Macroscopic Stress Research Articles

Data-driven homogenisation of viscoelastic porous elastomers: feedforward versus knowledge-based neural networks

A computational framework is established to implement time-dependent data-driven surrogate constitutive models for the homogenised mechanical response of porous elastomers at large strains. The aim is to enhance the computational efficiency of multiscale analyses through the use of these surrogate models. To achieve this, explicit finite element (FE) simulations are conducted to predict the homogenised response of a cubic unit cell of a porous elastomer, using two different viscoelastic descriptions of the parent material, subject to pseudo-random, multiaxial, non-proportional histories of macroscopic strains. The histories of homogenised variables extracted from each set of FE predictions form a training dataset, which is used to train two different surrogate models, both relying on artificial neural networks (NNs). The first model predicts the increment in macroscopic stress over a simulation step, as a function of the macroscopic stress and strain at the beginning of the step, of the prescribed macroscopic strain increment, and of the corresponding time increment. The second model uses the same inputs and outputs but tests a knowledge-based modelling approach: it relies on the aid of an additional nonlinear elastic constitutive model, which is time- and path-independent and known a priori. This model represents an existing base of knowledge which is augmented and corrected by an NN after training on viscoelastic data. The data-driven surrogate model, therefore, learns the viscoelastic behaviour of the unit cell starting from knowledge of its elastic response. The two surrogate models are found to have comparable and very high accuracies at capturing the homogenised unit cell response to highly complex loading cases across a range of viscoelastic properties. Hyperparameter optimisation shows that the second, knowledge-based model requires a simpler NN and therefore incurs a smaller computational cost.

Effect of Rate-Dependent Breakage on Strength and Deformation of Granular Sample—A DEM Study

The mechanical response of granular materials is influenced significantly by both the magnitude and strain rate. While traditionally considered rate-independent in the quasi-static regime, granular media can exhibit rate effects in certain instances. This research uses two-dimensional discrete element modelling (DEM) to investigate the rate effects in one-dimensional compression tests by comparing non-crushable with crushable granular samples. This study indicates that micromechanical properties such as particle breakage and contact force distributions are predominant factors in dictating the macroscopic responses of the material. The DEM simulations highlight differences in macroscopic changes between crushable and non-crushable samples, demonstrating a clear correlation between mechanical properties and underlying microstructural features. Notably, the distribution of contact forces varies with strain rates, influencing the degree of particle breakage and, consequently, the overall rate-dependent behaviour. Further, this study explores the impact of post-breakage contact creation and progressive force redistribution, which contributes to observable differences in macroscopic stress under varying loading rates, which is quantified using coordination number, particle velocity, and fabric tensor profiles at two loading rates.

Mechanics and Morphology of Proliferating Cell Collectives with Self-Inhibiting Growth.

We study the dynamics of proliferating cell collectives whose microscopic constituents' growth is inhibited by macroscopic growth-induced stress. Discrete particle simulations of a growing collective show the emergence of concentric-ring patterns in cell size whose spatiotemporal structure is closely tied to the individual cell's stress response. Motivated by these observations, we derive a multiscale continuum theory whose parameters map directly to the discrete model. Analytical solutions of this theory show the concentric patterns arise from anisotropically accumulated resistance to growth over many cell cycles. This Letter shows how purely mechanical processes can affect the internal patterning and morphology of cell collectives, and provides a concise theoretical framework for connecting the micro- to macroscopic dynamics of proliferating matter.

Research on defect image inversion method based on multiple lift-off values magnetic memory signals

Metal magnetic memory (MMM) technique can detect macroscopic defects and stress concentration zones of ferromagnets, and it can identify the approximate positions of these flaws, while a little further information about defects characteristics can be provided. To promote study in this area, defects were modeled as located magnetic dipoles whose strength and locations should be determined, and the technique of truncated generalized inverse and reduced space inversion were used to image the dipole strength. Through the simulation experiment, we found that the inversion image quality was influenced by the lift-off value. When the magnetic field data for inversion was measured with a small lift-off value, the inner dipoles contributions were easily buried and the inversion image can only shown the surface dipole well. In contrast, if the magnetic field data was measured with a greater lift-off value, it was possible to inverse the deep dipoles while the image was somewhat out of focus. To overcome this limitation, we composed the magnetic field data measured under different lift-off values together for inversion. We used the same model to test this approach and applied it on real crack defects magnetic field data. It demonstrates that the new inversion approach shows better accuracy than the single lift-off value and it was possible to infer the location and size of defect by the evaluation of preset dipoles.

