution equations are parabolic in the case of a single internal variable and hyperbolic if dual internal variables are employed.

Establishing structure–property linkages for wicking time predictions in porous polymeric membranes using a data-driven approach

The goal of this study is to develop correlations between microstructure morphology and macroscopic material behavior, known as structure–property linkages. These correlations can be used to predict material behavior and enable virtual materials design efforts. In this work the structure–property linkages for the capillary-driven fluid transport through highly porous open-pored polymeric membranes are determined by a data-driven approach. To establish linkages, about 400 porous microstructures with different geometrical features are algorithmically generated and characterized in 3D, using fluid flow simulations and image analysis methods. The data processing pipeline for the generation and analysis of the microstructures is implemented by a generic workflow tool called KadiStudio, which is embedded in the research data infrastructure Kadi4mat. The data-driven analysis enables predictions about the propagation time of a fluid over definable distances when only the porosity and the ligament radius are known as microstructural properties. The generated knowledge can be utilized for an accelerated development of novel polymeric membranes with an optimized pore structure.

Constitutive modelling of idealised granular materials using machine learning method

Predicting the constitutive response of granular soils is a fundamental goal in geomechanics. This paper presents a machine learning (ML) framework for the prediction of the stress-strain behaviour and shear-induced contact fabric evolution of an idealised granular material subject to triaxial shearing. The ML-based framework is comprised of a set of mini-triaxial tests which provide a benchmark for the setup and validation of the discrete element method (DEM) model of the granular materials, a parametric DEM simulation programme of virtual triaxial tests which provides datasets of micro- and macro-mechanical information, as well as a multi-layer perceptron (MLP) neural network which is trained and tested using the DEM-based datasets. The ML model only requires the initial void ratio of the granular sample as the input for predicting its constitutive response. The excellent agreement between the ML model prediction and experimental test and DEM simulation results indicates that the ML–based modelling approach is capable of capturing accurately the effects of initial void ratio on the constitutive behaviour of idealised granular materials, bypassing the need to incorporate the complex micromechanics underlying the macroscopic mechanical behaviour of granular materials. Lastly, a detailed comparison between the used MLP model and long short-term memory (LSTM) model was made from the perspective of technical algorithm, prediction accuracy, and computational efficiency.

Role of particle rotation in sheared granular media

When granular assemblies are subject to external loads or displacements, particles interact with each other through contact and may exhibit translations and rotations. From a micromechanical perspective, particle rotations are an essential mechanism influencing the macroscopic behavior of granular materials. In this study, biaxial shearing tests were conducted on assemblies of dual-sized circular particles at different confining pressures. A high-precision image analysis method was developed to extract the particle-level motion of all the particles, including the rotational behavior. Experimental results showed that most of the particles exhibited rotations. Particles within the shear band exhibited more significant rotations and were characterized by low connectivity (number of contacts per particle). In contrast, the particles outside the shear band rotated lesser, only in the beginning stage of shearing. Every rotation in either direction is accompanied by an opposite rotation of almost the same magnitude in the neighboring region, and rotation clusters have been observed. Rotations in both directions are normally distributed within the assembly, and the average particle rotation is zero. The average rotations in both directions evolve symmetrically with major principal strain. Generally, the rotation rate (degrees per incremental strain) is observed to be maximum at the start of the shearing, and gradually it becomes constant toward the end of the shearing. The average value of the absolute cumulative rotation observed for whole particles is 18.6° at the end of shearing, i.e., 20% deviatoric strain. Smaller size particles tend to exhibit 67% higher rotations than bigger particles. Confining pressures have no significant effect on the rotational behavior of circular particles.

Polymorphic Uncertain Structural Analysis: Challenges in Data‐Driven Inelasticity

