Macroscopic Response Research Articles

Magnetostatic response and field-controlled haloing in binary superparamagnetic mixtures.

Nowadays, magnetoresponsive soft materials, based not simply on magnetic nanoparticles but rather on multiple components with distinct sizes and magnetic properties in both liquid and polymeric carriers, are becoming more and more widespread due to their unique and versatile macroscopic response to an applied magnetic field. The variability of the latter is related to a complex interplay of the magnetic interactions in a highly nonuniform internal field caused by spatial inhomogeneity in multicomponent systems. In this work, we present a combined analytical and simulation study of binary superparamagnetic systems containing nanoclusters and dispersed single-domain nanoparticles in both liquid and solid carrier matrices. We investigate the equilibrium magnetic response of these systems for wide ranges of concentrations and interaction energies. It turns out that, while the magnetization of a binary solid can be both above and below that of an ideal superparamagnetic gas, depending on the concentration of the dispersed phase and the interparticle interactions, the system in a liquid carrier is highly magnetically responsive. In liquid, a spatial redistribution of the initially homogeneously dispersed phase in the vicinity of the nanocluster is observed, an effect that is reminiscent of the so-called haloing effect previously observed experimentally on micro- and milliscales.

Analytical estimates for deformation behavior of fluid-filled elastomers with random microstructures

Macroscopic response of fluid filled elastomers with random microstructures, is obtained for aligned, cylindrical pores with circular cross-section. Results are derived for mono-disperse as well as poly-disperse pores, for Newtonian fluids. The obtained estimates are validated for plain strain compression loadings using numerical simulations performed in commercial multiphysics software COMSOL. Good agreement is observed between the analytical estimates and numerical solutions for different initial porosities and loading rates. Standard deviation in numerical results is seen to be high for polydisperse pores. Nonetheless, the mean response in numerical solutions matches well with analytical estimates. The obtained results can form the basis for design and fabrication of a new class of materials which have the potential to replace conventional spring–damper systems, particularly where space is limited.

Sample size effects on the critical state shear strength of granular materials with varied gradation and the role of column-like local structures

Assessing the shear strength of coarse granular soils is challenging because testing devices in the laboratory often limit the maximum particle size (dmax). Although engineering standards define representative elementary volumes (REVs) using the aspect ratio α = X/dmax, where X is the characteristic sample size, they often disagree on the minimum α, as the effects of sample scale on shear strength are still not well understood. This paper presents a discrete-element study on the combined effect of specimen size and grading on the critical state shear strength of granular materials. The study covers a wide range of aspect ratios and demonstrates that the macroscopic response is stable for α ≥ 15 – which is significantly higher than the standard requirement of α ≥ 10 for simple shear tests. The granular microstructure is also strongly affected by α and the formation of column-like structures of grains carrying strong contact forces, reaching sample size independent conditions only for α ≥ 20. Such column-like structures are shown to be primarily composed of the largest classes of grains, supporting the fact that grading has no effect on the critical state shear strength and dmax correctly serves to scale a granular sample to the size of the testing device.

Damage behavior of high particle volume fraction composites with initial damage by finite element meso-modeling

Analyzing the deformation and damage processes of high particle volume fraction composites (HPVFCs) based on the meso-structure modeling plays an important role in their service lifetime and functional reliability. The reported mesoscopic structural models are usually ideal models without initial damage and apply to composites with the volume fraction of particles less than 80%. This work provides a new mesoscopic structure model called aggregate settlement-merging model to successfully simulate the mechanical behavior and damage mechanism of the polymer-bonded explosive (PBX) under quasi-static loads, and the macroscopic response is accurately predicted by the cohesive finite element method. This simulation commendably predicts the failure modes including interface debonding, binder filaments, and grain failure, which is consistent with the observation in micromechanical experiments. The multi-scale relationship between macroscopic mechanical properties and microscopic initial interface damage is quantitatively established in a form of an exponential function. This study shows a relationship between meso-structures and performance and provides strategy for designing next generation high-performance HPVFCs.

Simultaneously measuring the dichroism and the dielectric response of an azobenzene-doped organic glass former

We have designed an experimental setup allowing to simultaneously measure both the dielectric response of a supercooled liquid and the dynamics of azobenzene chromophores dispersed in it. Both the azobenzene chromophores and the organic glass former have been synthesized with similar reaction paths: they are chemically similar, apart from the azobenzene group responsible for the strong optical absorption in the [350; 450 nm] range for the chromophores, while the embedding supercooled liquid is optically transparent. This material is deposited on transparent electrodes with an inter-electrode gap as small as 4 µm—obtained thanks to optical lithographic techniques. We show that our setup is sensitive enough to measure the coupling between the dielectric macroscopic response and the isomerization dynamics of 1% of chromophores excited by a 0.5–5 mW/cm2 light beam. We demonstrate that this coupling neither comes from the heating of the sample due to the light absorption nor from changes of the sample shape with light. Finally, we discuss the few physical effects, which may give rise to this coupling, and show that our experiment could test some recent predictions done in the framework of random first order transition theory of the glassy state.

