Description Of Material Properties Research Articles

Parameterized Reduced-Order Models for Probabilistic Analysis of Thermal Protection System Based on Proper Orthogonal Decomposition

The thermal protection system (TPS) represents one of the most critical subsystems for vehicle re-entry. However, due to uncertainties in thermal loads, material properties, and manufacturing deviations, the thermal response of the TPS exhibits significant randomness, posing considerable challenges in engineering design and reliability assessment. Given that uncertain aerodynamic heating loads manifest as a stochastic field over time, conventional surrogate models, typically accepting scalar random variables as inputs, face limitations in modeling them. Consequently, this paper introduces an effective characterization approach utilizing proper orthogonal decomposition (POD) to represent the uncertainties of aerodynamic heating. The augmented snapshots matrix is used to reduce the dimension of the random field by the decoupling method of independently spatial and temporal bases. The random variables describing material properties and geometric thickness are also employed as inputs for probabilistic analyses. An uncoupled POD Gaussian process regression (UPOD-GPR) model is then established to achieve highly accurate solutions for transient heat conduction. The model takes random heat flux fields as inputs and thermal response fields as outputs. Using a typical multi-layer TPS and thermal structure as two examples, probabilistic analyses are conducted. The mean square relative error of a typical multi-layer TPS is less than 4%. For the thermal structure, the averaged absolute error of the radiation and insulation layer is less than 25 °C and 6 °C when the maximum reaches 1200 °C and 150 °C, respectively. This approach can provide accurate and rapid predictions of thermal responses for TPS and thermal structures throughout their entire operating time when furnished with input heat flux fields and structural parameters.

Modelling methacrylated chitosan hydrogel properties through an experimental design approach: from composition to material properties.

Hydrogels of biopolymers are gradually substituting synthetic hydrogels in tissue engineering applications due to their properties. However, biopolymeric hydrogels are difficult to standardize because of the intrinsic variability of the material and the reversibility of physical crosslinking processes. In this work, we synthesized a photocrosslinkable derivative of chitosan (Cs), namely methacrylated chitosan (CsMA), in which the added methacrylic groups allow the formation of hydrogels through radical polymerization triggered by UV exposure. We then performed a systematic study to link the physical properties of the materials to its preparation parameters to standardize its preparation according to specific applications. We studied the properties of CsMA solutions and the derived hydrogels using a statistical method, namely, response surface method, which allowed us to build empirical models describing material properties in terms of several selected processing factors. In particular, we studied the viscosity of CsMA solutions as a function of CsMA concentration, temperature, and shear rate, while hydrogel compression modulus, morphology, degradation and solubilization were investigated as a function of CsMA concentration, photoinitiator concentration and UV exposure. CsMA solutions resulted in shear thinning and were thus suitable for extrusion-based 3D printing. The CsMA hydrogel was found to be highly tunable, with a stiffness in the 12-64 kPa range, and was stable over a long timeframe (up to 60 days). Finally, the possibility to engineer hydrogel stiffness through an empirical model allowed us to hypothesize a number of possible applications based on the mechanical properties of several biological tissues reported in the literature.

Variationally mimetic operator networks

In recent years operator networks have emerged as promising deep learning tools for approximating the solution to partial differential equations (PDEs). These networks map input functions that describe material properties, forcing functions, and boundary data to the solution of a PDE. This work describes a new architecture for operator networks, called the variationally mimetic operator network (VarMiON ), that mimics the form of the numerical solution obtained from an approximate variational or weak formulation of the problem. Like the conventional Deep Operator Network (DeepONet) the VarMiON is also composed of a sub-network that constructs the basis functions for the output and another that constructs the coefficients for these basis functions. However, in contrast to the DeepONet, the architecture of these sub-networks in the VarMiON is precisely determined. An analysis of the error in the VarMiON solution reveals that it contains contributions from the error in the training data, the training error, the quadrature error in sampling input and output functions, and a “covering error” that measures the distance between the test input functions and the nearest functions in the training dataset. It also depends on the stability constants for the exact solution operator and its VarMiON approximation. The application of the VarMiON to a canonical elliptic PDE and a nonlinear PDE reveals that for approximately the same number of network parameters, on average the VarMiON incurs smaller errors than a standard DeepONet and a recently proposed multiple-input operator network (MIONet). Further, its performance is more robust to variations in input functions, the techniques used to sample the input and output functions, the techniques used to construct the basis functions, and the number of input functions. Moreover, it consistently outperforms baseline methods at various dataset sizes. The data and code accompanying this manuscript are publicly available at https://github.com/dhruvpatel108/VarMiON.