AbstractThis contribution addresses polymorphic uncertainty quantification within structural analysis of reinforced concrete structures composed of heterogeneous concrete and reinforcement (e.g. steel bars or carbon fibres). The macroscopic material behaviour of concrete is strongly dependent on the mesoscopic heterogeneities, which are considered by multiscale modelling. The heterogeneous mesoscopic material behaviour is characterized by representative volume elements (RVE) and the transition of scales is carried out by utilizing numerical homogenization methods.The concept of data‐driven computational mechanics enables material model free finite element analyses directly based on material data sets, overcoming the necessity of assumptions in material modelling. This approach mainly consists in assigning a stress‐strain state, which leads to a minimum of an objective function and fulfils equilibrium as well as compatibility constraints of every integration point. Inelastic material behaviour is taken into account through the definition of local data sets containing only data set states which are consistent with respect to the past local history . The realistic modelling of structures requires the consideration of data uncertainty. Generalized polymorphic uncertainty models are utilized in order to take variability, imprecision, inaccuracy and incompleteness of material data into account by combining aleatoric and epistemic uncertainty models.In this contribution, a computationally efficient approach for the consideration of data sets containing uncertain stress‐strain states within data‐driven analysis based on information reduction measurements is presented. Due to generalization, the approach is applicable to various aleatoric, epistemic and polymorphic uncertainty models. The identification of admissible local data sets for taking inelastic material behaviour into account within data‐driven analysis is realized by an energy based history parametrization which is extended to uncertain data. An approach for the efficient selection of these local data sets is presented and challenges in data‐driven inelasticity, particularly in the use case of polymorphic uncertain analyses of concrete structures, are pointed out.

A micro-investigation on water bridge effects for unsaturated granular materials with constant water content by discrete element method

The most common state of surface soil is unsaturated. Changes in water content will substantially impact its strength, leading to geological and engineering catastrophes. This paper used LIGGGHTS software to simulate the water bridge effect of unsaturated granular materials with constant water content and verify the rationality of the simplification of the stress-force-fabric (SFF) relationship. The results showed that the capillary force was not isotropic, which was different from the previous study, thus it cannot be overlooked in the simplification of the SFF relationship. Moreover, the influence of water content on the macroscopic mechanical behavior of unsaturated granular materials was interpreted through the evolutions of coordination number, interparticle force, fabric and force anisotropy, and other microscopic parameters. Compared to the literature, we found that different water bridge models would not change the characteristics of the solid skeleton.

Evolution TANN and the identification of internal variables and evolution equations in solid mechanics

Data-driven and deep learning approaches have demonstrated to have the potential of replacing classical constitutive models for complex materials, displaying path-dependency and possessing multiple inherent scales. Yet, the necessity of structuring constitutive models with an incremental formulation has given rise to data-driven approaches where physical quantities, e.g. deformation, blend with artificial, non-physical ones, such as the increments in deformation and time. Neural networks and the consequent constitutive models depend, thus, on the particular incremental formulation, fail in identifying material representations locally in time, and suffer from poor generalization.Herein, we propose a new approach which allows, for the first time, to decouple the material representation from the incremental formulation. Inspired by the Thermodynamics-based Artificial Neural Networks (TANN) and the theory of the internal variables, the evolution TANN (eTANN) are continuous-time and, therefore, independent of the aforementioned artificial quantities. Key feature of the proposed approach is the identification of the evolution equations of the internal variables in the form of ordinary differential equations, rather than in an incremental discrete-time form.In this work, we focus attention to juxtapose and show how the various general notions of solid mechanics are implemented in eTANN. The laws of thermodynamics are hardwired in the structure of the network and allow predictions which are always consistent, independently of the range of the training dataset.Inspired by previous works, we propose a methodology that allows to identify, from data and first principles, admissible sets of internal variables from the microscopic fields in complex materials. The capabilities as well as the scalability of the proposed approach are demonstrated through several applications involving a broad spectrum of complex material behaviors, from plasticity to damage and viscosity (and combination of them). Finally, we show that the proposed approach can be used to speed-up state-of-the-art multiscale analyses, by virtue of asymptotic homogenization. eTANN provide excellent results compared to detailed fine-scale simulations and offer the possibility not only to describe the average macroscopic material behavior, but also micromechanical, complex mechanisms.

Swelling characteristics of DNA polymerization gels.

The development of biomolecular stimuli-responsive hydrogels is important for biomimetic structures, soft robots, tissue engineering, and drug delivery. DNA polymerization gels are a new class of soft materials composed of polymer gel backbones with DNA duplex crosslinks that can be swollen by sequential strand displacement using hairpin-shaped DNA strands. The extensive swelling can be tuned using physical parameters such as salt concentration and biomolecule design. Previously, DNA polymerization gels have been used to create shape-changing gel automata with a large design space and high programmability. Here we systematically investigate how the swelling response of DNA polymerization gels can be tuned by adjusting the design and concentration of DNA crosslinks in the hydrogels or DNA hairpin triggers, and the ionic strength of the solution in which swelling takes place. We also explore the effect hydrogel size and shape have on the swelling response. Tuning these variables can alter the swelling rate and extent across a broad range and provide a quantitative connection between biochemical reactions and macroscopic material behaviour.