Microstructural effects in rate-dependent responses of smooth and notched magnesium bars

We perform three-dimensional crystal plasticity simulations of smooth and notched bar geometries made of polycrystalline hexagonal close-packed material representing a magnesium alloy. The polycrystalline microstructure is explicitly resolved to investigate the combined effect of initial texture and grain size on the rate-dependent macroscopic responses and their micromechanical underpinnings under uniaxial and multiaxial stress states. The simulations reveal that in addition to the textural effect recently investigated by Ravaji et al. (2021), grain size plays an important role in the anisotropy of macroscopic responses. For a given texture, the lateral deformation anisotropy increases with grain size refinement for all strain rates considered here. The load-deformation responses exhibit a synergistic strengthening effect in microstructures with stronger initial textures and finer grain sizes, which is enhanced with increasing notch acuity. A transition from a conventional power-law type load-deformation response to a sigmoidal load-deformation response may occur, which depends on the imposed strain rate. It is a result of the interaction between textural weakening and grain size refinement that influence extension twinning together with an equitable landscape of the different slip mechanisms. We discuss possible implications of the net material plastic anisotropy due to texture and grain size on macroscopic failure using a micromechanical basis.

Study on Dynamic Parameters and Energy Dissipation Characteristics of Coal Samples under Dynamic Load and Temperature

Coal and rock dynamic disasters such as rock burst and outburst seriously threaten the sustainable development of the coal mining industry, which are intimately correlated with the nonlinear dynamic response process of the deep coal and rock mass. This study conducts coal dynamic experiments under vibration load from room temperature to 60 °C by using the split Hopkinson bar (SHPB) with a temperature real-time control system and analyzes the variation in stress and strain and the energy dissipation characteristics of coal during the dynamic load process. The expression equation of dissipated energy of coal at different scales is established, and the judgment conditions of the macroscopic mechanical behavior of coal are analyzed theoretically. The stress curves show a multi-stress peak phenomenon when the coal samples are subjected to different temperatures and dynamic loads, and the coal’s dynamic stress and temperature show a polynomial fitting relationship at different stages. When the coal sample is subjected to temperature and dynamic load, the macroscopic changes in incident energy, reflected energy, and dissipated energy are consistent; that is, various energies gradually increase to a fixed value and tend to stabilize with the time of stress wave action. The transmission energy exhibits a rising trend in correlation with the duration of the dynamic load action, but the value is less than 0.1 J. The growth gradients of the different energies, in descending order, are: the growth gradient of incident energy, reflection energy, dissipation energy, and transmission energy. The energy inflection point appears at 60 °C. Based on the linear elastic fracture mechanics and damage mechanics theories, the expression for coal energy dissipation from the nanoscale to the microscale is established, and the relationship between energy dissipation and macroscopic mechanical behavior response of the coal samples is analyzed. The main physical components of the coal sample are calcite and kaolinite. Within the temperature range of 18–60 °C, the macroscopic failure form of the coal is horizontal tensile failure. The study results are introduced into dynamic disaster prevention and control and the surrounding rock system stability evaluation in deep mines.

Experimental and numerical analysis of the compression behavior of aluminum syntactic foams reinforced with alumina hollow particles

In this study, analytical, numerical, and experimental methods are used to investigate the compressive behavior of alumina hollow particles reinforced aluminum matrix syntactic foams (AMSF). The representative volume element (RVE) models are generated for different volume fractions to analyze the elastic and elastio-plastic behavior of AMSFs using the FE solver ABAQUS. The geometric feature of the hollow particles is selected close to the actual physical dimensions. The effective elastic properties are estimated using linear homogenization models. For example, the elastic properties predicted using the Mori-Tanaka model are close to the FE-based RVE model data. Later, the macroscopic response (stress-strain data) is determined using the volume-averaging method proposed in the literature. The stress-strain response of the FE model with a 30% volume fraction has shown close agreement with the experimental data. Further, a parametric study is conducted for different particle wall thicknesses. These FE models have great potential in studying the ceramic hollow particles reinforced metal matrix syntactic foams and developing new porous composites under compression loading using RVE-based models.