Dynamic deformation behavior and constitutive model of a Zr–W alloy

In this paper, a Zr–5W alloy was fabricated via casting. In order to obtain the mechanical properties of the material, quasi-static compression tests at room temperature and split Hopkinson pressure bar tests at various temperatures were carried out. The x-ray diffraction result showed that the main components of the alloy were αZr and W2Zr, where αZr is the matrix and W2Zr is the reinforcement. The metallographic characterization results showed that there were two main forms of W2Zr in the material, namely, large particle boundary and small diffuse submicrometer precipitates. The reinforcements of both distributions have the effect of increasing the strength of the material, but the small submicrometer W2Zr precipitates would cause microcrack nucleation during the late plastic deformation stage, resulting in damage softening. In order to make theoretical calculations of the mechanical properties of materials, the Johnson–Cook (JC) constitutive model and Zerilli–Armstrong (ZAM) constitutive model of the material were obtained. It was found that the JC constitutive model had poor consistency in describing material properties. Although the consistency of the ZAM constitutive model was higher than that of the JC constitutive model, it still had obvious shortcomings. Combined with the deformation mechanism of the alloy, a modified constitutive relation was established by adding damage softening terms based on the hexagonal close-packed metal constitutive model inferred by the kinetics of heat-activated dislocations. The relative error results of all working conditions show that the correlation consistency of the improved constitutive model in this paper is significantly better than that of JC constitutive and ZAM constitutive.

Description of Material Properties of Degraded and Damaged Segments of Multi-Leaf Masonry in Analyses of Large Three-Dimensional Structures.

This article focuses on the description of material properties of segments of masonry structures in three-dimensional analyses. It mainly considers degraded and damaged multi-leaf masonry walls. In the beginning, the causes of degradation and damage to masonry are described with examples. It was reported that the analysis of such structures is difficult due to the adequate description of the mechanical properties in the individual segments of the structure and the amount of computational cost of large three-dimensional structures. Next, a method of describing large fragments of masonry structures by means of macro-elements was proposed. The formulation of such macro-elements in three-dimensional and two-dimensional problems was given by introducing limits of variation in material parameters and damage of structures expressed by the limits of integration of macro-elements with specified internal structures. Then, it was stated that such macro-elements can be used to build computational models by the finite element method, which allows the analysis of the deformation-stress state, and at the same time, reduce the number of unknowns in such issues. A strategy for performing analyses and examples of practical applications in masonry analyses were proposed. It was reported that the results of the analyses can be used to plan the repairs and strengthening of structures. Finally, the conducted considerations and proposals were summarised, as well as examples of practical applications.

Geometric potential of the exact electron factorization: Meaning, significance, and application

The theoretical and computational description of materials properties is a task of utmost scientific and technological importance. A first-principles description of electron-electron interactions poses an immense challenge that is usually approached by converting the many-electron problem to an effective one-electron problem. There are different ways to obtain an exact one-electron theory for a many-electron system. An emergent method is the exact electron factorization (EEF) -- one of the branches of the exact factorization approach to many-body systems. In the EEF, the Schr\"odinger equation for one electron, in the environment of all other electrons, is formulated. The influence of the environment is reflected in the potential ${v}^{\mathrm{H}}$, which represents the energy of the environment, and in a potential ${v}^{\mathrm{G}}$, which has a geometrical meaning. In this paper, we focus on ${v}^{\mathrm{G}}$ and study its properties in detail. We investigate the geometric origin of ${v}^{\mathrm{G}}$ as a metric measuring the change of the environment, exemplify how translation and scaling of the state of the environment are reflected in ${v}^{\mathrm{G}}$, and explain its shape for homo- and heteronuclear diatomic model systems. Based on the close connection between the EEF and density functional theory, we also use ${v}^{\mathrm{G}}$ to provide an alternative interpretation to the Pauli potential in orbital-free density functional theory.