Shear-induced migration of rigid spheres in a Couette flow

Concentration inhomogeneities occur in many flows of non-Brownian suspensions. Their modeling necessitates the description of the relative motion of the particle phase and of the fluid phase, as well as the accounting for their interaction, which is the object of the suspension balance model (SBM). We systematically investigate the dynamics and the steady state of shear-induced migration in a wide-gap Couette flow for a wide range of particle volume fraction, and we test the ability of the SBM to account for the observations. We use a model suspension for which macroscopic particle stresses are known. Surprisingly, the observed magnitude of migration is much lower than that predicted by the SBM when the particle stress in the SBM is equated to the macroscopic particle stress. Another noteworthy observation is the quasi-absence of migration for semidilute suspensions. From the steady-state volume fraction profiles, we derive the local particle normal stress responsible for shear-induced migration according to the SBM. However, the observed dynamics of migration is much faster than that predicted by the SBM when using this stress in the model. More generally, we show that it is not possible to build a local friction law consistent with both the magnitude and the dynamics of migration within the standard SBM framework. This suggests that there is a missing term in the usual macroscopic constitutive law for the particle normal stress driving migration. The SBM is indeed capable of accurately predicting both the magnitude and the dynamics of migration when a tentative phenomenological term involving a concentration gradient is added to the particle normal stresses determined in macroscopic experiments.

The role of water mobility on water-responsive actuation of silk

Biological water-responsive materials that deform with changes in relative humidity have recently demonstrated record-high actuation energy densities, showing promise as high-performance actuators for various engineering applications. However, there is a lack of theories capable of explaining or predicting the stress generated during water-responsiveness. Here, we show that the nanoscale confinement of water dominates the macroscopic dehydration-induced stress of the regenerated silk fibroin. We modified silk fibroin’s secondary structure, which leads to various distributions of bulk-like mobile and tightly bound water populations. Interestingly, despite these structure variations, all silk samples start to exert force when the bound-to-mobile (B/M) ratio of confined water reaches the same level. This critical B/M water ratio suggests a common threshold above which the chemical potential of water instigates the actuation. Our findings serve as guidelines for predicting and engineering silk’s WR behavior and suggest the potential of describing the WR behavior of biopolymers through confined water.

Study on the mechanical behavior of millennium-ancient bricks based on microscopic characteristics

The wide performance variation and inability for destructive testing make accurately determining ancient brick mechanical properties crucial for assessing structural safety in ancient masonry. This paper uses multiscale modeling with microscopic finite element analysis to quantitatively assess ancient brick macroscopic stress–strain relationship and compressive strength based on microstructural characteristics. The basic parameters such as porosity, pore size distribution, mineral composition and volume ratio, and microstructure characteristics of ancient bricks were obtained by corresponding methods. The Mori-Tanaka homogenization theory was applied to derive a three-phase equivalent brick matrix using elastic moduli and Poisson’s ratios of quartz, kaolinite, and montmorillonite at the microscale. The Representative Volume Element model with pores was created based on this matrix and pores, integrating Drucker-Prager plastic damage for finite element analysis of ancient brick mechanical behavior. The results indicate that stress–strain curves from the multi-scale micromechanics model resemble macroscopic experimental curves and maintain consistent peak strength. This shows that combining microscopic testing with finite element simulation for analyzing the mechanical properties of ancient bricks is feasible, providing a new non-destructive means of obtaining these properties.