Observation of dislocation-controlled domain nucleation and domain-wall pinning in single-crystal BaTiO3

Electro-mechanical interactions between topological defects and domain walls play a key role in the macroscopic response of bulk and thin-film ferroelectrics. The applications of ferroelectrics are derived from their inherent ability to nucleate new domains and to move the domain walls that separate adjacent domains. Here, we report dislocation-mediated domain nucleation in single-crystal BaTiO3, achieved by dislocations generated via high-temperature uniaxial compression on a notched sample. We also present a direct observation of domain-wall pinning of 90° ferroelastic domain walls by dislocations using in situ transmission electron microscopy. Dense and well-aligned “forest” dislocations, featuring {100}⟨100⟩ slip systems oriented in the out-of-plane [001] direction, exclusively nucleate in-plane domain variants. We reveal that the 90° domain walls are strongly pinned by imprinted dislocations due to the presence of their associated stress fields. Our findings may advance our understanding of the control of defects in ferroelectrics and propose a strategy applicable to both emerging nanoelectronic and bulk applications.

Micromechanics and Ultrasonic Propagation in Consolidated Earthen-Site Soils.

Although nondestructive ultrasonic technologies have been applied in laboratory and field tests in the field of heritage conservation, few studies have quantified the relationship among the real microstructures, micromechanical properties, and macroscopic acoustic responses of earthen-site soils. This paper develops a micromechanics-based multiscale model for quantitatively exploring the ultrasonic propagation characteristics of elastic waves in untreated and consolidated earthen-site soils. Scanning electron microscope images and image processing technology are integrated into the finite-element simulation. The effects of microstructure and wave features on the acoustic characteristics of soils are quantitatively investigated under pulsive loading. The simulation results of untreated and consolidated soils are efficiently compared to ultrasonic test data. It is demonstrated that the integration of microstructure image processing and multiscale modeling can predict the ultrasonic pulse velocity well, which improves the accuracy of laboratory testing and field monitoring and better serves the evaluation and implementation of engineering practice in the field of heritage conservation.

Modeling of hysteretic response of porous piezo/ferroelectric ceramics

The hysteretic character of the electromechanic coupling in porous piezoeceramics is a fundamental issue to be investigated in order to design porous materials with enhanced functional responses and increased figure of merit. In the present work, the porosity-dependent evolution of polarization-field PE and strain-field sE hysteretic responses of porous ferro/piezoceramics are simulated by using the Jiles-Atherton model for switching, combined with Finite Element Analysis in order to determine the local electrical and mechanical responses and the effective dielectric and piezoelectric constants. By considering 2D arrays of porous structures, the local electric field, potential and strain–stress local distributions are firstly evaluated in discrete elements. The macroscopic polarization and deformation responses vs. the applied field are determined by computing the response of each dense region subjected to its corresponding local field. The obtained nonlinear decrease of polarization and deformation vs. porosity are comparatively discussed for square, hexagonal regular pore arrays and for randomly distributed porosity. Further, the effective permittivity and piezoelectric constant d33 and conversion figure of merit vs. porosity computed in different polarization states are estimated and discussed. The present approach may offer a support for the design of porous structures with enhanced piezoelectric response.

The anisotropic grain size effect on the mechanical response of polycrystals: The role of columnar grain morphology in additively manufactured metals

Additively manufactured (AM) metals exhibit highly complex microstructures, particularly in terms of grain morphology which typically features heterogeneous grain size distribution, irregular and anisotropic grain shapes, and the so-called columnar grains. The conventional morphological descriptors based on grain shape idealization are generally inadequate for representing complex and anisotropic grain morphology of AM microstructures. The primary aspect of microstructural grain morphology is the state of grain boundary spacing or grain size whose effect on the mechanical response is known to be crucial. In this paper, we formally introduce the notion of axial grain size from which we derive mean axial grain size, effective grain size, and grain size anisotropy as robust morphological descriptors capable of effectively representing highly complex grain morphologies. We instantiated a discrete sample of polycrystalline aggregate as a representative volume element (RVE) featuring random crystallographic orientation and misorientation distributions. However, the instantiated RVE incorporates the typical morphological features of AM microstructures including distinctive grain size heterogeneity and anisotropic grain size owing to its pronounced columnar grain morphology. We ensured that any anisotropy observed in the macroscopic mechanical response of the instantiated sample primarily originates from its underlying anisotropic grain size. The RVE was then employed for mesoscale full-field crystal plasticity simulations corresponding to uniaxial tensile deformation along various axes via a spectral solver and a physics-based crystal plasticity constitutive model which was developed, calibrated, and validated in earlier studies. Through the numerical analyses, we isolated the contribution of anisotropic grain size to the anisotropy in the mechanical response of polycrystalline aggregates, particularly those with the characteristic complex grain morphology of AM metals. This contribution can be described by an inverse square relation.