Numerical Analysis of Degradation and Capacity Loss in Graphite Active Particles of Li-Ion Battery Anodes.

It is well known that the performance and durability of lithium-ion batteries (LIBs) can be severely impaired by fracture events that originate in stresses due to Li ion diffusion in fast charge–discharge cycles. Existing models of battery damage overlook either the role of particle shape in stress concentration, the effect of material disorder and preexisting defects in crack initiation and propagation, or both. In this work we present a novel, three-dimensional, and coupled diffusive-mechanical numerical model that simultaneously accounts for all these phenomena by means of (i) a random particle generator and (ii) a stochastic description of material properties implemented within the lattice method framework. Our model displays the same complex fracture patterns that are found experimentally, including crack nucleation, growth, and branching. Interestingly, we show that irregularly shaped active particles can suffer mechanical damage up to 60% higher than that of otherwise equivalent spherical particles, while material defects can lead to damage increments of up to 110%. An evaluation of fracture effects in local Li-ion diffusivity shows that effective diffusion can be reduced up to 25% at the particle core due to lithiation, while it remains at ca. 5% below the undamaged value at the particle surface during delithiation. Using a simple estimate of capacity loss, we also show that the C-rate has a nonlinear effect on battery degradation, and the estimated capacity loss can surpass 10% at a 2C charging rate.

Stochastic failure analysis of proximal femur using an isogeometric analysis based nonlocal gradient-enhanced damage model

Background and objectiveMedical imaging-based finite element methods are more accurate tools for fracture risk prediction than the traditional aBMD based methods. However, these methods have drawbacks like geometric errors, high computational cost, mesh-dependent results, etc. In this article, the authors have proposed an isogeometric analysis-based nonlocal gradient-enhanced damage model to overcome some of these issues. Moreover, there are uncertainties in the values of input parameters for such analysis due to various measurement errors. Hence, stochastic analysis is performed to quantify the effect of these parametric uncertainties on the fracture behavior of the proximal femur. MethodsComputed Tomography images of a patient are used to create a 2D proximal femur model with a heterogeneous description of material properties. A numerical model based on gradient-enhanced nonlocal continuum damage mechanics is used for fracture analysis of proximal femur to overcome the issues related to mesh dependency in traditional continuum damage mechanics models. Further, a multipatch isogeometric solver is developed to solve the governing equations. Monte Carlo simulations are used to understand the effect of parametric uncertainties on the fracture behavior of the proximal femur. ResultsThe developed numerical framework is used to solve the fracture problem of proximal femur under single leg stance loading conditions. The obtained results are validated by comparing the load-displacement response and the crack path with that given in the literature. Stochastic analysis is performed by considering a ±5% variation in the elastic modulus, damage initiation strain, and the neck-shaft angle values. ConclusionThe proposed numerical framework can correctly predict the damage initiation and propagation in a proximal femur. The results reveal that the heterogeneous nature of material properties of bone plays a significant role in determining the fracture characteristics of the proximal femur. Further, the results of the stochastic analysis reveal that the parametric uncertainties in the neck-shaft angle have a much more significant influence on the results of the analysis than the parametric uncertainties in the elastic modulus and damage initiation strain.

Valence energy correction for electron reactive force field.