Fluctuating Ru trimer precursor to a two-stage electronic transition in RuP

Superconductivity in binary ruthenium pnictides occurs proximal to and upon suppression of a nonmagnetic ground state, preceded by a pseudogap phase associated with Fermi surface instability, and its critical temperature, ${T}_{c}$, is maximized around the pseudogap quantum critical point. By analogy with isoelectronic iron-based counterparts, antiferromagnetic fluctuations became ``usual suspects'' as putative mediators of superconducting pairing. Here we report on a high-temperature local symmetry breaking in RuP, the nonsuperconducting parent of the maximum-${T}_{c}$ branch of these novel superconductors, revealed by combined nanostructure-sensitive powder and single-crystal x-ray total scattering analyses. Large local distortions of Ru chains associated with orbital-charge trimerization, further assembled into hexamers, exist above the two-stage electronic transition in RuP. In the pseudogap regime the precursors order with distortions retaining their strength, whereas they acquire spin-singlet characteristics which dramatically enhances the distortion as the nonmagnetic ground state establishes. The precursors enable the nonmagnetic ground state and presumed complex oligomerization, and the relevance of pseudogap fluctuations for superconductivity emerges as a distinct prospect. As a transition metal system in which partial d-manifold filling combined with high crystal symmetry promotes electronic instabilities, this represents a further example of local electronic precursors underpinning the macroscopic collective behavior of quantum materials.

Neutron Diffraction Measurements of Forged Ti–6A–4V Alloy under Tensile Loading

Herein, lattice‐specific elastic stiffnesses of a structural alloy with commercial, medical, and military aircraft applications are investigated by neutron diffraction. Macroscopic mechanical properties are characterized by conventional techniques and response to thermally induced strains is probed by X‐ray diffraction (XRD); these findings are compared to data given by neutron diffraction tools. The material used in this study is the forged Ti64 titanium alloy (6% aluminum and 4% vanadium). Diffraction elastic constants are found to range from 114 GPa to 138 GPa. Macroscopic moduli of 118 GPa and 116 GPa are found from extensometry and digital imaging correlation, respectively. The (101) reflection is the reflection that best matches the macroscopic material behavior with a modulus of 117 GPa for the studied material. The effect of mechanical and thermal strains on the axial ratio of the crystal structure is investigated. Texture is an important consideration when comparing micro‐ and macro‐scale behavior; texture from electron backscatter diffraction (EBSD) maps reveals minimal preferred orientation for the material under study thus indicating (101) planes suitably reflect overall material behavior.

Incremental Numerical Approach for Modeling the Macroscopic Viscoelastic Behavior of Fiber-Reinforced Composites Using a Representative Volume Element.

The objective of this study is to describe the stress relaxation behavior of an epoxy-based fiber-reinforced material. An existing incremental formulation of an orthotropic linear viscoelastic material behavior was adapted to Voigt notation and to the special case of an isotropic material. Virtual relaxation tests on a representative volume element were performed, and the behavior of individual components of the relaxation tensor of the transversely isotropic composite material was determined. The study demonstrated that in the case of only one viscoelastic material, each component of the relaxation tensor can be described in terms of a scalar form factor and the behavior of the neat resin. The developed method was implemented in an incremental finite element model (FEM) analysis to calculate the stress relaxation on the macroscopic ply level. A validation of the approach has shown a promising agreement up to a limit below the glass transition temperature of 15 °C in longitudinal and 35 °C in transverse direction. This study therefore demonstrates a novel way to incrementally describe the macroscopic viscoelastic behavior of materials with a single viscoelastic component with good controllability for engineering purposes.

Subsurface polycrystalline reconstruction based on full waveform inversion - A 2D numerical study

Microstructural mapping of polycrystalline metallic alloys is a key component in predicting macroscopic material behavior, and non-destructive subsurface polycrystalline imaging is a valuable yet challenging field that offers promise for metallic material characterization. This paper proposes a computational ultrasonic imaging method for high-resolution, subsurface polycrystalline reconstruction using signals measured on a sample’s boundary and a full waveform inversion technique. For this 2D numerical study, the anisotropic elastic coefficient parameterization is introduced and connected to the corresponding polycrystalline orientation. The forward wave propagation simulation is performed using a spectral finite element method. An inversion framework is developed for inverting the anisotropic elastic coefficients, and the crystalline orientations. Reconstruction performance benchmarking is systematically conducted for both rectangular regions and a representative polycrystal. Overall, the reconstructions have broad correspondence to the scanned, unknown models. We further discuss artifact mitigation strategies and the potential to extend this work.