Influence of microscopic parameters on the macroscopic mechanical response of sand

In order to study the influence of microscopic parameters on the macroscopic mechanical response of sand, the discrete element software PFC3D is used to establish the numerical model of the triaxial test of sand in this paper, the indoor triaxial test of sand is carried out to calibrate the numerical model. The triaxial tests are finished under the conditions of confining pressures of 100 kPa, 200 kPa, 300 kPa, and 400 kPa, respectively. The influence of the microscopic parameters on the macroscopic mechanical response of the sand is analyzed, the orthogonal experimental method is used to study the sensitivity of the numerical model to microscopic parameters such as porosity, flexible boundary stiffness, normal tangential stiffness ratio, and friction coefficient. The results show that the peak strength and residual strength of the stress-strain curve of sand are most affected by the friction coefficient, they are positively correlated with the friction coefficient under different confining pressures. The normal tangential stiffness ratio is negatively correlated, it is less affected by porosity and boundary flexibility stiffness, the sensitivities of different microscopic parameters are analyzed through the orthogonal tests, the results of orthogonal tests and numerical simulations show the consistent patterns in terms of sensitivity to microscopic parameters. The results can provide the reference for the influence of microscopic parameters and the macroscopic mechanical response of sand.

Modeling and validation of ablative thermal response combined with microscopic heat transfer for porous ablative materials

Porous ablative materials are the state-of-the-art thermal protection materials for extreme aerodynamic conditions during re-entry, but the precise analysis of heat transfer within microstructure and the ablative thermal response process is still a challenge. Herein, a numerical model that combines macroscopic ablative thermal response and microscopic heat transfer for porous ablative materials is presented. The microscopic heat transfer in the model is implemented through the conjugate solid and gas phases heat transfer. The model is validated by comparing the results of typical ablation cases with predictions made using another computational program PATO. In addition, analysis is performed to investigate the effect of parameters in the model such as thermal conductivity, heat capacity, surface emissivity, reaction kinetic parameters, and pressure. The results show that surface radiation is the majority of energy consumption mechanisms, and the internal temperature distribution of materials is primarily governed by thermal conductivity and heat capacity. Moreover, pressure serves as both the independent and dependent variable of thermal response, and the heat dissipation effect of pyrolysis gas exhibits a significant increase when it exceeds 10 atm. The results can improve the understanding of the ablative thermal response process and highlight areas for optimizing the design of TPS materials.

Compression of filled, open-cell, 3D-printed Kelvin lattices

The sensitivity of compressive strength of a polymeric Kelvin lattice to the presence of an epoxy core has been investigated both experimentally and numerically. Crush bands develop in the empty lattice, with large oscillations in load due to geometric softening and the sequential fracture of successive layers of struts. In contrast, the epoxy core has a sufficiently high modulus and strength that outward lateral flow of the epoxy through the open-cell lattice is negligible: the boundary layer, wherein migration of epoxy occurs through the lattice, extends less than one cell size from the surface of the specimen. The epoxy core supports the struts and stabilises the bulk macroscopic response against crush band formation. Finite element analysis of periodic unit cells show that the presence of an almost incompressible epoxy core changes the deformation mode of the lattice from one that is close to uniaxial straining to an isochoric mode. However, both the compressible collapse mode of the empty lattice and the isochoric deformation mode of the filled lattice are bending-dominated. At finite strain, the observed macroscopic strength of the filled lattice is degraded by bending failure of the struts and by tensile cracking of the adjacent core; the failure location is at a particular subset of the nodes of the lattice. Microcrack coalescence leads to the formation of a series of vertical fissures in the specimen.