Reactive force fields (ReaxFF) are a classical method to describe material properties based on a bond-order formalism, that allows bond dissociation and consequently investigations of reactive systems. Semiclassical treatment of electrons was introduced within ReaxFF simulations, better known as electron reactive force fields (eReaxFF), to explicitly treat electrons as spherical Gaussian waves. In the original version of eReaxFF, the electrons and electron-holes can lead to changes in both the bond energy and the Coulomb energy of the system. In the present study, the method was modified to allow an electron to modify the valence energy, therefore, permitting that the electron's presence modifies the three-body interactions, affecting the angle among three atoms. When a reaction path involving electron transfer is more sensitive to the geometric configuration of the molecules, corrections in the angular structure in the presence of electrons become more relevant; in this case, bond dissociation may not be enough to describe a reaction path. Consequently, the application of the extended eReaxFF method developed in this work should provide an improved description of a reaction path. As a first demonstration this semiclassical force field was parametrized for hydrogen and oxygen interactions, including water and water's ions. With the modified methodology both the overall accuracy of the force field but also the description of the angles within the molecules in presence of electrons could be improved.

Small‐amplitude homogenization of elastic plates via H‐measures

AbstractSmall‐amplitude homogenization is a procedure for computing the first correction in the homogenization limit. By using H‐measures, we calculate the first correction in the small‐amplitude homogenization limit of a non‐periodic sequence of tensors describing material properties in the Kirchhoff‐Love model for pure bending of a thin solid symmetric plate under a transverse load.

Experimental Methods to Enable High-Throughput Characterization of New Structural Materials

Data-driven methods for developing new structural materials require large databases to identify new materials from known process routes, the resulting microstructures, and their properties. Due to the high number of parameters for such process chains, this can only be achieved with methods that allow high sample throughputs. This paper presents the experimental approach of the "Farbige Zustände" method through a case study. Our approach features a high-temperature drop-on-demand droplet generator to produce spherical micro-samples, which are then heat-treated and subjected to various short-time characterizations, which yield a large number of physical, mechanical, technological, and electrochemical descriptors. In this work, we evaluate achievable throughput rates of this method resulting in material property descriptions per time unit. More than 6000 individual samples could be generated from different steels, heat-treated and characterized within 1 week. More than 90,000 descriptors were determined to specify the material profiles of the different alloys during this time. These descriptors are used to determine the material properties at macro-scale.

Review of and a new approach to elastic modulus evaluation for fatigue design of metallic components

The elastic modulus is a key parameter for the description of material properties when evaluating metallic components under service loads. In particular, when evaluating strain-controlled tests for the application of the strain-life approach, there are numerous different possibilities in standards for determining this material parameter. These can lead to different results and confront the user with a certain challenge in selecting the most suitable method. In this publication, an overview of different evaluation methods is given and a new evaluation method is presented, in which the elastic modulus is determined using the reversal points of a strain-controlled cyclic test under macroscopic linear-elastic deformation. This allows a simple and clear, widely user-independent determination of the elastic modulus. In addition, the differences between the new and the commonly used evaluation methods are shown, using the example of the aluminum alloy EN AW-7075, and their influence on the strain-life curve, the PSWT and PJ damage parameter curves, and the cyclic stress-strain curve by Ramberg-Osgood are investigated.