Multi-scale modeling of damage evolution for particle-filled polymer composites

In this study, a multi-scale modeling framework that spans from molecular chains to macroscopic structure was proposed for a typical particle-filled polymer composite (HTPB propellants). The cohesive zone model (CZM) is utilized in the RVE model of HTPB propellants to capture the debonding phenomena at the AP/HTPB interface. For the HTPB matrix, a free energy function based on the Gaussian chain network is employed. To depict the chain scission behavior, the phase fracture (PF) method along with gradient-damage theory is introduced. Subsequently, microscale fracture behavior under uniaxial tensile load was investigated based on the constructed RVE model, and a phenomenological macroscopic damage model was developed correspondingly. In this developed model, two damage factors related to the debonding of AP/HTPB interface and the growth of voids in matrix are introduced respectively. Thus, it can not only predict the macroscopic stress–strain response, but also can give the microscopic damage evolution information. Overall, this multi-scale modeling framework can offer us a deeper insight into the microstructural changes and the resulting macroscopic mechanical behavior of HTPB propellants.

A polycrystal plasticity-cellular automaton integrated modeling method for continuous dynamic recrystallization and its application to AA2196 alloy

Continuous dynamic recrystallization usually dominates the microstructural evolution in hot working of aluminum alloys, in which the high-angle grain boundaries of new grains mainly originate from the gradual increase in subgrain misorientation angles. In this work, an integrated computational method is proposed to simulate continuous dynamic recrystallization process of aluminum alloys by coupling three-dimensional cellular automaton and visco-plastic self-consistent models. The stress response, dislocation accumulation and recovery, and evolution of crystal orientations are computed in the context of polycrystal plasticity; the formation and rotation of subgrains, followed by stored energy and curvature-driven boundary migration, are captured and visualized by cellular automaton. The non-octahedral slip mode {110}<110> is additionally introduced to capture the 〈001〉 texture during hot compression. A universal cell topology deformation method is adopted to achieve an effective track of grain morphology evolution during plastic deformation. The proposed simulation framework is validated through simulating the isothermal uniaxial compression process of AA2196 alloy under different temperatures and strain rates. The orientation dependence of CDRX during compression is numerically reproduced by correlating the subgrain formation and rotation process with the activation state of slip systems. The simulated macroscopic flow stress, 3D microstructure and inherent microstructural characteristics such as subgrain size, subgrain boundaries and textures are in good agreement with the experimental results. The proposed method provides an effective and efficient tool for multi-scale simulation of hot forming process of aluminum alloys.

Instabilities in a two-dimensional granular fault gouge: Particle dynamics and stress fluctuations

Predicting stress fluctuations in granular media under steady-state shear loading is crucial for applications ranging from geophysical processes to construction engineering. Stress fluctuations emerge from particle rearrangement, usually enabled by frictional slip and force-chain buckling. Existing models used to predict stress fluctuations are largely phenomenological, often accounting for the force chain phenomena implicitly through the introduction of internal variables, or explicitly through assumptions of force chain mechanics. Improper consideration of particle mechanics or mesoscale effects can lead to inaccurate predictions of shear strength and instability, making it difficult to predict the onset of yielding, shear band formation, and other instabilities. Furthermore, while recent advancements in machine learning methods have established links between microscale behavior and macroscopic stress drops in granular fault gouges, their predictive capabilities are limited due to their black-box nature. To gain a deeper understanding of stress fluctuations, and ultimately predict them in a physics-informed manner, it is necessary to examine how system energetics change with stress fluctuations. In this paper, we analyze stress fluctuations in a 2D granular fault gouge loaded under quasistatic, steady-state shear. We track the flow of potential energy between force networks and understand how energy and force networks vary with stress rises and drops. We derive an analytical, dynamic force chain model from first principles to illustrate how interactions between force networks lead to the emergence of localized instability phenomena. Finally, we offer insights into how these localized instabilities ultimately enable shear stress fluctuations at the continuum scale.

Mesogen Organizations in Nematic Liquid Crystal Elastomers Under Different Deformation Conditions.