Coexistence of five domains at single propagating interface in single-crystal Ni[sbnd]Mn[sbnd]Ga shape memory alloy

Coexistence of both austenite and martensite during phase transformation is a common feature of all Shape Memory Alloys (SMAs). The martensite has different variants featuring characteristic deformations rotationally linked to each other due to the symmetries of the austenite parent phase, and the martensite variants can form twins with different mean characteristic deformations. Multiple-domain microstructures (consisting of austenite, martensite twins and individual martensite variants) evolve collectively within an SMA sample during the phase transformation, contributing thus to the material's macroscopic response (e.g., its global deformation). Particularly, the multiple domains can exist at the diffuse austenite-martensite interface nucleating and propagating in a single crystal in certain conditions. This implies an energy barrier for this interfacial structure, influencing the interface kinetics and the driving force (energy dissipation) of the phase transformation. In this paper, we report an experimentally observed interface consisting of five domains (austenite, one martensite variant and three twins) in a Ni–Mn–Ga single-crystal initially consisting of one martensite variant and subjected to a uniaxial thermal gradient. The compatibility analysis (performed from the characteristic strains of the three martensite variants having approximately a tetragonal symmetry) reveals that the five-domain interface is not a perfectly compatible pattern like the basic habit plane (consisting of only one twin compatible with austenite). However, its level of non-compatibility is similar to that of the quite common X-interface (four-domain coexistence) which is observed in many SMAs. Further, the significant effects of the thermal loading path and the material initial state (the initial martensite variant) on the domain pattern formation are demonstrated and analyzed. The experimental observation and the theoretical analysis of the domain patterns can provide hints to better understand diffuse interface kinetics and phase transformation hysteresis.

Investigation into the fracture behavior of ZK60 Mg alloy rolling sheet under different stress triaxiality

In order to investigate the fracture behavior of the ZK60 Mg alloy rolling under different stress triaxiality, the different nominal stress triaxiality samples were well-designed, and the in-situ DIC tensile tests were carried out. The finite element method (FEM) model was validated by experimental results and the stress triaxiality evolution of samples was determined by modeling. The fracture strain of the ZK60 Mg alloy was non-monotonic with the nominal stress triaxiality increase and the best deformation performance of the central hole sample was indicated via the experimental and modeling results. The low stress triaxiality gradient of the central hole sample led to better deformation performance in terms of the macroscopic mechanical response. The transformation of the fracture mechanism from shear transgranular fracture to intergranular fracture and then to transgranular fracture during the stress triaxiality increased from 0 to 2/3 and was revealed via scanning electron microscope (SEM) characterization and FEM modeling. To further confirm the above fracture mechanism, X-ray computed tomography (XCT) was carried out to characterize the micro damage volume fraction and morphology. Due to the transgranular fracture induced by the high stress triaxiality at the initial fracture position of the central hole sample, the micro damage was smaller, delaying the fracture failure and achieving higher strain.

A new multiscale model for ferroelectric materials considering hysteresis

A new multi-scale model for ferroelectric materials is proposed. It can model hysteresis effect through a bistable “locked/unlocked” state for the grains, and the domain wall motion is described through free energy functions that pertain the elasto-electric coupling symmetry. The model is able to consider for electro-mechanical coupling with simultaneous electrical and mechanical loadings. The model also captures the field distribution in the polycrystal which has a strong influence on the macroscopic response of these materials. The comparison with experimental data shows that this new model is able to qualitatively and quantitatively describe electrically induced hysteresis for various levels of compressive stress, and mechanically induced hysteresis as well.

Strain-Controlled Critical Slowing Down in the Rheology of Disordered Networks.

Networks and dense suspensions frequently reside near a boundary between soft (or fluidlike) and rigid (or solidlike) regimes. Transitions between these regimes can be driven by changes in structure, density, or applied stress or strain. In general, near the onset or loss of rigidity in these systems, dissipation-limiting heterogeneous nonaffine rearrangements dominate the macroscopic viscoelastic response, giving rise to diverging relaxation times and power-law rheology. Here, we describe a simple quantitative relationship between nonaffinity and the excess viscosity. We test this nonaffinity-viscosity relationship computationally and demonstrate its rheological consequences in simulations of strained filament networks and dense suspensions. We also predict critical signatures in the rheology of semiflexible and stiff biopolymer networks near the strain stiffening transition.

Compacting an assembly of soft balls far beyond the jammed state: Insights from three-dimensional imaging.

Very soft grain assemblies have unique shape-changing capabilities that allow them to be compressed far beyond the rigid jammed state by filling void spaces more effectively. However, accurately following the formation of these systems by monitoring the creation of new contacts, monitoring the changes in grain shape, and measuring grain-scale stresses is challenging. We developed an experimental method that overcomes these challenges and connects their microscale behavior to their macroscopic response. By tracking the local strain energy during compression, we reveal a transition from granular-like to continuous-like material. Mean contact geometry is shown to vary linearly with the packing fraction, which is supported by a mean field approximation. We also validate a theoretical framework which describes the compaction from a local view. Our experimental framework provides insights into the granular micromechanisms and opens perspectives for rheological analysis of highly deformable grain assemblies in various fields ranging from biology to engineering.