Fatigue Life Testing of Locally Additive Manufactured AlSi10Mg Test Specimens

In order for additive manufacturing to become a viable manufacturing method for aerospace engineering, it is required that exhaustive static and fatigue testing be performed. The testing is required in order to describe material properties in a statistical manner. Fatigue tests were performed on standard additive manufactured ASTM E466 test specimens in order to obtain the low (1000 cycles) to high cycle (1E6 cycles) behaviour of AlSi10Mg. The specimens were manufactured using non-heat treated, but stress relieved specimens. Specimens were printed in three build directions, namely the XY (parallel with build plate), 45 degree and vertical direction as measured with respect to the build baseplate. The three different directions were chosen to investigate the sensitivity of the material properties to the build direction. The specimens were stress relieved on the baseplate. Static testing was also performed on specimens according to ASTM E8/E8M. The specimens were produced to have a surface finish representative of standard deburring techniques used in the aerospace industry. The surface roughness on the specimens were measured. The scatter in test data as a result of the surface finish on material properties is quantified. It is a requirement to quantify the effect of the surface roughness on fatigue failure allowable values since a machined type finish (less than 3.2 micrometer) is not always practically possible to achieve with additive manufactured structures. This is because the organic shapes produced with additive manufacturing makes some surfaces inaccessible to normal surface finishing techniques. Furthermore, some internal structures such as lattice structures are completely inaccessible to surface finishing techniques such as polishing or lapping. In addition to the surface roughness the roundness of the test section was also measured using inspection equipment. This was required since the industrial deburring techniques did not yield a completely concentric test section as a lathe operation would produce. Once again this is representative of an additive manufactured structure. The fatigue tests were performed at an R-ratio of 0.1. The test results were used to produce Wöhler or S-N curves for the material in all three material directions. The scatter was quantified using industry accepted methods. The results were compared with fatigue test results from literature of specimens produced with a lathe in order to compare a practical industrial surface finish on an additive manufactured component with a machined surface finish. It was found that the build support structures of the additive manufacturing process causes stress concentrations in the fatigue test specimens. This leads to a reduction in fatigue life and an increase in the scatter of the results.

Material Model for Predicting Dynamic Response of Copper and Nickel at Very High Strain Rates Under Cold Spray Conditions

Numerous material models have been proposed to describe material properties under impact-induced extreme conditions. All these models suffer from the fact that the tests used to provide the required empirical parameters were performed on bulk material at limited strain rates, much lower than those found in the cold spray process. In this work, recent published results available in the literature that were obtained using advanced imaging techniques are used to modify material plasticity models to accurately predict the material plastic flow stress under cold spray conditions. The capability of two frequently used material models, Johnson–Cook and Preston–Tonks–Wallace models, to predict real-time experimental data for copper and nickel particles is evaluated. A series of finite element simulations are conducted and the comparison is made with the coefficient of restitution from laser-induced projectile impact test data. The original empirical parameters in Preston–Tonks–Wallace model are re-calibrated so that the coefficient of restitution matches the laser-induced projectile impact test data, providing an enhanced quality in the particle impact behavior predictions. Additionally, experiments and modeling are conducted to explore the bonding mechanism and rebound phenomena of copper powder cold sprayed on low carbon steel substrate.

Automatic image segmentation for material microstructure characterization by optical microscopy

This work shows the utility to have a microstructure characterization to analysis the properties of materials. For this, digital image segmentation is used on microscopic images of materials to extract the number of phases and their proportion present in the material to obtain a quantitative description of material properties and to better control product quality. In this way, we present here an automated method for segmenting the phases present in microscopic scanning images of metallographic samples using a multiphase level set with Mumford Shah formulation. Experience shows that the proposed model successfully detects phase regions for a variety of real micrographic images and provides the required accuracy and robustness to the process..

Microstructural and Mechanical Properties of Grafts Commonly Used for Cruciate Ligament Reconstruction.

Injuries to the anterior cruciate ligament and posterior cruciate ligament are common, and often are treated with reconstruction. Limited quantitative data are available describing material properties of grafts used for reconstructions such as the bone-patellar tendon-bone (BPTB), hamstring tendon (HS), and quadriceps tendon (QT). The purpose of this study was to quantify and compare microstructural and mechanical properties of BPTB, HS, and QT grafts. Forty specimens (13 BPTB, 13 HS, and 14 QT grafts) from 24 donors were used. Specimens were subjected to preconditioning, stress relaxation, and ramp to failure. Mechanical parameters were calculated for each sample, and polarization imaging was used to evaluate the direction and strength of collagen fiber alignment during testing. QT had the largest modulus values, and HS had the smallest. BPTB exhibited the least disperse collagen organization, while HS were the least strongly aligned. Microstructural properties showed more strongly aligned collagen with increasing load for all grafts. All tissues showed stress relaxation and subtle microstructural changes during the hold period. The mechanical and microstructural properties differed significantly among BPTB, HS, and QT grafts. QT exhibited the largest moduli and greatest strength of collagen alignment, while HS had the smallest moduli and least strongly aligned collagen. This study identified mechanical and microstructural differences among common grafts and between these grafts and the cruciate ligaments they replace. Further research is needed to properly interpret the clinical relevance of these differences.