Liquid crystal elastomers (LCEs) exhibit unique mechanical properties of soft elasticity and reversible shape-changing behaviors, and so serve as potentially transformative materials for various protective and actuation applications. This study contributes to filling a critical knowledge gap in the field by investigating the microscale mesogen organization of nematic LCEs with diverse macroscopic deformation. A polarized Fourier transform infrared light spectroscopy (FTIR) tester is utilized to examine the mesogen organizations, including both the nematic director and mesogen order parameter. Three types of material deformation are analyzed: uniaxial tension, simple shear, and bi-axial tension, which are all commonly encountered in practical designs of LCEs. By integrating customized loading fixtures into the FTIR tester, mesogen organizations are examined across varying magnitudes of strain levels for each deformation mode. Their relationships with macroscopic stress responses are revealed and compared with predictions from existing theories. Furthermore, this study reveals unique features of mesogen organizations that have not been previously reported, such as simultaneous evolutions of the mesogen order parameter and nematic director in simple shear and bi-axial loading conditions. Overall, the findings presented in this study offer significant new insights for future rational designs, modeling, and applications of LCE materials.

The influence of mineral inclusion on the effective strength of rock-like geomaterials

The influences of microstructure on the macroscopic mechanical behavior of a composite with a porous matrix reinforced by mineral inclusions are investigated in the present work by both numerical and theoretical methods. The mineral inclusions are embedded at the mesoscopic scale and much bigger than the pores which are located at the microscopic scale. In order to consider the properties of the studied rock-like geomaterials, such as the dissymmetry between tension and compression, the solid phase at the microscopic scale is assumed to obey to a Drucker–Prager criterion. Based on the studied microstructure, the Fast Fourier Transform (FFT) based numerical method is firstly adopted to investigate the macroscopic plastic yield stress of the studied composite. Different microstructure having different volume fraction of inclusion, micro-porosity and frictional coefficient of the solid phase are considered. Based on these numerical results, the existing theoretical yield criterion is estimated. One finds that it should be improved for the case of a microstructure having a high inclusion content. Then, a new macroscopic yield criterion is constructed in the present work by using the modified secant method. This criterion ameliorates fundamentally the one proposed in Shen et al. (2013), specially for the case of a deviatoric loading. It is then estimated and validated by comparing with the FFT based numerical results which were carried out in this work with different volume fractions of heterogeneous phase.

Analysis of the mechanical behavior of porous materials containing two populations of voids under dynamic spherical loading

A computational homogenization analysis is performed on three-dimensional representative volume elements (RVE) that contain two distinct populations of voids, to demonstrate the influence of the interaction between cavities. RVEs are constructed as cubic elastic perfectly-plastic matrices embedding two families of spherical voids, and subjected to dynamic loading under homogeneous kinematic boundary conditions. Multiple microstructure models are considered by varying the number, position, and size of voids to evaluate the micro-inertia contribution to the overall macroscopic stress. Velocity fields within numerical RVEs are investigated to reveal the interaction of voids and their key role in the dynamic macroscopic response of the porous material. Based on numerical simulation results, a homogenization analytical model considering void interaction is proposed to describe the mechanical behavior under dynamic loadings. This model relies on adjusting the strain rate level at the boundary of unit cells composing the porous material. Comparison between our numerical and analytical results with those obtained using the classical Taylor homogenization scheme highlights the limitations of the Taylor model in the case of porous materials under dynamic loading.

Elastic-plastic conductor damage evaluation at over 0.4% strain using a high-stress REBCO coil

Recent reports on screening current stress simulations of high-field REBCO magnets frequently present peak stresses over 1 GPa. However, this result is probably an unrealistic artifact of purely elastic calculations, considering the macroscopic yield and fracture stresses of approximately 900 MPa and less than 1.1 GPa for Hastelloy substrate-coated conductors. Here, we evaluate elastic-plastic conductor damage at over 0.4% strain using a high-stress REBCO coil exposed to a high field to explore this elastic-plastic regime. The coil was located off-center in a low-temperature superconductor magnet so as to induce a significant screening current in the enhanced radial field. Voltage taps, a Hall sensor, and two strain gauges were used for the instrumentation. We obtained strains exceeding 0.4% near the outward edge during the coil current charge from 350 A to 390 A, where the coil was exposed to external axial and radial magnetic fields of 13 T and 0.5 T. Post mortem results showed wavy plastic deformation, electrical damage, and REBCO defects. An elastic-plastic simulation reproduced the measured strains and predicted that ∼1 GPa stress is sufficient to induce ∼0.9% strain, thus validating our initial concerns with purely elastic models. This paper provides our experimental and simulation results.

Unraveling the plastic deformation, recrystallization, and oxidation behavior of Waspaloy during thermal fatigue crack propagation

Thermal fatigue is one typical failure mode for engine components involving cyclic thermal stresses/strains. However, the microstructure evolution and its microscopic interaction with thermal fatigue cracking in Ni-based superalloys featuring intragranular γ′ and intergranular carbides have yet to be clarified. In this study, cyclic temperature variations ranging from 25 °C to 700 °C were conducted on Waspaloy to unravel the synergistic damage mechanisms including stress distribution, plastic deformation, recrystallization, oxidation, and crack propagation. The thermal fatigue cracks are found to predominantly propagate along grain boundaries with a gradually descending rate from 3.5 μm/cycle to 1.5 μm/cycle. Compared with the macroscopic thermal stress up to ∼800 MPa, the local thermal stress induced by different sizes of M23C6 carbides marginally affects the crack propagation. Intensive slip bands and sparse deformation twins in the deformed matrix are observed, indicating the plastic deformation is mainly achieved by dislocation slipping and supplemented by twinning. Trans-granular cracks parallel to {111} planes form occasionally when the propagation directions of intergranular cracks are almost parallel to the {111} slip bands. Besides, dislocations promote the oxidation damage of the crack surface through pipe diffusion of solutes, and the γ′-precipitate free zones (PFZs) and recrystallized areas are produced accordingly. The quantitation analysis of the PFZ thickness provides a reference for predicting crack initiation time during thermal fatigue.

Analysis of transient energy conversion performance improvement of thermoelectric generator with penetrating crack under pulsed heat source

To simulate the performance of a thermoelectric generator (TEG) in practical applications more accurately and comprehensively analyse the influence of transient heat source and crack on such devices, it is necessary to examine the transient performance of TEGs with cracks under periodic pulsed heat source. In this study, a three-dimensional nonlinear dynamic finite element model with thermal, electrical, and mechanical coupling was established, and the laws describing the macroscopic electrical energy output and thermal stress distribution were derived. The position of the maximum thermal stress changed as the crack size varied. When the crack field axis was increased from 0.2 mm to 1.8 mm, the total output energy increased by 14.4 %, whereas the thermal stress increased to 447 MPa. The total energy growth rate under pulsed heat source conditions reached 52.3 % (from 62.71 J to 95.52 J) compared with that of the steady-state heat source. However, the maximum thermal stress increased by 173.6 % (from 91 MPa to 249 MPa). The results show that the crack and pulsed heat source can effectively improve the electrical output performance of TEGs; however, their mechanical properties deteriorated. This study is useful in terms of predicting the performance of TEGs in practical applications more accurately.

Evolution characteristics of calcareous sand force chain based on particle breakage

Abstract Calcareous sand is easily broken under external force, which brings great difficulties to island reef engineering. Based on the particle flow program, a discrete element model that can reproduce the results of laboratory tests is established, the large principal stress method is introduced to identify the particle force chain, and the bond strength between particles is increased to obtain an unbreakable model with the same initial conditions, and different confining pressures are compared and analyzed. The evolution law of the force chain of the following two models establishes a macro-meso cross-scale analysis in the deformation process of calcareous sand, explores the internal mechanism of the crushing of calcareous sand particles. The results show that particle breakage plays an important role in the evolution of the force chain. Particle breakage will reduce the probability of the force chain on both sides of the axis, forcing the probability of the axial force chain to rise steadily. The macroscopic deviatoric stress is the external manifestation of the probability of the axial force chain on the meso level. The faster the probability of the force chain in the direction of the potential shear band increases, the more obvious the shear band is.