Effects of porosity and flexoelectricity on static bending and free vibration of AFG piezoelectric nanobeams

Abstract In this paper, based on the strain gradient theory, a size-dependent porous axially functional gradient (AFG) flexoelectric Euler-Bernoulli nanobeam model is developed. A modified power-law formula incorporating porosity volume fraction is presented to describe material properties of porous AFG nanobeam, and two typical porosity distributions patterns are considered. The generalized differential quadrature method is employed to discretize governing equations into a series of linear algebraic equations, so that the static bending deflections and free vibration frequencies are calculated conveniently for various boundary conditions. The credibility of the present mathematical formulation and the associated numerical solution are validated by comparing the results in previous literatures. Parametric studies are performed to illustrate the effects of the flexoelectricity, material length scale parameters, functionally graded index, porosity volume fraction, porosity distribution patterns on the static bending and free vibration behaviors of porous AFG flexoelectric nanobeam. The numerical results may provide support for the application of porous AFG flexoelectric nanobeam in Nano-electro-mechanical system.

Dynamics of the spin-1/2 Ising two-leg ladder with four-spin plaquette interaction and transverse field.

Multiple-spin coupling is a key tool for investigating magnetic quantum systems. In particular, models with four-spin interactions became of great interest since they have been applied to describe material properties such as superconductivity. In this framework, the dynamics of the spin-1/2 Ising two-leg ladder with four-spin plaquette interaction in a transverse field is investigated. By means of the recurrence relations method, the first four recurrants are determined exactly for the general model, while five exact recurrants are calculated for two particular models. In all cases, higher-order recurrants are computed through extrapolation to obtain time-dependent autocorrelation functions and spectral densities in the long-time regime and infinite-temperature limit. It is found that the relaxation functions decay slower than the expected behavior of the one-dimensional transverse Ising model. The spectral lines, characterized by a Lorentzian behavior in the central body and a Gaussian shape in the tails, display exchange narrowing as the coupling intensities increase.

An efficient evolutionary structural optimization method for multi-resolution designs

This paper presents a computationally efficient multi-resolution topology optimization framework by establishing a novel bi-directional evolutionary structure optimization (BESO) method based on extended finite element method (XFEM). In the proposed framework, the high-resolution designs preserving the topological complexity can be obtained with low degree of freedoms (DOFs). The implementation of the presented multi-resolution optimization framework takes good use of the ability of XFEM at accurately modeling material discontinuities within one element. On the basis of XFEM, a strategy of triangulated partition and a new material interpolation model are introduced to represent the finer material distribution. We employ the coarser finite element (FE) mesh to perform the finite element analysis, the sub-parts partitioned from finite elements to describe material properties and the nodal design variables to perform the optimization. To circumvent artificially stiff patterns, a modified sensitivity filter is applied to regularize the solution. The effectiveness and high efficiency of the presented approach are highlighted by typical 2D and 3D examples.

Experimental behavior and analysis of high strength concrete beams reinforced with PET waste fiber

This paper describes material properties of high strength concrete containing different PET waste fiber in terms of fiber volume and length. Structural behavior of reinforced concrete beams made of this newly developed concrete has been fairly investigated. Cracking performance of beams was found to improve as a result of using PET waste fiber, but there is no chance to increase the ultimate load capacity. There is some strength loss of the beam mainly attributed to the degradation take place in compressive strength of concrete, but mode of failure of tested concrete beams was almost identical to that of control beam without PET waste fiber. Ultimate moment capacity of concrete section with PET fiber can be calculated accurately following the recommendation of the ACI 318 code. The results are interested and can encourage researchers to work on this kind of recycled high strength concrete for structural applications in future.