Mechanism of strain-induced magnetic signal change in ferromagnetic materials under weak magnetic environment

Weak magnetic detection based on force-magnetic coupling effect is widely used in nondestructive testing of ferromagnetic materials, but the weak magnetic signals caused by the deformation of ferromagnetic materials under the action of external load show nonlinear changes, and the existing theories can not make a unified conclusion on the mechanism of nonlinear changes of magnetic signals, which limits the further application of weak magnetic detection. In this paper, a microscopic model of ferromagnetic material is established with the strain of the material as the independent variable. Firstly, the reasonableness of the established model is verified by the stress–strain relationship, and the stress concentration phenomenon generated by the change of the microscopic structure of the model is studied in depth by using the XRD diffraction method, so as to put forward the idea of characterizing the macroscopic stress with microscopic dislocations; secondly, the mechanism of the change of the magnetic signals of the ferromagnetic material caused by strain is analyzed by using the atomic magnetic moments and the density of states. The model explains the mechanism of strain-induced magnetic signal change in ferromagnetic materials, and has a guiding role in the further application and promotion of the weak magnetic method.

Superior Lightness-Strength and biocompatibility of bio-inspired heterogeneous glass sponge Ti6Al4V lattice structure fabricated via laser powder bed fusion

Ti6Al4V lattice structures (LSs) have great potentials in medical implants due to their excellent biocompatibility and high strength-to-weight ratio. This paper investigates the manufacturability and performance of unique Ti6Al4V heterogeneous glass sponge (GS) LSs fabricated via laser powder bed fusion (LPBF). Compared with the commonly used LSs, including Cross, body-centered cubic (BCC), Diamond and octet-truss (OCT), Ti6Al4V GS LSs exhibit the strongest compressive strength and energy absorption ability of 58 MPa and 23.84 J/cm3, respectively. Finite element (FE) models are established to evaluate the macroscopic deformation, microscopic stress and strain evolution in the solid struts of five different LSs. Local plastic stresses are found to generate near the nodes of Cross, BCC, Diamond and OCT LSs, thus forming plastic hinges, while the GS LSs can evenly transfer local plastic stresses to the grid-like rods of each layer, eventually showing a uniform stress distribution. Moreover, all the LSs are featured with satisfactory biocompatibility concerning cytotoxicity, cell proliferation, and cell attachment. The results indicate that the Ti6Al4V GS LSs can address the conflict between lightness and strength simultaneously, thus achieving excellent energy absorption performance, compressive properties and great biocompatibility, endowing it with tremendous application potential in the field of medical implants.

Micromechanism insights and constitutive modeling for deformation in a novel high manganese austenitic steel

We explore the mechanical behavior and microstructural evolution of a novel high manganese austenitic steel (HMAS), extensively applied in underground engineering and structural construction. Our investigation focuses on two variants of HMAS, namely HMAS-1.9 and HMAS-10, which exhibit distinct yield strengths and elongation behaviors. Electron backscatter diffraction (EBSD), transmission electron microscopy (TEM) and X-ray diffraction (XRD) were employed to elucidate the evolution of microstructures during plastic deformation. Based on these experimental results, we developed a new phenomenological multiscale constitutive model that captures the mechanical behavior of HMAS, integrating micromechanisms and microstructural evolutions. Optimized with the MATLAB genetic algorithm toolbox, this model was successfully implemented in a uniaxial tensile finite element model (FEM) within ABAQUS, proving its efficacy in predicting both macroscopic flow stress and microstructural evolutions. Our findings highlight the important roles of initial grain size, dislocation density, and twin fraction in determining the mechanical properties of HMAS. Throughout the deformation process, both HMAS variants demonstrate similar plastic deformation behaviors, characterized by comparable rates of increase in dislocation density and twinning fraction, accompanied by a consistent trend of grain refinement. These findings not only deepen our understanding of the complex relationship between microstructure and mechanical properties of the HMAS steel, but also provide an effective multiscale constitutive modeling approach for predicting its deformation behavior.